1. a.) For a given spring, F has the value 35 when the spring has stretched 8 inches. What is the constant of proportionality for that spring?
b) What is the value of F when the spring has stretched 11 inches?
2. The distance d that an automobile travels varies directly as the time ta) that it travels. After 2 hours, the car has traveled 115 miles.
b) Write the equation that relates d and t.b) The units on the right must be same as those of d on the left, that is, a) distance. What are the units, then, of 57.5?c) How far has the car traveled after 7 hours?
3. In a microwave receiver circuit, the resistance R of a wire 1m long is given by R = k/d2, where d is the diameter of the wire. Find R if k = 0.000 000 021 96 Ω m2 and d = 0.000 079 98m.
4. A computer can do an addition in 7.5 x 10^-15 s. How long does it take to perform 5.6 x 10^6 additions?
5. Show by first principle that the differential of y = 4x^2 -3x is 8x.
6. Water leaked into a gasoline storage tank at an oil refinery. Finding the pressure in the tank leads to the expression -4(b – c) – 3(a – b). Simplify this expression.
7. A shipment contain x film cartridges for 15 exposures each and x + 10 cartridges for 25 exposures each. What is the total number of photographs that can be taken with the film from the shipment?
8. In determining the size of a V belt to be used with an engine, the expression 3D – (D – d) is used. Simplify this expression.
9. When finding the current in a transistor circuit, the expression i1 – (2 – 3 i2) + i2 is used. Simplify this expression.
10. Each of two stores has 2n + 1 mouse pads costing $3 each and n – 2 mouse pads costing $2 each. How much more is the total value of the $3 mouse pads than te $2 mouse pads in the two stores?
11. In designing a certain machine part, it is necessary to perform the following simplification
16(8 – x) – 2(8x – x^2) – (64 – 16x + x^2)
What will be result be?
12. When analyzing the potential energy associated with gravitational forces, the expression
(GMm[(R + r) – (R – r)]) /2rR
arises. Preform the indicated division.
13. In the optical theory dealing with lasers, the following expression arises:
(8A^5 + 4A^3µ^4E^4)/8A^4
Perform the indicated division.
14. In finding the total resistance of the resistors, the expression
(6R1 + 6R2 + R1R2)/ 6R1R2
is used. Perform the indicated division.
15. The ratio of electric current I (in A) to the voltage V across a resistor is constant. If I = 1.52A for V= 60.0V, find I for V = 82.0V.
16.In order to find the distance such that weights are balanced on a lever, the equation
210(3x) = 55.3x + 38.5(8.25 – 3x)
must be solved. Find x.
17. In the study of the forces on a certain beam, the equation
W = L(wL + 2P)/8
is used. Solve for P.
18. A medical researcher finds that a given sample of an experimental drug can be divided into 4 more slides with 5mg each than with 6mg each. How many slides with 5mg each can be made up?
Subscribe to:
Post Comments (Atom)
for ques. 16
ReplyDelete210(3x)=55.3x+38.5(8.25-3x)
(210*3x)=55.3x+(38.5*8.25)+(38.5*-3x)
630x=55.3x+317.625-115.5x
630x-55.3x+115.5x=317.625
690.2x=317.625
x=317.625/690.2
x=0.0460
>firstly i multiply what is outside the brackets by everything inside of it.
ReplyDelete>secondly i paired off the common terms,ie. numbers one side and variables on the other side of the equal sign.
>then i made X the subject of the formular, by carrying across the 690.2 and finding the value of x
for ques 5 y=4x^2-3x
ReplyDeletelet (x+Zx)represent a small change
x1=x x2=(x+Zx)
y1=4x^2+3 y2=4(x+Zx)^2+3
dy/dx=y2-y1/x2-x1=lim/Zx>0
dy/dx=[4(x+Zx)^2+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4(x^2+2xZx+Zx^2)+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4x^2+8xZx+4Zx^2+3-4x^2+3]
[ (x+Zx) - (x)]
lim/Zx>0=[4Zx^2+8xZx]
=[ Zx ]
lim/Zx>0= 4Zx^2/Zx + 8xZx/Zx
lim/Zx>o=4Zx+8x
=8x
hints
>let (x+Zx) represent a small change
>where u see (x+Zx)^2 multiply (x+Zx) by itself
and u should get (x+Zx)(x+Zx)
=x^2+xZx+xZx+Zx^2
=x^2+2xZx+Zx^2
2.a)d is propotional to t
ReplyDeletetherefore,d is proprtional to k (constant)t.
2.b)miles should be converted to kilometers so that the units would be km/hr
ReplyDelete3. R = k/d2
ReplyDeleteie.R = k divided by d squred
therefore 0.00000002196/(0.00007998)2
=3.432966269
4. 1 addition takes 7.5 X 10^-15 s
ReplyDeletetherefore 5.6 X 10^6 additions would take
7.5 X 10^-15 (5.6 X 10^6) = 4.2 X 10^-8 s
6. -4(b-c)-3(a-b)
ReplyDelete-4b+4c-3a+3b
4c-3a-b
16...210(3x)=55.3x+38.5(8.25-3x)
ReplyDelete630x=55.3x+317.625-115.5
630x-55.3x+115.5=317.625
690x=317.625
x=317.625/690.2
x=0.46
1st i expand the brackets
2nd i put all the x on one side and the number on the oher side, making them equal to each other.
3rd i work out each side to one relevant number/ variable.
4th i carry the numbers on one side and leave "x" by itself making x equal to the number divded by it number of times.
5th it is worked out and therefore x is equal to 0.46
This comment has been removed by the author.
ReplyDelete6. -4(b-c)-3(a-b) = -4b+4c-3a+3b
ReplyDelete= -4b+3b+4c-3a
= -b+4c-3a
1(a)
ReplyDeleteevery 8inches is equal to 35
so 1inch is equal to 35/8= 4.375
(b)4.375*11=48.125
someone please tell me if i am correct?
for solving question 11. the most suitable process in solving the simplifications is to firstly expand the brackets by multiplying the coefficient(number infront of the brackets) by the interior of the brackets. The detailed steps which i used are seen below:
ReplyDelete16(8-x)-2(8x-x^2)-(64-16x+x^2)
step 1:( expand brackets)
=(16*8)-(16*x)-(2*+8x)-(2*-x^2)-(1*64)-(1*-16x)-(1*x^2)
=(128)-(16x)-(16x)-(-2x^2)-(64)-(-16x)-(x^2)
=128-16x-16x+2x^2-64+16x-x^2
step 2: calculate the values(addition an subtraction)
=64-16x+x^2
Step 3: state the answer
Answer= 64-16x+x^2
number(5)
ReplyDeleteshow by first principal do you mean to differentiate the normal way
y=4x^2-3x
dy/dx=8x-3 the question said that it was to be equal to 8x am i incorrect or is that a mistake on the blog
i think d question means that the resulting answer will be 8x
ReplyDelete4)Firstly you multiply the powers of both.
ReplyDeleteThen you can proceed on multiplying the two
decimal numbers in attaining your answer.
4) for instance
ReplyDelete-15 * 6 = -90.
7.5 * 5.6= 42.
therefore the answer is 42*10^-90
(i stand to be corrected).
number (3)
ReplyDeletethe formular given is R=k/d^2
d=0.000079 to find d^2 put in standard form
7.998*10^5*7.998*10^5 add the powers
7.998*7.998*10^-10 d^2=64*10^-10
k=2.196*10^-8 so divide k/d^2
2.196/6.4*10^-8/10^9= .343125*10
R=.343125*10
number(13)
ReplyDelete8a^5+4a^3u^4e^4/8a^4
8aaaaa +4aaa u^4e^4/8aaaa
a+u^4e^4/2a
i stand to be corrected
number(11)
ReplyDelete16(8-x)-2(8x-x^2)-(64-16x+x^2)
128-16x-16x+2x^2-64+16x-x^2
64+x^2+16x
i stand to be corrected
(9) i1-(2-3i2)+i2= i1-2+3i2+i2
ReplyDelete= i1-2+4i2
procedure:
(a)open out the bracketsby multiplying -1 by all components in the brackets
(b)simplify the equation by grouping all the common terms togethertomake it simple to work out
(c)then work out equation.
11. 16(8-x)-2(8x-x^2)-(64-16x+x^2)
ReplyDelete128-16x-16x+2x^2-64+16x-x^2
128-64-16x-16x+16x+2x^2-x^2
64-16x+x^2
question15) it has been said that:
ReplyDelete60.0V=1.52A
1V=1.52/60.0=0.0253
82.0V=0.0253*82.0=2.0746A
1.
ReplyDeleteF=35-8 inches
35=8 inches
1= 35/8
4.37
35-11inches
1= 35/11= 3.18
2.miles - km/hr
d= 115* 2hrs
d=s*t
57.5*7
402.5km/hr
3.
R=k/d2
2.196*10^-8/(7.998*10^-5)2
4.
7.5*10^-15 * 5.6*10^6
estimate- 8*6=48
5.
Y= 4x^2-3x =8x
Y2 Y1
[4(x+^h)2 -3]- [4x^2-3]
X2[x+^h] - X1 [X]
4x^2+8x^h+4^h^2-3-4x^2-3/x+^h-x
8x^h+4^h^2-0
8x
6.
-4(b-c)-3(a-b)
-4b+4c-3a+3b
-4b+3b-3a+4c
7.
x film catridges - 15 exposures
x+10 catridges - 25 exposures
X^2+10 - 40
x^2 = 40/10
x= 4
x=2
8.
3D-(D-d)
3D^2-3Dd
9.
i1-(2-3i2) +i2
i12-i13i2+i2
10.
3(2n+1) - 2(n-2)
11.
16(8-x)-(8x-x^2)-(64-16x+x^2)
128-16x-16x+2x^2-64-16+x^2
-16x-16x-16X+2x^2+x^2+128-64
-14x+64
12.
(GMm[R+r)-(R-r)])/2rR
2GMnr
13.
8A^5+4A^3U^4E^4/8A^4
8A^5/8A^4 + 4A^3U^4E^4/8A^4
A^1+U^4E^4/2A
14.
(6R1+6R2+R1R2)/6R1R2
6R1R2
15.
R=V/I
60.0/1.52
39.47 ohms
I=V/R
82.0/39.47
2.08 amps
16.
210 (3x)= 55.3x+38.5(8.25-3x)
630x= 93.8x(8.25-3x)
773.85-281.4/630
492.45/630
x=0.781
7.81*10^-1
17.
W=L(wL+2P)/8
8W=LwL+L2P
L2P=LwL-8W
2P=LwL-8W/L
P= LwL-8w/2L
18.
6x=5(x+4)
HELP!!!!
ReplyDeleteexpress in scientific notation:
560000/28000000 X 140000000 /2800000
purple rain i think i made a mistake in ques 8 it suppose to be
ReplyDelete(8) 3D-(D-d)
=3D-D+d
=2D+d
ques (9) suppose to be
ReplyDeletei1-(2-3i2)+i2
=1i-2+3i2+i2
=1i-2+4i2
for question one...
ReplyDeletelet k = the constant of proportionality
let l = the length of the spring wen stretched
a)
therefore the equation = F = k x l
when l= 8, F = 35;
so the equation = 35 = k (8)
therefore k = 35 / 8
k = 4.375
b)
therefore, when l = 11;
F = (4.375) x (11)
F = 48.125
F ~ 48
R= k/ d^2
ReplyDeletek = 0.000 000 021 96 m2
= 2.196 x 10^-8 m^2
d = 0.000 079 98 m
= 7.998 x 10^-5m
d^2 = 6.3968004 x 10^-9
therefore R = 2.196 x 10^-8 m2 / 6.3968004 x 10^-9
= 3.43 (3 s.f.)
This comment has been removed by the author.
ReplyDeletequestion four...
ReplyDeletetime taken for one addition = 7.5 x 10^-15 s
time taken for 5.6 x 10^6 additions = (7.5 x 10^-15) x (5.6 x 10^6)
= (7.5 x 5.6)x (10^6 x 10^-15)
= (42) x (10^6 + -15)
= 42 x (10^6-15)
= 42 x 10^-9
= 4.2 x 10^-8 seconds
1(a)F=35,when stretched 8inches
ReplyDeletelet k =constant
let i = inches
F = k*i
35=k*8
k=35/8
k=4.375
1(b)
when i = 11inches
F=k*i
F=4.375*11
F=48.125
question five...
ReplyDeletei dont know how to show the first principle on the computer...but the differential of 4x^2 - 3x is not equal to 8x, but rather 8x - 3...
question six...
ReplyDelete-4(b – c) – 3(a – b)
expanding brackets...
-4(b) -4(-c) -3(a) -3(-b)
-4b +4c -3a +3b
-3a -4b +3b +4c
-3a - b + 4c
2(a)
ReplyDeletespeed=distance/time
distance=speed*time
speed being the constant
2(b)
distance is directly proportional to time so
d=k*t
distance=115miles
time=2hr
speed=?
speed=distance/time
speed=115/2
speed=57.5kms^1
distance=speed*time
distance=57.5*7
distance=402.5miles
This comment has been removed by the author.
ReplyDeletequestion seven...
ReplyDeletex catridges = 15 exposures each
x + 10 catridges = 25 exposures each
therefore total no. of exposures = 15(x) + 25(x + 10)
= 15x + 25x + 250
= 40x + 250 exposures
3(a)
ReplyDeleteR=k/d2
R=2.196*10^-8/(7.998*10^-5)2
R=2.196*10^-8/1.598*10^-4
R=1.37421*10^-4
munchkin baby said...
ReplyDeleteHELP!!!!
express in scientific notation:
560000/28000000 X 140000000 /2800000
REPLY
5.6x10^5/2.8x10^7*1.4x10^8=3.92x10^15/2.8x10^6
God Of War said...
ReplyDelete3(a)
R=k/d2
R=2.196*10^-8/(7.998*10^-5)2
R=2.196*10^-8/1.598*10^-4
R=1.37421*10^-4
REPLY
now i understand that you multiply d by 2 but i really think that it may have been d squared eh, but the rest of the equation correct
question eight...
ReplyDelete3D – (D – d)
3D -1(D) - 1(-d)
3D - D + d
2D + d
question nine...
ReplyDeletei1 – (2 – 3 i2) + i2
i1 -1(2) -1(-3 i2) + i2
i1 -2 + 3i2 + i2
i1 - 2 + 4i2
question ten...
ReplyDelete3(2n + 1)
:- 3(2n) + 3(1)
:- 6n + 3
2(n - 2)
2(n) + 2(-2)
2n - 4
how much more is the value of the $3 mouse pads than the $2 mouse pads?
(6n + 3) - (2n - 4)
6n + 3 - 2n + 4
6n - 2n + 3 + 4
4n + 7 more...
question eleven...
ReplyDelete16(8 – x) – 2(8x – x^2) – (64 – 16x + x^2)
16(8) + 16(-x) -2(8x) -2(-x^2) -1(64) -1(-16x) -1 (x^2)
128 -16x - 16x + 2x^2 - 64 + 16x - x^2
128 - 64 -16x - 16x + 16x + 2x^2 - x^2
64 - 16x + x^2
RE: HELP!!!
ReplyDeleteby munchkin baby...
560000/28000000 X 140000000 /2800000
= [(5.6 x 10^5) / (2.8 x 10^7)] x [(1.4 x 10^8) / (2.8 x 10^6)]
= [(5.6 / 2.8) x (10^5 / 10^7)] x [(1.4 / 2.8) x (10^8 / 10^6)]
[(2) x (10^5-7)] x [(0.5) x (10^8-6)]
=[(2) x (10^-2)] x [(0.5) x (10^2)]
=[2 x 10^-2] x [0.5 x 10^2]
=[2 x 0.5] x [10^-2 x 10^2]
= 1 x 10^-2 + 2
= 1 x 10^0
= 1
(GMm[(R + r) – (R – r)]) /2rR
ReplyDeleteGMm[ (R + r - 1(R) -1(-r))] / 2rR
GMm[ (R + r - R + r)]/2rR
GMm[ R - R + r + r ]/ 2rR
[GMm (2r)] / 2rR
-->GMm / R
question fourteen...
ReplyDelete(6R1 + 6R2 + R1R2)/ 6R1R2
6R1/6R1R2 + 6R2/6R1R2 + R1R2/6R1R2
1/R2 + 1/R1 + 1/6
I = 1.52A for V= 60.0V, find I for V = 82.0V
ReplyDeleteV = kI
k = V/I
I = V/k
when V = 60.0V and I =1.52A;
k = 60.0/1.52
k = 39.5 (3 s.f.)
therefore, when V = 82.0V;
I = V/k
I = 82.0 / 39.5
I = 2.08A (3 s.f.)
question sixteen...
ReplyDelete210(3x) = 55.3x + 38.5(8.25 – 3x)
630x = 55.3x + 38.5(8.250) + 38.5(-3x)
630x = 55.3x + 317.625 - 115.5x
630x - 55.3x + 115.5x = 317.625
690.2x = 317.625
x = 317.625 / 690.2
x = 0.46
question seventeen...
ReplyDeleteW = L(wL + 2P)/8
W = [L(wL) + L(2P)] / 8
W = (wL^2 + 2LP) / 8
8W = wL^2 + 2LP
8W - wL^2 = 2LP
(8W - wL^2) / 2L = P
P = (8W / 2L) - (wL^2 / 2L)
P = (4W / L) - (wL / 2)
i really suck at maths so i hope u all would kinda give me a hand with this
ReplyDelete1) f = kl
ReplyDeletetherefore:
35= k *8
k = 8/35
= 4.375
for quest 1b) i see that there are 2 different ans but i THINK the correct ans is
ReplyDeletef=k*l
therefore
f= 4.357*11
= 48.375
can someone explain no 2 a little more please?
ReplyDeleteis the ans for no6 -b+4c-3a?
ReplyDeleteWell for part a) The question simply wants the equation that relates d and t (distance and time) which in this case is s=d/t i.e. speed=distance/time.
ReplyDeletefor part b) I believe the question just wants the unit of 57.5 and when 115 miles is divided by 2, the answer is 57.5 so i believe the units of 57.5 is miles i.e. 57.5 miles
for part c) The reason why 115 is divided by two in part b), is to find the distance travelled in one hour therefore,
if one hour = 57.5 miles,
7 hrs = 57.5*7
=402.5 miles
And concerning question 6:
ReplyDelete-4(b – c) – 3(a – b)
-4b+4c-3a+3b
4c-3a-b
which can also be written as:
-b+4c-3a
and the answer is of course is still the same
so yes $$Empress$$ your answer to question 6 is completely correct and I hope I made question 2 a little clearer for you in my previous post
1. f=35 when l = 8
ReplyDeletewhen l=1, f= 35/8 = 4.375...or 4 3/8
when l=11, f= 4.375*11 = 48.125...or 48 1/8
2.a) d is directly proportional to t
ReplyDeleted (proportional sign) t
d = k x t (where k is a constant)
2.b) d=kt
ReplyDelete115miles=k*2hours
k=115miles/2hours
k= 57.5 miles per hour
units of 57.5 is miles per hour.
2.c) d=kt
ReplyDeleted= 57.5miles/hour * 7 hours
d = 402.5 miles
14.
ReplyDelete(6R1 + 6R2 + R1R2)/ 6R1R2
6R1/6R1R2 + 6R2/6R1R2 + R1R2/6R1R2
6/6R2 + 6/6R1 + 1/6
1/R2 + 1/R1 + 1/6
18. Let X represent the number of slides
ReplyDelete6(X) = 5(X)+4
6X = 5X + 4
X = 4
therefore:
at 6mg, 4 slides can be made, whereas at 5mg, 8 slides can be made.
thank you 7NewStarLight7
ReplyDelete-4(b – c) – 3(a – b)
ReplyDelete-4b +4c -3a +3b
-4b-3b+4c-3a
-7b-3a+4c
7.
ReplyDeletex cartridges produce 15 exposures each
x + 10 cartridges produce 25 exposures each
total number of cartridges = 2x+10
total number of exposures = 15*x + 25 (x*10)
= 15x + 25x + 250
= 40x + 250
2x+10 cartridges produce 40X + 250 exposures
therefore:
2x+10 = 40x + 250
38x = -240
...this is as far as i got with this question...a negative value is probably wrong...hey purple rain...can u explain how u arrived at those answers for number 7??
what is a term???
ReplyDeleteis 2x+5y+3y
one or two or three terms??
Can someone please help me to simplify this expression.. It would be greatly appreciated!!:)..
ReplyDelete[5X - 2Y)^2) * 12] /3
[5X-2Y)^2)*12] /3
ReplyDeleteFirstly expand (5X-2Y) (5X-2Y)
=+25X^2-10XY-10XY+4Y^2
=+25X^2-20XY+4Y^2
=(+25X^2-20XY+4Y^2) *12
=300X^2-240XY+48Y^2
=[300X^2-240XY+48Y^2] /3
=100X^2-80XY+16Y^2
=[100X^2-80XY+16Y^2] /4
=25X^2-20XY+4Y^2
okay then.. thanks XOXO i hope it correct eh..lol..
ReplyDeletehellomoto....i hope u understand the calculations that i jus post.if u have any question feel free to ask....
ReplyDeletequestion (1)
ReplyDelete(a)let x represent the extension of the string produce by F.
if F=35 when x=8
every time F increases x increases as well
therefore F is proportional to x
so F=kx
35=k X 8
35/8=k
k=4.375
(b)what is F=? when x=11
using F=kx
F=unknown k=4.375 x=11
F=kx
F=(4.375) X 11
F=48.125
no problem $$Empress$$, anytime ;)
ReplyDelete1. F=kL
ReplyDelete35=k8
k=35/8
=4.375
when L=11
F=4.375*11=48.125
2. d is directly proportional to t
d=kt
s=d/t=115/2
57.5
units is in miles
in 7hours the car travelled 57.5*7=402.5miles
3. (2.196*10^-8)/(7.998*10^-5)^2=3.432966269
4. (7.5*10^-5)(5.6*10^6)=4.2*10^-8s
6. -4(b-c)-3(a-b)
-4b+4c-3a+3b
4c-3a-b
8. 3D-(D-d)
3D-D+d
2D+d
9. i1-(2-3i2)+i2
i1-2+3i2+i2
i1-2+4i1
10. 3(2n+1)=6n+3
2(n-2)=2n-4
(6n+3)-(2n-4)=6n+3-2n+4
=4n+7
11. 16(8-x)-2(8x-x^2)-(64-16x+x^2)
128-16x-16x+2x^2-64+16x-x^2
64-16x+x^2
12. [GMm[(R+r)-(R-r)]]/2rR
[GMm[R+r-R+r]]/2rR
[GMm(2r)]/2rR
GMm/R
14. (6R1+6R2+R1R2)/6R1R2
(6R1/6R1R2)+(6R2/6R1R2)+(R1R2/6R1R2)
(1/R2)+(1/R1)+(1/6)
15. 1.52/60.0=0.0253
wen V=82.0
I=0.0253*82.0=2.0746
16. 210(3x)=55.3x+38.5(8.25-3x)
630x =55.3x+317.625-115.5x
630x =317.625-60.2x
630x+60.2x=317.625
690.2x=317.625
x=317.625/690.2=0.460192697
17. W=L(wL+2P)/8
8W=wL^2+2LP
8W-wL^2=2LP
P=(8W-wL^2)/2L
6) -4(b-c)-3(a-b)
ReplyDelete-4b+4c-3a+3b
-b+4c-3a
12) (GMm[R+r]-[R-r])\2rR
ReplyDelete2Gm\2rR.
17) W= l(wl=2P)\8
ReplyDeleteW=LwL+L2P\8
8W=LwL+L2P
2P=LwL-8W\L
MAKE P THE SUBJECT OF THE FORMULA!!
P=LwL-8W\2L
TO: munchkin baby...a term is either a single number or variable or the product of several numbers and/or variables.they are separated from other terms by '+' or '-'. the expression that you have has three terms in it but can be simpified to two terms as the two like terms, 5y and 3y can be added together (8y).
ReplyDeleteto: Nena
ReplyDeletecheck # 16
210(3x) = 55.3x + 38.5 (8.25 - 3x)
210(3x) = 55.3x + (38.5*8.25)+ (38.5*-3x)
210(3x) = 55.3x + 317.625 - 38.5(3x)
210(3x) + 38.5/3x =55.3x+317.625- 38.5(3x)+38.5/3x
210+38.5 = 55.3x + 317.625
248.5 = 55.3x - 317.625
248.5 + 317.625 = 55.3x - 317.625 + 317.625
566.125 = 55.3x
566.125/55.3 = 55.3x/55.3
566.125/55.3 = x
10.23 =x
for ques 5 y=4x^2-3x
ReplyDeletelet (x+Zx)represent a small change
x1=x x2=(x+Zx)
y1=4x^2+3 y2=4(x+Zx)^2+3
dy/dx=y2-y1/x2-x1=lim/Zx>0
dy/dx=[4(x+Zx)^2+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4(x^2+2xZx+Zx^2)+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4x^2+8xZx+4Zx^2+3-4x^2+3]
[ (x+Zx) - (x)]
lim/Zx>0=[4Zx^2+8xZx]
=[ Zx ]
lim/Zx>0= 4Zx^2/Zx + 8xZx/Zx
lim/Zx>o=4Zx+8x
=8x
this above stated was nena's solution but there is a mistake in this line
dy/dx=[4(x+Zx)^2+3-4x^2+3]/
[(x+Zx) - (x)]
which should read
lim/Zx>0=dy/dx [4(x+Zx)^2-3]-[4x^2-3]/[x+Zx]-[x]
lim/Zx>0=dy/dx [4(x^2+2xZx+Zx^2)-3]-[4x^2-3]/Zx
lim/Zx>0=dy/dx [4x^2+8xZx+4Zx^2-3]-[4x^2-3]/Zx
lim/Zx>0=dy/dx [4x^2+8xZx+4Zx^2-3-4x^2+3]/Zx
lim/Zx>0=dy/dx 8x+4Zx
dy/dx 8x
do i still have to comment on this even thought the exam is over!!!!!!!!
ReplyDelete(1) f = 35 at 8 inches
ReplyDeletefor 1 inch f = 35/8
so therefore 11 inches = 35/8 *11
2.a)d is propotional to t
ReplyDeletetherefore,d is proprtional to k (constant)t.
for question one...
ReplyDeletelet k = the constant of proportionality
let l = the length of the spring wen stretched
a)
therefore the equation = F = k x l
when l= 8, F = 35;
so the equation = 35 = k (8)
therefore k = 35 / 8
k = 4.375
b)
therefore, when l = 11;
F = (4.375) x (11)
F = 48.125
F ~ 48
4x^2 -3x = 8x (by first principles)
ReplyDeletey= 4x^2 -3x
(x1,y1) = (x, 4x^2-3x)
(x2,y2) = (x+dx, y2)
(x2,y2) = [x+dx, 4(x+dx)^2 -3(x+dx)]
dy/dx = lim as dx approaches 0 [(y2-y1)/(x2-x1)]
= lim as dx approaches 0 of[(4(x+dx)^2-3(x+dx))-(4x^2-3x)]/[(x+dx)-(x)]
= lim as dx approaches 0 of 8xdx+dx^2/dx
= lim as dx approaches 0 of dx(8x+dx)/dx
= lim as dx approaches 0 of 8x+dx
= 8x + (0) = 8x
To jimnycricket check #16
ReplyDelete210(3x) = 55.3x + 38.5 (8.25 - 3x)
630x=55.3x+317.62-115.5x
630x-55.5x+115.5=317.62
690.2x=317.62
x=317.62/690.2
x=0.4602
nena final ans is wrong but her cals are correct check it
1.F=35-8 inches
ReplyDelete35=8 inches
1= 35/8
4.37
35-11inches
1= 35/11= 3.18
2.miles - km/hr
ReplyDeleted= 115* 2hrs
d=s*t
57.5*7
402.5km/hr
12.(GMm[R+r)-(R-r)])/2rR
ReplyDelete2GMnr
17. W=L(wL+2P)/8
ReplyDelete8W=wL^2+2LP
8W-wL^2=2LP
P=(8W-wL^2)/2L
1) using hooks law.. Force is directly proportional to the extention or the streching effect..
ReplyDeletethe mass is the constant of proportionality.
f=35 when there is 8 inches
therefore to find one inche 35/8 which is 4.37.then multiply 4.37 by 11 and the resulting answer will be 48.07
calculation
f=35
1 inch 35/8
=4.37
11 inches =4.37*11
=48.07
W=L(WL+2P)/8
ReplyDeleteW=WL^2+2PL/8
W8/L=WL^2+2PL
W8/L=WL^2+2PL/L
W8/L=WL+2P
W8/L - WL=2P
make P the subject of the formula
W8/2L -WL=P
4W/L- WL=P
4)1 sec=7.5*10^-15
ReplyDeletetherefore the calculations will be:
7.5*10^-15*5.6*10^6
when the bases are the same add the powers so therefore the resulting answer will be
7.5*10^-15 * 5.6*10^6= 42*10^-9
the base has 2 be less than 10 so it will be
4.2*10^-8
(1) in this question F is the force and e is the extension, according to hooke's law:-
ReplyDeleteForce α extension
in order to get rid of the extension sign u multiply the equation by a constant.
force= constant * extension
in this case the constant is known as the mass..
(1) (a)given that the force =35 and the extension= 8 inches.
ReplyDeleteF= k *e
35= k * 8
k= 35 /8
k= 4.375
(1) (b) since it was K(constant) was found in part (a) to be 4.375 and given that the extension = 11.. the force is therefore:
ReplyDeleteF= k * e
F= 4.375 * 11
F=48. 125
1.a
ReplyDeleteF-kx
35=k8
k=35/8
k=4.375
1.b
ReplyDeleteF=kx
F=4.375*11
F=48.125
3.
ReplyDeleteR = k/d2
R = k divided by d squared
0.00000002196/(0.00007998)^2
=3.432966269
4.
ReplyDelete1 calculation takes 7.5 X 10^-15 s
so 5.6 X 10^6 calculations would take
(7.5 X 10^-15)*(5.6 X 10^6) = 4.2 X 10^-8 s
6.
ReplyDelete-4(b-c)-3(a-b)
-4b+4c-3a+3b
4c-3a-b
7.
ReplyDeletex cartridges = 15 exposures
x+10 cartridges = 25 exposures
2x+10 = 40
15.
ReplyDeletewhen v=60, I=1.52
when v=1, I=1.52/60
when v=82, I=(1.52/60)*82
v=82 , I=2.077
W=L(wL+2P)/8
ReplyDelete8W=wL^2+2PL
2PL=8W-wL^2
P=(8W-wL^2)/2L
14.
ReplyDelete(6R1+6R2+R1R2)/6R1R2
(6R1/6R1R2)+(6R2/6R1R2)+(R1R2/6R1R2)
(1/R2)+(1/R1)+(1/6)
Question 1.
ReplyDelete(a)
Let stretch= S
FαS
F=k S
When F= 35 and S= 8
F/S = k
k= 35/8
k= 4.375
Question 1.
ReplyDelete(b) when S= 11
F= kS
From previous part, k=4.375
Therefore F= 4.375x11
F = 48.125
Question 2.
ReplyDelete(a) distance d varies directly with time t.
dα t (this means that d is directly proportional to t)
d= kt is the equation that relates d and t
Question 2
ReplyDelete(b) when d= 115miles and t= 2hours
115= k2
k= 115/2
k= 57.5 is the constant proportionality
The units, however, is in miles per hour.
In order for the units on the right to be equal to that of the left…
k= 57.5miles/hrs
Question 2
ReplyDelete(c) (c) Using the equation
d= kt
when k= 57.5 and t= 7
d= 57.5miles/hrs x 7hrs
d= 402.5 miles
This comment has been removed by the author.
ReplyDeleteQuestion 3.
ReplyDeleteR= k/d2
When, k= 0.000 000 021 96 and d= 0.000 07998
R= 0.000 000 021 96/ 2(0.000 07998)
R= 2.196x10^-8/ 2(7.998x10^-5)
R= 2.196x10^-8/ 1.5996x10^-4
R= 1.3728x10^-4
Question 4.
ReplyDeleteTime for 1 addition= 7.5 x 10^-15 s
Time for 5.6 x 10^6 additions = [7.5 x 10^-15 s] x [5.6 x 10^6]
= [7.5x5.6] x [10^-15x10^6]
= 42 x 10^-15+6
= 42 x 10^-9
Answer in standard form = 4.2 x 10^-8
Question 5.
ReplyDeletey= 4x2-3x to show by first principal that the differential equals 8x
(x, 4x2-3x) ( x+∆h, [ 4(x+∆h)2 – 3(x+∆h) ] )
dy/dx ∆h lim.--->0 y^2 – y^1/ x^2 – x^1
dy/dx ∆h lim.--->0 4(x+∆h)^2 – 3(x+∆h) – 4x^2-3x / x+∆h+x
dy/dx ∆h lim.--->0 4(x^2+ 2x∆h+∆h^2) – 3x – 3∆h – 4x^2+ 3x / x+∆h+x
dy/dx ∆h lim.--->0 4x^2+ 8x∆h+ 4∆h^2 – 3x – 3∆h – 4x^2+ 3x / x+∆h+x
dy/dx ∆h lim.--->0 4x^2+ 8x∆h+ 4∆h^2 – 3x – 3∆h – 4x^2+ 3x / x+∆h+x
dy/dx ∆h lim.--->0 8x∆h+ 4∆h^2 – 3∆h / ∆h
dy/dx ∆h lim.--->0 8x + 4∆h– 3
= 8x– 3
Proven 8x– 3 is NOT equal to 8x using first principal
Question 6.
ReplyDelete-4(b – c) – 3 (a – b)
-4b + 4c – 3a + 3b
-4b+ 3b +4c – 3a
-b +4c– 3a
4c – b – 3a
Question 7.
ReplyDelete15 of x catridges = 15x------> number of photos in one container
25 of x+10 = 25 (x+10) -----> number of photos in other container
Total number of photos = 15x+ 25 (x+10)
= 15x+ 25x+250
= 40x+250 photos
Question 8.
ReplyDeleteSimplify: 3D – (D - d)
3D – D+d
2D + d
Question 9.
ReplyDeleteI agree with bornagain16
i1 – (2 – 3 i2) + i2
i1 – 2 + 3 i2 + i2 (i1 and i2 are two totally different identities such as x and y)
Add like terms, 3 i2 and i2 are like terms, this is like saying 3x and x, assuming i2 is a term by itself. So we can therefore add them
i1 – 2 + 4 i2
Question 10
ReplyDelete3(2n + 1) is the number of mouse pads at $3
6n + 3
2(n – 2) is the number of mouse pads at $2
2n – 4
(6n + 3) – (2n – 4) how much more s the $3 than the $2
6n + 3 -2n + 4
4n + 7
Question 11
ReplyDelete16(8 – x) - 2(8x – x^2) – (64 – 16x + x^2)
128 – 16x – 16x + 2x^2 - 64 + 16x – x^2
128 – 64– 16x – 16x+ 16x+ 2x^2– x^2
64 – 16x + x^2
x^2 – 16x +64 to find the values of x we can use the quadratic formula
Question 12
ReplyDelete(GMm[(R + r) – (R – r)]) /2rR
Expand brackets
(GMm[( R + r –R + r)]) /2rR
(GMm[2r]) / 2rR
GMm2r / 2rR
GMm / R
Question 13
ReplyDeleteI assume there was an error in writing this question because I do not understand how an exponent can be raised to another power several times. That is 4A^3µ^4E^4. I mean it can be done, but i am unsure how to work it out.
Question 14
ReplyDelete(6R1 + 6R2 + R1R2)/ 6R1R2
6R1/ 6R1R2 + 6R2/ 6R1R2 + R1R2/ 6R1R2
1/ R2 + 1/R1 + 1/6
Question 15
ReplyDeleteI= 1.52A, V= 60V
I:V
1.52:60
1.52/60 = 0.025333
When V=82V
I = 82 x 0.025333
I= 2.08V (to 2 dec. places)
Question 16
ReplyDelete210(3x) = 55.3x + 38.5(8.25 – 3x)
630x = 55.3x + 317.625 – 115.5x
630x - 55.3x + 115.5x = 317.625
690.2x = 317.625
x = 317.625/690.2
x = 0.46 (to 2 dec. places)
Question 17
ReplyDeleteW = L(wL + 2P)/8
8W = wL^2 + 2PL
Make P subject of the formula
8W - wL^2 = 2PL
8W - wL^2/2L = P
Therefore P= 8W - wL^2/2L
Question 18
ReplyDelete6mg ------> x slides
5mg-------> x + 4 slides
So let y equal given sample
y = 6x is the total amount of sample is 6 by the unknown number of slides x
y= 5(x + 4) is the total amount of sample is 5 by the unknown number of slides x + 4
So, Solving for x, will give the amount of slides that can be divided
6x = 5(x + 4)
6x = 5x + 20
6x – 5x = 20
x = 20
sub x= 20 into x+4
20 + 4= 24
Therefore the sample can be divided into 20 slides using 6mg
However the same sample can be divided into 24 slides using 5mg
1)
ReplyDeleteif
8in= 35
1in=35/8
therefore for 11in = (35/8)*11
F= 48.07
3)
ReplyDeleteR=k/2d
R=(2.196*10^-7)/2(7.998*10^-5)
R=1.37*10^-3
4)
ReplyDeletefor one addition = 7.5*10^-15s
for 5.6 * 10^6 = (5.6*10^6)*(7.5*10^-15)
= 4.2*10^-8s
6)
ReplyDelete-4(b-c)-3(a-b)
-4b+4c-3a+3b
-7a+7b
7(b-a)
8)
ReplyDelete3D-(D-d)
3D-D+d
2D+d
i-(2-3i2)+i2
ReplyDeletei-2+4i2+i2
i-2+5i2
11)
ReplyDelete16(8-x)-2(8x-x^2)-(64-16x+x^2)
128-16x-16x+2x^2-64+16x+x^2
3x^2-16x+64
2.
ReplyDeletea)d is propotional to t
therefore,d is proprtional to k (constant)t.
2.
b)miles should be converted to kilometers so that the units would be km/hr
1.
ReplyDeletef=35
when l = 8
when l=1, f= 35/8 = 4.375...or
4 3/8
when l=11
f= 4.375*11 = 48.125...or 48 1/8
3. R = k/d2
ReplyDeleteR = k divided by d squared
therefore 0.00000002196/(0.00007998)^2
=3.432966269
number 4
ReplyDelete\
1 addition takes 7.5 X 10^-15 s
therefore 5.6 X 10^6 additions would take
7.5 X 10^-15 (5.6 X 10^6) = 4.2 X 10^-8 s
for number 5:
ReplyDeletey=4x^2-3x
let (x+Zx)represent a small change
x1=x x2=(x+Zx)
y1=4x^2+3 y2=4(x+Zx)^2+3
dy/dx=y2-y1/x2-x1=lim/Zx>0
dy/dx=[4(x+Zx)^2+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4(x^2+2xZx+Zx^2)+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4x^2+8xZx+4Zx^2+3-4x^2+3]
[ (x+Zx) - (x)]
lim/Zx>0=[4Zx^2+8xZx]
=[ Zx ]
lim/Zx>0= 4Zx^2/Zx + 8xZx/Zx
lim/Zx>o=4Zx+8x
=8x
this above stated was nena's solution but there is a mistake in this line
dy/dx=[4(x+Zx)^2+3-4x^2+3]/
[(x+Zx) - (x)]
which should read
lim/Zx>0=dy/dx [4(x+Zx)^2-3]-[4x^2-3]/[x+Zx]-[x]
lim/Zx>0=dy/dx [4(x^2+2xZx+Zx^2)-3]-[4x^2-3]/Zx
lim/Zx>0=dy/dx [4x^2+8xZx+4Zx^2-3]-[4x^2-3]/Zx
lim/Zx>0=dy/dx [4x^2+8xZx+4Zx^2-3-4x^2+3]/Zx
lim/Zx>0=dy/dx 8x+4Zx
dy/dx 8x
For Question 15
ReplyDeleteI= 1.52A
V= 60V
I:V
1.52:60
1.52/60 = 0.025333
When V=82V
I = 82 x 0.025333
I= 2.08V
for question 14
ReplyDelete(6R1 + 6R2 + R1R2)/ 6R1R2
6R1/6R1R2 + 6R2/6R1R2 + R1R2/6R1R2
6/6R2 + 6/6R1 + 1/6
1/R2 + 1/R1 + 1/6
question 6
ReplyDelete-4(b – c) – 3(a – b)
expanding brackets...
-4(b) -4(-c) -3(a) -3(-b)
-4b +4c -3a +3b
-3a -4b +3b +4c
-3a - b + 4c
question ans
ReplyDeletethey ask for constant proportionality
and the formula is a = kb or F = KI
they gave us F = 35 and I=8 so therefore all you have to do is make k the subject of the formula and you would get K= f/I
so therefore K= 35/8 = 4.375
i think so correct if wrong please to work part b
ReplyDeletewhere they ask find the value for F when the it is streched 11I
you work using the pervious constant and multiplyby the streched
F=11(35/8)=48.125
Answering ques 6
ReplyDelete-4(b – c) – 3(a – b). Simplify this expression.
first thing to do is multiply what outside THE BRACKETS TO WHAT INSIDE and then group.
-4(b – c) – 3(a – b)= -4b+4c-3a+3b
-4b+4c-3a+3b= -4b+3b+4c-3a =-b+4c-3a
I forgot to mention when work out bracket remember the rule of the function (-)*(+)=(-)
ReplyDeleteand so on
working question 8
ReplyDelete3D – (D – d) is used. Simplify this expression
3D-D+d=2D+d
W = L(wL + 2P)/8
ReplyDeletemake p the subject you simple have to transpose
w*8=L(wL+2P)then move the L out
W*8/L=wl+2P then move the wL
w*8-wL/L=2P then move the 2
W*8-wL/2L=p
Also remember when work out the above question remember that when yourare dividing and crossing the = you multiply and when you are multiplying you divided
ReplyDeletealso that a plus becomes a minus and a minus a plus to the change in direct
1) a. F=35 when L=8
ReplyDelete1L=35/8 = 4.375
K of spring = 4.375
1) b. 11L = k x 11
ReplyDelete= 4.375 x 11
@ 11 inches spring = 48.125
2) a. s=d/t
ReplyDeleted = constant>K x t
2) b. d = st
ReplyDelete115 miles = K x 2hours
K = 115/2hours
K = 57.5 mph
2) c. d = Kt
ReplyDeleted = 57.5 x 7hours
d = 402.5 miles
4) 1 addition = 7.5 x 10^-15 seconds
ReplyDelete5.6 x 10^6 addns = 7.5 x 10^-15 x 5.6 x 10^6
5.6 x 10^6 additions = 0.000000042 seconds
= 4.2 x 10^-8 secs.
6) -4(b-c) - 3(a-b)
ReplyDelete-4b + 4c - 3a + 3b
pressure = 4c - 3a - b
8) 3D - (D-d)
ReplyDelete3D - D + d
2D + d
7) (x = 15 exposures)
ReplyDeletex + x + 25(10)
Total amt of exposures = 2(15) + 25(10)
= 30 + 250
Total = 270 exposures!
9) i1 - (2-3i2) + i2
ReplyDelete> i1 -2-3i2 + i2
> i2 - 2 - 4i2
2(a)use the formula
ReplyDeletespeed=distance/time
distance=speed*time
so therefore you have to make distance the subject of the equation
speed becomes the constant
2(b)Its is said that the distance is directly proportional to time
ReplyDeletetherefore
d=k*t
where k is the constant of proportionality
d=115miles
t=2hr
find speed
then therefore you use the above equation where speed = distance/time or d=k*t where you make k the unknown subject which can be seen as speed
speed=115/2
speed=57.5kms
distance=speed*time
distance=57.5*7
distance=402.5
Question 15
ReplyDeleteI= 1.52A, V= 60V
use equation v=k*i
find k by transposing and making k the subject
k=1.52/60
1.52/60 = 0.025333
b)When V=82V find i
ReplyDeleteI = v*k
i = 82 x 0.025333 or 82*(1.52/60)
I= 2.07V (to 2 dec. places)
ques 5 y=4x^2-3x
ReplyDeletelet (x+Zx)represent a small change
x1=x x2=(x+Zx)
y1=4x^2+3 y2=4(x+Zx)^2+3
dy/dx=y2-y1/x2-x1=lim/Zx>0
dy/dx=[4(x+Zx)^2+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4(x^2+2xZx+Zx^2)+3-4x^2+3]/
[(x+Zx) - (x)]
lim/Zx>0=[4x^2+8xZx+4Zx^2+3-4x^2+3]
[ (x+Zx) - (x)]
lim/Zx>0=[4Zx^2+8xZx]
=[ Zx ]
lim/Zx>0= 4Zx^2/Zx + 8xZx/Zx
lim/Zx>o=4Zx+8x
=8x
hints
>let (x+Zx) represent a small change
>where u see (x+Zx)^2 multiply (x+Zx) by itself
and u should get (x+Zx)(x+Zx)
=x^2+xZx+xZx+Zx^2
=x^2+2xZx+Zx^2
question one...
ReplyDeletelet k = the constant of proportionality
let l = the length of the spring wen stretched
a)
therefore the equation = F = k x l
when l= 8, F = 35;
so the equation = 35 = k (8)
therefore k = 35 / 8
k = 4.375
b)
therefore, when l = 11;
F = (4.375) x (11)
F = 48.125
F ~ 48
question six...
ReplyDelete-4(b – c) – 3(a – b)
expanding brackets...
-4(b) -4(-c) -3(a) -3(-b)
-4b +4c -3a +3b
-3a -4b +3b +4c
-3a - b + 4c
question seven...
ReplyDeletex catridges = 15 exposures each
x + 10 catridges = 25 exposures each
therefore total no. of exposures = 15(x) + 25(x + 10)
= 15x + 25x + 250
= 40x + 250 exposures
question ten...
ReplyDelete3(2n + 1)
:- 3(2n) + 3(1)
:- 6n + 3
2(n - 2)
2(n) + 2(-2)
2n - 4
how much more is the value of the $3 mouse pads than the $2 mouse pads?
(6n + 3) - (2n - 4)
6n + 3 - 2n + 4
6n - 2n + 3 + 4
4n + 7 more...