If PV = 800, then P can be written as a function of V,
P(V) = 800 / V
(a) The average rate of change of P as V increases from 200 to 250 in³ is then
(P (250) - P (200)) / (250 in³ - 200 in³) = (3.2 lb/in² - 4lb/in²) / (50 in³)
... = -0.016 (lb/in²)/in³
(Or -0.016 lb/in⁵, but I figure writing the rate as (units of pressure) per (unit volume) makes more sense.)
(b) We can also write V as a function of P :
V(P) = 800 / P
Take the derivative:
V'(P) = - 800 / P²
which immediately demonstrates that V'(P) ∝ 1 / P², as required. (The fish-looking symbol, ∝, means "is proportional to".)
If differentiating is supposed to be more involved, you can use the limit definition:
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{V(P+h)-V(P)}h[/tex]
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800}{P+h}-\frac{800}P}h[/tex]
[tex]V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800P-800(P+h)}{P(P+h)}}h[/tex]
[tex]V'(P)=\displaystyle800\lim_{h\to0}\frac{-\frac h{P(P+h)}}h[/tex]
[tex]V'(P)=\displaystyle-800\lim_{h\to0}\frac1{P(P+h)}=-\dfrac{800}{P^2}[/tex]
Part(a): The average rate of change of [tex]\frac{dP}{dV}[/tex] is [tex]-0.0164 lb/in^{2}[/tex]
Part(b): The required answer is [tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]
Part(a):
Given,
[tex]PV=800[/tex]
Differentiating the above equation with respect to [tex]V[/tex].
[tex]\frac{dP}{dV}=-\frac{P}{V}[/tex]
Now, at [tex]V=200 in^{3}[/tex] and [tex]P=4 lb/in^2[/tex]
At [tex]V=250 in^3[/tex] and [tex]P=\frac{80}{25} lb/in^2[/tex]
Hence, we can write,
[tex]\frac{dP}{dV}[/tex] at [tex]V=200[/tex] we get,
[tex]\frac{-1}{200}=\frac{-1}{50}[/tex]
Again [tex]\frac{dP}{dV}[/tex] at [tex]V=250[/tex] we get,
[tex]\frac{-80}{25\times 250}[/tex]
So, the average rate of change of [tex]\frac{dP}{dV}[/tex] is,
[tex]\frac{-\frac{1}{50}- \frac{8}{25\times25} }2\\=-\frac{1}{100}-\frac{1}{625}\\=-0.0164 lb/in^2[/tex]
Part(b):
Given,[tex]PV=800[/tex] then,
[tex]V=\frac{800}{P}[/tex]
Now,[tex]\frac{dV}{dP} =-\frac{800}{P^2}[/tex]
Then the above implies,
[tex]\frac{dV}{dP} \infty \frac{1}{P^{2}}[/tex]
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Casey has 8 1/2 yards of fabric she uses 2 1/2 yards to make a pillow and 3 yards to make curtains how much fabric is remaining
Answer:
3 yards
Step-by-step explanation:
8 1/2 - 2 1/2 = 6
6 - 3 = 3
Your answer is 3.
Please mark as brainliest.
⅔+(-⅓)=?????????????????????
Answer:
1/3
Step-by-step explanation:
2/3 - 1/3
Since the denominators are the same, we subtract the numerators
1/3
Answer:
1/3
Step-by-step explanation:
NEED HELP GIVING 15 POINTS
Answer:
Jack is incorrect. The correct answer is 2
Step-by-step explanation:
The question is given as:
4x-24 / (y+w) where x=5, y=3 and w= -5
Substitute values of x, y and w in the equation as;
4*5 - 24 / (3+-5)
20 - 24 / (-2)
-4 / -2 = 2
Jack's answer is 7 which is wrong. The correct answer is 2
2 is correct because you have substituted the real values of x,y and w in the expression and performed the operation right.
PLZZZZ ANSWER QUICKKKKKK BY MIDNIGHTTTT
HELPPPP!!!! PLEASEEE!!!
Which statement below is true?
A. If p → q is true, then q → p is true.
B. If p → q is true and p is true, then q is true.
C. If p → q and q → r are true, then q → p is true.
D. If p → q and q → r are true, then r → p is true.
Answer:
D is correct
Step-by-step explanation:
p=q then q is the same as p and if r=p that is true
solve and then write the sum in standard form. 1 tenth +2 tenths = -------tenths== -----
Answer:
Solve: 3 tenths
Standard form: 0.3
A construction worker needs to move 120 ft squared (3) of dirt by using a wheelbarrow. One
wheelbarrow load holds 8 ft squared(3) of dirt and each load takes him 10 minutes to complete
. One
correct way to figure out the number of hours he would need to complete this job is
Answer:
it would take him 1.5 hours (an hour and 30min.)
Step-by-step explanation:
120 divided by 8 = 15
15 divided by 10 = 1.5
The number of hours he would need to complete this job is 2.5 hours.
What is PEDMAS rule?"PEDMAS is an order of operation used in mathematics to deal easily with complex calculations. It states that we start solving any arithmetic expression by solving the terms written in parentheses or brackets and then we simplify exponential terms and move ahead to division and multiplication operations and then, at last, we can find the answer by solving addition and subtraction operations."
According to the question
A construction worker needs to move 120 feet squared (3) of dirt by using a wheelbarrow.
One wheelbarrow load holds 8 feet squared(3) of dirt and each load takes him 10 minutes to complete.
Writing the above statement in mathematical form
= (120 ÷ 8) × 10
By using PEDMAS rule, we get
= 15 × 10
= 150 mins
= 150 ÷ 60
= 2.5 hours
Thus, the number of hours he would need to complete this job is 2.5 hours.
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What is .82 written as a percent?
-8.2%
- 82%
-820% ANSWER QUICK PLS
Answer:
82
Step-by-step explanation:
get rid of dicemal
Answer: 82%
0.82 as a percent can be written as 82%. Just make 0.82 into an 82%.
0.82 as a fraction can be 82/100.
The answer to the question is 82%.
Hope this helps you!
Find the comthon ratio of the geometric sequence 10,60, 360,...
Answer:
10
Step-by-step explanation:
The common ratio of the geometric sequence 10,60, 360,... is 6.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, A geometric sequence 10,60, 360,...
We know the common ratio r in a geometric sequence is
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Therefore,
The common ratio in this geometric sequence 10,60, 360,... is,
= 60/10 = 360/60 = 6.
So, The common ratio is 6.
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When you barter, you must ______ in order to buy something ?
Answer: exchange
Step-by-step explanation:
Answer:
Trade it for something else.
Step-by-step explanation:
when bartering, you trade for items you want, and give away items you don’t want. You should also consider if the item you are trading for works. Be skeptical about the things you are trading Or giving. And make sure to also to get a good trade, and not blame others for them doing a bad trade.
Hope this helps!- Artistsani
In crest view middle school, 12 out.of 16 students are right handed. If there are 400 students in the school, how many are right handed?
Estimated sum of 71,458
Answer:
there can be a lot example:
71,000
71,500
71,460
Step-by-step explanation:
A container holds 13 pencils, 5 black pens, and 3 blue pens. What is the ratio, in fraction form, of pens to all writing tools?
Answer:
8/21
Step-by-step explanation:
which list shows the triangles in order from greatest area to least area
Answer:
H - Triangle Z, Triangle X, Triangle Y
Step-by-step explanation:
Triangle X area = rad(66.5) cm^3 ≈ 8.155cm^3
Triangle Y area = 8.15cm^3
Triangle Z area = (17.5/2)cm^3 = 8.75cm^3
8.75cm^3 > 8.155cm^3 > 8.15cm^3
Therefore:
Triangle Z area > Triangle X area > Triangle Y area
Help please
What is the slope of the line:
3y - 4 = 5 (x + 2)
Answer:
The answer is m = 5/3
Step-by-step explanation:
HELPPP PLEASE!!!!! SHOW ALL WORK!!!
Answer:
22
Step-by-step explanation:
2x+12=x+34
2x-x=34-12
x=22
The frequency distribution chart below represents scores from a math quiz. A histogram titled frequency has score on the x-axis and frequency on the y-axis. 65 to 70 is 1, 71 to 76 is 1, 77 to 82 is 1, 83 to 88 is 3, 89 to 94 is 4, 95 to 100 is 2. Which statement best describes the data? a. The data is skewed left. c. The data is skewed right. b. The data is symmetric. d. There is no pattern to the data.
Answer:
a. the data is skewed to the left
Step-by-step explanation:
on the left most of the data is lower than the data on the right + i took the quiz
Answer:
A
Step-by-step explanation:
5/9 is rational or irrational
Robert I'm $10 which was 4less than twice which Eric earned how much money did Eric earn
Answer: Eric earned $7
Step-by-step explanation:
Let's define:
R = money that Robert earned.
E = Money that Eric earned.
Now we want to find how much money did Eric earn.
We know that:
R = $10 = 2*E - $4
Whit this equation, we can find the value of E. So we must isolate the variable E in one side of the equation:
2*E = $10 + $4 = $14
E = $14/2 = $7
Eric earned $7
What is the cardinal number of the set C={0,5,−4,25,103,56}
Answer:
I wanna say its Hence n (Q) =7
I may be mistaken
Answer:
6
Step-by-step explanation:
The set is made up of 6 elements. Therefore, the cardinal number is 6.
complete the division. The quotient is 3x^2+__x+__.
Answer: 3x^2+ -2x+5. I hope this helped
Step-by-step explanation:
Plzz do correctly also worth a lot of points
Answer:
I believe the Answer is B
I'm really sorry if this is wrong.
Step-by-step explanation:
I tried my best :)
Find j. 6 + 2(3j – 2) = 4(1 + j)
Answer:
j=1
Step-by-step explanation:
Simplifying radicals maze
Answer:
sihdhdhdjjdjdjdjdjsjjsjejdjje
The solution to the radical expression √36 is 6.
What is a radical expression?A radical expression is a mathematical expression that contains a radical symbol (√), which represents the square root (or nth root) of a number or variable. The radical symbol is typically followed by a number or expression inside a set of parentheses, which indicates what is being rooted.
The square root of 36 is a number that, when multiplied by itself, equals 36. In this case, we know that the number is 6, because 6 x 6 = 36.
The square root of 36 is simply:
√36 = 6
So the solution of the given radical expression √36 is 6.
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The complete question is given below.
Solve the radical expression: √36.
Joe told Mickey he got an hourly raise at work and his new rate will be $10.25 per hour. Mickey wants to know what Joe’s hourly rate was before his raise. If r represents the amount of the raise, which expression represents Joe’s hourly rate before his raise?
r minus 10.25
10.25 minus r
10.25 + r
r + 10.25
Answer:
10.25 minus r
Step-by-step explanation:
because amount of money minus how much the raise was equals what he had before.
Answer:
✨b✨
Step-by-step explanation:
how many steps do we take from 0 to -13???
Answer:
13
Step-by-step explanation:
because thats how u get to 13
Maliah goes to an electronic store. Let y represent the price of a laptop and let x
represent the price of a television. The equation y= 3x + 22 relates the prices.
Which of the following statements are true? Select all that apply.
Answer:
A and C if this was ABCDE
Step-by-step explanation:
150 times 3 plus 22 would equal 450 plus 22 which is 472,
265 times three is 795 plus 22 is 817,
for the BDE, 175 times 3 is 525 plus 22 is 547, 300 times 3 is 900 plus 22 is 922, and 345 times 3 is 1035 plus 22 is 1057
An electric company calculates a person's monthly bill from the number of kilowatt-hours (kWh), x, used, x 200 The function b(ar) = { 0.102, 0.15(x - 200) +20, 200 determines the bill How much is the bill for a person who uses 800 kWh in a month?
Answer:
$110
Step-by-step explanation:
=0.15(x-200)+20
=0.15(800-200)+20
=0.15(600)+20
=90+20
=$110 paid
What is the rule for reflecting a figure over the x-axis?
A
(x, y) --> (y, x)
B
(x, y) --> (x, -y)
C
(x, y) --> (-x, y)
D
(x, y) --> (-y, -x)
Answer:
(x,y)→(−x,y) .
Step-by-step explanation:
16. A section of an exam contains four True-False questions. A completed exam paper is selected at random, and the four answers are recorded. a. List all outcomes in the sample space. b. Assuming the outcomes to be equally likely, find the probability that all the answers are the same. c. Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is "True." d. Assuming the outcomes to be equally likely, find the probability that at most one of the four answers is "True."
Answer:
a
[ FFFF] , [FFFT] , [FFTF] , [FFTT]
[FTFF] , [FTFT] , [FTTF], [FTTT]
[TFFF] , [TFFT] , [TFTF] , [TFTT]
[TTFF] , [TTFT],[TTTF] , [TTTT]
b
[tex]P(A) = \frac{1}{8}[/tex]
c
[tex]P(B) = \frac{1}{4}[/tex]
d
[tex]P(C) = \frac{5}{16}[/tex]
Step-by-step explanation:
From the question we are told that
The number of True - False question is n = 4
The number of answers recorded are k = 4
Generally the outcomes in the sample space are 16 and they are listed below
[ FFFF] , [FFFT] , [FFTF] , [FFTT]
[FTFF] , [FTFT] , [FTTF], [FTTT]
[TFFF] , [TFFT] , [TFTF] , [TFTT]
[TTFF] , [TTFT],[TTTF] , [TTTT]
Generally from the list of the possible outcome we see that the number of outcome where the answers are the same is 2 i.e [TTTT] and [FFFF]
So the probability that all the answers are the same is mathematically represented as
[tex]P(A) = \frac{2}{16}[/tex]
=> [tex]P(A) = \frac{1}{8}[/tex]
Generally from the list of the possible outcome we see that the number of outcome where exactly one answer is true is 4 i.e [FFTF] , [FFFT],[TFFF] , [FTFF]
So the probability that exactly one of the four answers is "True." is mathematically represented as
[tex]P(B) = \frac{4}{16}[/tex]
=> [tex]P(B) = \frac{1}{4}[/tex]
Generally from the list of the possible outcome we see that the number of outcome where at most one of the four answers is true is 5 i.e [FTFF] , [FFFF] , [FFTF] , [FFFT] ,[TFFF]
So the probability that at most one of the four answers is mathematically represented as
[tex]P(C) = \frac{5}{16}[/tex]
The probabilities of all same, exactly one true, and most one of the four are true is 0.125, 0.25, and 0.3125 respectively.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
A section of an exam contains four True-False questions.
A completed exam paper is selected at random, and the four answers are recorded.
Total event = 16
A. The sample space will be shown in the table below.
[tex]\rm Sample \ space = 16 \ \begin{Bmatrix}FFFF & FFFT & FFTF & FFTT \\FTFF & FTFT & FTTF & FTTT \\TFFF & TFFT & TFTF & TFTT \\TTFF & TTFT & TTTF & TTTT\end{Bmatrix}[/tex]
B. The probability that all the answers are the same will be.
Favorable event = 2 ={(TTTT, FFFF}
Then we have the probability,
[tex]\rm P(B) =\dfrac{2}{16} =\dfrac{1}{8} = 0.125[/tex]
C. The probability that exactly one of the four answers is "True".
Favorable event = 4 {(FFFT, FFTF, FTFF, TFFF}
Then we have the probability,
[tex]\rm P(C) =\dfrac{4}{16} =\dfrac{1}{4} = 0.25[/tex]
D. The probability that at most one of the four answers is "True".
Favorable event = 5 {(FFFF, FFFT, FFTF, FTFF, TFFF}
Then we have the probability,
[tex]\rm P(D) =\dfrac{5}{16} =0.3125[/tex]
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