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]
Learn more:https://brainly.com/question/12817429
A jar that contains quarters and dimes is worth $7.15. If there are a total of 40 coins,
how many of each type of coin is there?
Answer:
21 quarters and 19 dimes
Step-by-step explanation:
Create a system of equations where q is the number of quarters and d is the number of dimes.
0.25q + 0.1d = 7.15
q + d = 40
Solve by elimination by multiplying the bottom equation by -0.25
0.25q + 0.1d = 7.15
-0.25q - 0.25d = -10
Add them together and solve for d:
-0.15d = -2.85
d = 19
Then, plug in 19 as d into the second equation to solve for q:
q + d = 40
q + 19 = 40
q = 21
So, there are 21 quarters and 19 dimes
Answer:
21 Quarters, 19 Dimes.
Step-by-step explanation:
21 x .25 = 5.25
19 x .10 = 1.90
5.25 + 1.90 = 7.15
The area of the top face of a cube is 16 square inches. Use 8 of these cubes to make a rectangular
prism. What is the volume of the rectangular prism? Hint: The shape of each face of a cube is a
square.
Answer:
The volume of the rectangular prism is 512 inches³
Step-by-step explanation:
Any cube has 6 square faces
Area of any square = L × L, where L is a length of each side
The volume of the cube = L × L × L
∵ The area of the top face of a cube = 16 inches²
→ Find which number multiply by itself = 16
∵ 16 = L × L
∵ 16 = 4 × 4
∴ L = 4 inches
Let us find the volume of 1 cube
∵ The volume of the cube = L × L × L
∵ L = 4 inches
∴ The volume of each cube = 4 × 4 × 4
∴ The volume of each cube = 64 inches³
∵ We will use 8 of this cube to make a rectangular prism
→ That means the volume of the rectangular prism is 8 times
the volume of 1 cube
∴ The volume of the prism = 8 × volume of 1 cube
∵ The volume of each cube = 64 inches³
∴ The volume of the prism = 8 × 64
∴ The volume of the prism = 512 inches³
The volume of the rectangular prism is 512 inches³
What is an equation of a line with slope −2/3 and a y-intercept of −4?
what is midpoint if tu =4× and uv =X +9
Answer:
12Step-by-step explanation:
Given
TU = 4xUV = x + 9Finding the value of x
TU = UV4x = x+93x = 9x = 3Midpoint = 4x = 4*3 = 12
A fraction is ?
Please help
Answer:
In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole
Answer:
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Find the missing side of the triangle !!!
HELP MEEE!!!!!!!!!!!!!!
Which equations are true and can be used to find some multiples of 7? Check all that apply.
O 7x 0 = 7
O 7x1=7
O 7*4= 27
O 7x 10 = 70
O 7 x 12 = 84
Answer:
7 × 1 = 7 7 × 10 = 70 7 × 12 = 84
Step-by-step explanation:
I need help on this ASAP
Answer:
ITZ A
Step-by-step explanation:
4 less than a number n is −15.
Answer:
n-4= -15
Step-by-step explanation:
"4 less than a number n" is represented by n-4.
it says it "is" -15, so this equals -15.
n-4= -15
A pyramid has a square base with an area of 169 ft.2. What is the perimeter of the base of the pyramid?
Answer:338
Step-by-step explanation:
169/2 = 84.5 (base is 84.5) 84.5 * 4 (sides) = 338
Answer:
:)
Step-by-step explanation:
52
Sq rt(169) - 13
13 is the side length
13*4=52
Solve for x.
bx-10=8
Answer: x = 18/b
................................
Answer:
you can put your answer as 9 or 2
Step-by-step explanation:
How many liters are in 260 ounces?
Answer:
7.68912
Step-by-step explanation:
A train travels 100 miles per minute. One mile is about 1.61 kilometers and 1 hour is 60 minutes.
Convert train's speed in kilometers per hour?
Answer:
9660 kn per hour
Step-by-step explanation:
one more than a number
Answer:
x+1
Step-by-step explanation:
Can somebody help me find the perimeter of this figure?
Answer: P = 64in,
Step-by-step explanation: P = 17 + 13 + 25 + 9
x-13=62 idk know it
20 + 3 (7 + 4) + 5 + 2 (7 + 9)
Answer:
90
Step-by-step explanation:
i did the math hope this helps you out
You purchased a stock at a price of $51.17. The stock paid a dividend of $1.75 per share and the stock price at the end of the year was $56.79. What was the total return for the year?
Answer: i think it is 109.51
Step-by-step explanation:
Can someone plz help me
Answer:
Your table might look something like this:
The dads steps:
3
6
9
12
15
18
Sons steps:
5
10
15
20
25
30
You can notice the pattern. If dad walks 3 steps, son walks 5. If dad walks another 3, son walks another 5. And so on. This means dad walks 12 steps when the sin walks 20 steps.
Step-by-step explanation:
The ratio is 3:5. This means dad wlaks 3 steps so son must walk 5 steps basically. So.......... You can now create the table. Y I just have to multiply or divide each side ( of the colon:) so. Whatever you do to one side, you do to the other side. If you x3 on one side, you do it to other. Same goes for division. In the 'table' I did above, I x2 to get 6 and 10. Then I took the 3 and the 5 again and timsed those by 3. You can also change the 6 and the 10. So:
3:5
Then x2
6:10
Then I take the top layer (you can either choose to change the top layer, or layer above as long as you do the same thing to each side. Remember, only x and ÷. No + or-.) and I x3
9:15
Then I could take 9 and 15 and x5
45:75
It's crazy that all these. Ratios mena the same thing! 45 steps from dad would take the son 75 steps. You can also divide the last ratio of 45:75 to find the one you started with, 3:5.
So you get the idea.
It is probably best to do what I did in the table in the answer part because I did a pattern. Take the top layer, and x2, then x3, then x4, ect. Rather then doing random things.
Solve x^2 - 4x +18= 0 by completing the square.
Answer:
Your answer is: x = 2 ± i√14
Step-by-step explanation:
Hope this helped : )
I need help please! this is on EDGE2020 !
Answer:
D
Step-by-step explanation
A. there are 6 triangles so not this
B. Only 2 rectangles
C. 6 triangles once again
D. everything matches
Answer:
for every 6 triangles there are 2 rectangles
Write the expression in simplest form
50 - 62c +38-43c I’m confused on how to solve this problem need help ASAP
Answer:
88 - 105c
Step-by-step explanation:
Hey there!
Step 1: Collect like terms.
(50 + 38) + (-62c - 43c)
Step 2: Simplify.
88 - 105c
~I hope I helped you! :)~
Answer: 88-105c
Step-by-step explanation:
Combine like terms
Solve for x: x + b = C
Answer:
x=C-b
Step-by-step explanation:
Subtract b from both sides to get x alone.
What are the partial products of 73 × 8
The partial products of 73 x 8 is = 584
What is partial product?The partial products algorithm allows students to multiply two long numbers fast and easily by breaking down a more challenging product into a series of simpler problems.
Steps to calculating the partial product for 73 x 8(70 +3 ) * (8)
= 70 x 8 = 560 and ;
= 3 x 8 = 24
Step 2 - Add all the products together
560 + 24 = 584
Learn more about partial product at:
https://brainly.com/question/24716925
#SPJ2
PLEASE HELPP!!!!! Will mark you as Brainliest!!!!
Answer:
Yes! if this was an option then this one would be correct
Step-by-step explanation:
In order to see if the ordered pair are a function you could graph them, or you could look at the x-values and see if there are any duplicates. in this case there are not.
High Hopes^^
Barry-
Which equation has exactly one solution?
A. 4x – 4 + 2x = 6x - 4
B. 3x + 5 = 2x - 6
C. 2(4x + 5) = 8x + 10
D. 4x - 8 = 4(x - 4)
Answer:
its B
Step-by-step explanation:
I calaulated all the numbers
1.) Expand and simplify (6x-7)+(x-3)+(4x-5) *
a.)11x-5
b.)11x-15
c.)10x-15
d.)10×1
Answer:
the answer is b 11x-15
Step-by-step explanation:
your collecting like terms then combining them
wolverine and cyclops ordered large pizzas for dinner. Wolverine ate 1-3/8 pizzas and cyclops ate 1/12 of a pizza. which of the following statements is true
Answer:
What statements are you talking about
Step-by-step explanation:
Simplify 8/-3 divided by -4/9 . (5 points)
A. −8
B. −6
C. 6
D. 8
I'd appreciate if you would help :)
Answer:
6
Step-by-step explanation:
Because 17/12=6
0.00062 as a scientific notation
Answer:
6.2 x 10^-4
Step-by-step explanation:
Since it is a decimal you would move the decimal point to the right. Making the exponent a negative number.
