Answers
Answer:
1) -0.016 pounds per square inch per cubic inch.
2) [tex]\displaystyle V'(P)=-\frac{800}{P^2}[/tex]
Step-by-step explanation:
We are given the equation [tex]PV=800[/tex].
Part A)
We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.
To find the average rate of change between two points, we find the slope between them.
Rewrite the given equation as a function of V:
[tex]\displaystyle P(V)=\frac{800}{V}[/tex]
Hence, the average rate of change for V = 200 and V = 250 is:
[tex]\displaystyle \begin{aligned} m &= \frac{P(250) - P(200)}{250 - 200} \\ \\ & = \frac{3.2 - 4}{250 - 200} \\ \\ & = -0.016\end{aligned}[/tex]
Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.
Part B)
We want to express V as a function of P. This can be done through simple division:
[tex]\displaystyle V(P)=\frac{800}{P}[/tex]
We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:
[tex]\displaystyle \frac{d}{dP}\left[V(P)\right]=\frac{d}{dP}\left[\frac{800}{P}\right][/tex]
Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:
[tex]\displaystyle \begin{aligned} V'(P) & = 800\frac{d}{dP}\left[ P^{-1}\right] \\ \\ & = -800(P^{-2}) \\ \\ & = -\frac{800}{P^2}\end{aligned}[/tex]
Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.
Related Questions
1 point
3. A bus driver stops at a gas station to put some gasoline in the bus. He
pays $2.48 per gallon for 15 gallons of gas. How much did he pay for the
gas?
Answers
Minerva is trying to estimate v 55. She uses this table of values:
Square 7.02 7.12 7.22 7.32 7.42 7.52
Value
49.0 50.4 51.8 53.3 54.8 56.3
Square 7.62 7.72 7.82 7.92 8.02
Value
57.8 59.3 60.8 62.4 64.0
What should she do next to find 55 to the nearest hundredth?
Answers
Answer: B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Test!
Simplify: (x3 y-2)12 (x-5y)-12
A) xy
B) x12xy
C) yx
D) y12xy
Answers
Answer: b
Step-by-step explanation:
What is the retail price of a shirt that has a wholesale price of $12 and is marked up by 60 percent?
$7.20
$19.20
$31.20
$72.00
Answers
Answer: 19.20
Step-by-step explanation: What I did was figure out what 10% of 12 was (1.2) then multiplied it by 6 which was 7.2. Then I added that to 12 and got 19.2.
Let me know if this was helpful! :D
Answer:
19.20
Step-by-step explanation:
I just did this and payed attention during the lesson.
Write a valid conclusion using the Law of Detachment or Law of Syllogism given the statements below.
1. If you drive above 55mph you will get a ticket
2. Kate is driving 60 mph.
Answers
Answer:
Step-by-step explanation:
Ok so we are going to start with the first statement. If you drive above 55mph you will get a ticket. Lets say that is P. The second statement. Kate drives 60mph. That is our Q.
P>Q
Q>R
P>R
R is our conclusion.
So our conclusion is indeed. Kate will get a ticket.
Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, and backpacking. Based on the breathability, durability, ver-satility, features, mobility, and weight of each jacket, an overall rating ranging from 0 (lowest) to 100 (highest) was assigned to each jacket tested. The following data show the results for 20 top-of-the line jackets (OutdoorGearLab website, February 27, 2013).
42 66 67 71 78 62 61 76 71 67
61 64 61 54 83 63 68 69 81 53
a. Compute the mean, median, and mode.
b. Compute the first and third quartiles.
c. Compute and interpret the 90th percentile.
Answers
Answer:
(a) The mean is 65.9, the median is, 66.5 and the mode is. 61.
(b) The first and third quartiles are 61 and 71 respectively.
(c) The value of the 90th percentile is, 78.3.
Step-by-step explanation:
The ratings of 20 top-of-the line jackets, arranged in ascending order are as follows:
S = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66 , 67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}
(a)
Compute the mean as follows:
[tex]\bar x=\frac{1}{n}\sum\limits^{n}_{i=1}{x_{i}}=\frac{1}{20}\times 1318=65.9[/tex]
Compute the median as follows:
For an even number of values the median is the average of the middle two values.
[tex]M=\frac{10^{th}obs.+11^{th}obs.}{2}=\frac{66+67}{2}=66.5[/tex]
Compute the mode as follows:
The mode of a dataset is the term that occurs most of the time.
[tex]m=61[/tex]
Thus, the mean is 65.9, the median is, 66.5 and the mode is. 61.
(b)
The first quartile is the median of the first half of the data set.
S₁ = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66}
[tex]Q_{1}=\text{Median of }S_{1}=\frac{5^{th}obs.+6^{th}obs.}{2}=\frac{61+61}{2}=61[/tex]
The third quartile is the median of the second half of the data set.
S₂ = {67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}
[tex]Q_{3}=\text{Median of }S_{2}=\frac{15^{th}obs.+16^{th}obs.}{2}=\frac{71+71}{2}=71[/tex]
Thus, the first and third quartiles are 61 and 71 respectively.
(c)
The pth percentile is a data value such that at least p% of the data set is less-than or equal to this data value and at least (100 - p)% of the data-set are more-than or equal to this data value.
Use the Excel formula "=PERCENTILE.INC(array,0.9)" to compute the 90th percentile.
The value of the 90th percentile is, 78.3.
This value implies that 90% of the ratings are less than 78.3.
Simplify. 27x15y24−−−−−−−√3
Answers
Answer:
I also believe the answer is 3x^5 y^8
Step-by-step explanation:
The expression ∛(27 x¹⁵ y²⁴) in the simplified form will be 3 x⁵ y⁸.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ ∛(27 x¹⁵ y²⁴)
Simplify the expression, then we have
⇒ ∛[3³ (x⁵)³ (y⁸)³]
⇒ ∛(3 x⁵ y⁸)³
⇒ 3 x⁵ y⁸
The expression ∛(27 x¹⁵ y²⁴) in the simplified form will be 3 x⁵ y⁸.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
The total sales tax in a certain city is 8.75%. The state sales tax rate is 7.25%, and the county adds an additional sales tax of 0.5%. How much in sales tax is added by the city?
a.) 0.1%
b.) 0.25%
c.) 1%
d.) 2.5%
Answers
Answer:
C.1%
Step-by-step explanation:
-8= 3-5(x+6) solving algebraicaily
Answers
Let's solve your equation step by step
-8=3-5(x+6)
Step 1: simplify both sides of the equation
-8=3-5(x+6)
-8=3+(-5)(x)+(-5(6) (distribute)
-8=3+-5x+-30
-8=(-5x)+(3+-30) (combine like terms)
-8=-5x+-27
-8=-5x-27
Step 2: flip the equation
-5x-27=-8
Step 3: add 27 to both sides
-5x-27+27=-8+27
-5x=19
Step 4: Divide both sides by -5
-5x/-5 = 19/-5
Answer : x= -19/5
Answer:
x = -19/5
Step-by-step explanation:
-8 = 3-5(x+6)
Distribute.
-8 = 3-5x-30
Combine like terms.
-8 = -27-5x
Add 27 on both sides.
-8 = -27-5x
+27 +27
19 = -5x
Divide by -5 on both sides.
19 = -5x
/-5 /-5
-19/5 = x
Hope this helps you a little bit! Sorry if it get confusing...have an amazing day c:
Help!!!!!!!! I will give 10 points!
Answers
18:
multiply both sides
move the constants to the right
calculate
I added a picture if you need it. I hope this helps
Ameera had $10.50 with her. She bought some pencils costing $2.50 each and some erasers costing $1.00 each. Could she buy 4 pencils and 3 erasers with the money she had?
Answers
Answer:
Step-by-step explanation:
please answer 9 or 11 or both pleasseeee
Answers
Answer:
hi the picture doesn't appear
Perform he operations in the correct order :
10 + 8 ÷ 1 -5
Answers
step 1: divide first (8 divided by 1 = 8)
step 2: add since it’s first (10 + 8 = 18)
step 3: subtract (18 - 5 = 13)
(x+4)(x-5)+(x+4)(x-2)
Answers
Answer:
(x+4)⋅(2x−7)
Step-by-step explanation:
Combine the like terms.
What is equivalent to 64^(1/2)
Exponential Functions Algebra 1
Answers
[tex]64^{\frac{1}{2}}=\sqrt{64}=\sqrt{8^2}=8[/tex].
Hope this helps.
Answer:8
Step-by-step explanation: first you have to see what the base number is in this case the base number is 64 so you see that it 64 and then you you divide 1 by 2 then you divide or you can just put it into the calculator
Olivia buys 4 masks that each cost the same amount and a scarecrow. She spent a total of $176.75. If the scarecrow costs $56.75, write an equation she can use to find the cost of each mask. * 10 points 4m + 56.75 = 176.75 5m + 56.75 = 176.75 4m - 56.75 = 176.75 5m - 56.75 = 176.75
Answers
4m+56.75=176.75
Solve the equation to find the cost of each mask.
Prime number between 60 and 80 with the 10’s digit being one less than the 1st digit
Answers
It would be 89.
You can also just look up a list of prime numbers online.
What is the value of X+1/9=1/3
Answers
Answer:
x = 2/9
Step-by-step explanation:
x + 1/9 = 1/3
Subtract 1/9 from each side
x + 1/9 -1/9 = 1/3 - 1/9
Get a common denominator
x = 1/3 *3/3 - 1/9
x = 3/9 -1/9
x = 2/9
x=3/9-1/9
x=2/9=0.222
what is the slope.of the line passing points (1, -5) and (4, 1)
Answers
Answer:
[tex]\huge{\boxed{\sf{ 2 }}}[/tex]
Step-by-step explanation:
Let the points be A and B
A ( 1 , -5 ) [tex]\longrightarrow[/tex] ( x1 , y1 )
B ( 4 , 1 ) [tex]\longrightarrow[/tex] ( x2 , y2 )
Finding the slope :
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{1 - ( -5 )}{4 - 1}[/tex]
Slope = [tex]\frac{1+5}{4-1}[/tex]
Slope = [tex]\frac{6}{3}[/tex]
Slope = [tex]2[/tex]
Hope I helped!
Best regards!
~TheAnimeGirl
Aaliyah invested $350 in an account paying an interest rate of 4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 20 years?
Answers
Answer:779
Step-by-step explanation:
Delta
Which of these expressions is the simplified form of the expression (StartFraction sine (x) Over 1 minus cosine squared (x) EndFraction) tangent (StartFraction x Over 2 EndFraction) ?
Answers
Given:
[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex].
To find:
The expression, which is equivalent to the given expression.
Solution:
We have,
[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex]
[tex]=\dfrac{\sin (x)}{1^2-\cos ^2 (x)}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex] [tex][\because \tan \left(\dfrac{x}{2}\right)=\dfrac{1-\cos (x)}{\sin (x)}][/tex]
[tex]=\dfrac{\sin (x)}{(1-\cos (x))(1+\cos (x))}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
Cancel out the common factors.
[tex]=\dfrac{1}{1+\cos (x)}[/tex]
Therefore, the correct option is C.
Given question is incomplete; find the complete question in the attachment.
Simplified form of the given trigonometric expression will be represented by Option C.
Given expression is,
[tex][\frac{\text{sin(x)}}{1-\text{cos}^2(x)}]\tan(\frac{x}{2} )[/tex][tex][\frac{\text{sin(x)}}{1-\text{cos}^2(x)}]\tan(\frac{x}{2} )=\frac{\text{sin(x)}}{1-\text{cos}^2(x)}\times \frac{1-\text{cos}x}{\text{sinx}}[/tex] [Since. [tex]\text{tan}\frac{x}{2} =\frac{1-\text{cosx}}{sinx}[/tex]]
[tex]=\frac{1-\text{cos}x}{(1-\text{cosx})(1+\text{cosx})}[/tex]
[tex]=\frac{1}{1+\text{cosx}}[/tex]
Therefore, Option C will be the correct option.
Learn more,
https://brainly.com/question/11607107
Write the equation of the line with the given point and slope.
(-5, -3); slope = -3/5
Answers
A line in point slope form is y = mx + b
m = the slope
b = y-intercept
So far our line looks like: y = -3/5x + b
Let's plug -5 into x and -3 into y to solve for b
-3 = -3/5(-5) + b
Let's multiply -5 by -3/5
-3 = 3 + b
Subtract 3 from both sides.
-6 = b
Our line is: y = -3/5x - 6
NEED HELP!!!!!!!! ASAP
Which expression shows the total area of the courtyard?
A) s^4 + 4
B) s^2 + 4
C) s^2
D) 4s^2
Answers
Answer:
D. 4s²
Step-by-step explanation:
There are 4 equal spaces that the square court yard room is divided to.
Area of a square = s², where s is the side Length.
Therefore,:
Area of 1 space = s²
Total area of the square courtyard room = area of the 4 spaces = 4(s²) = 4s²
D. 4s² is the expression for the total area of the courtyard.
Answer:
4s² is the expression for the total area of the courtyard.
Step-by-step explanation:
Evaluate 14/7+3*2-5
Answers
Answer:
3
Step-by-step explanation:
14/7
+(3)(2)−5
=2+(3)(2)−5
=2+6−5
=8−5
=3
Baron, Gab, and Oliver can paint a room together in 2 hours, 1f Gab does the job alone. he can paint the same room in 5 hours. If Baron works alone, he can paint the room in hours. If Oliver works alone, how long would it take him to paint the room?
Answers
Answer:
11 hours
Step-by-step explanation:
I hope this help!
determine the number of significant digits in the measurement 3.08cm
Answers
9514 1404 393
Answer:
3 significant digits
Step-by-step explanation:
If there is a decimal point with non-zero digits to its left, all digits to the right of the left-most non-zero digit are significant. Here, that is all of them. This number has 3 significant digits.
__
Comment on other cases
If there is no decimal point, the digits between any leading and trailing zeros are significant. For example, 02000 has 1 significant digit.
If there are no non-zero digits left of the decimal point. All digits except leading zeros are significant. 0.0031000 has 5 significant digits.
Which equation represents the unit fraction shown in the diagram? A grid model with 100 squares. 20 squares are shaded.
Answers
Answer:
20 over 100 = 1 over 5
Step-by-step explanation:
For a Saturday matinee, adult tickets cost $8.50 and kids under 12 pay only $7.00. If 80 tickets are sold for a total
of $605, how many of the tickets were adult tickets and how many were sold to kids under 12?
Answers
Answer:
30 adult tickets,50 kids ticketsStep-by-step explanation:
Given
Cost of adult ticket = $8.50Cost of kids ticket = $7.00Number of tickets = 80Total cost = $605Let the adult ticket be a and kids be k
We got equations
a + k = 808.5a + 7k = 605From the first equation we get
k = 80 -aSubstituting k in the second equation
8.5a + 7(80 - a) = 6058.5a - 7a + 560= 6051.5a = 45a = 45/1.5a = 30Then finding k
k = 80 - 30 = 50Need Help running out of time: Best answer will get brainliest
In Sam's drawer, there are 17 red socks, 13 green socks, and 20 black socks. Any two socks of the same color make a pair.
* If the first sock that Sam took out was black, how many more socks must he take out from the drawer without looking to be absolutely sure to have a pair of socks (of any color)?
Answers
Answer:
19:50
Step-by-step explanation:
well when you add all the socks you have 50 socks. if the first sock that Sam took out was black the second sock would be a ratio of 19:50.
(i think)
What does “is” mean in math
Answers
Answer:
Multiplication
I hope this helps!
