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
How is 41/1,000 written as a decimal? Enter your answer in the box.
Answers
Answer:
0.041
I know this because 1,000 has 3 zeros, so you would move 41 three places to the right.
The decimal equivalent of the fraction 41/1000 is 0.041.
What is a decimal?A decimal is represented by a dot that separates the whole part and the fractional part of a number. Decimals can also be converted into fractions and vice versa.
Given, a fraction 41/1000, here the numerator is less than the denominator so it is a proper fraction.
Now, As in the denominator we have three zeroes we'll put a decimal three places before the numerator value which is,
= 0.041/1.
= 0.041.
So, 41/1000 is equal to 0.041.
learn more about decimal numbers here :
https://brainly.com/question/4708407
#SPJ2
how to solve this equation x²=16
Answers
Step-by-step explanation:
Hey there!
To solve this type of question, you must take square of variable"X" to right side making it ±squareroot. As it is a quadratic equation it will have two values (±).
Given;
[tex] {x}^{2} = 16[/tex]
Taking (square) to right side. It becomes ± square root.
[tex]x = + - \sqrt{16} [/tex]
[tex]x = + - \sqrt{ {4}^{2} } [/tex]
Cancel square and square root.
[tex]x = + - 4[/tex]
Therefore, X = ±4
Hope it helps...
Answer:
There are two I results found which is x=4 and x=-4
Step-by-step explanation:
Step by Step Solution:
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-(16)=0
Step by step solution :
STEP
1 :
Trying to factor as a Difference of Squares:
1.1 Factoring: x2-16
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (x + 4) • (x - 4)
Equation at the end of step
1 :
(x + 4) • (x - 4) = 0
STEP
2 :
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation:
2.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4 and/or x=-4
3x+x√3-2=0. Find value of x
Answers
[tex] \sf \: 3x + x \sqrt{3} - 2 = 0 \\ \\ \sf \longrightarrow 3x + \sqrt{3} x = 2 \\ \\ \sf \longrightarrow \sqrt{3}x ( \sqrt{3} +1 ) = 2 \\ \\ \sf \longrightarrow \sqrt{3} x = \frac{2}{ \sqrt{3} + 1 } \\ \\ \sf \longrightarrow x = \frac{2}{ \sqrt{3}( \sqrt{3} + 1) } \\ \\ \sf \longrightarrow x = \frac{2}{3 + \sqrt{3} } \\ \\ \tt{You\:can\:stop\:here\:if\:you\:\bold{don't}\:want\:to }\\ \tt{ \:simplify\:in\:decimal\:form.}\\ \\ \sf \longrightarrow x = \frac{2(3 - \sqrt{3} )}{(3 + \sqrt{3})(3 - \sqrt{3} )} \\ \\ \sf \longrightarrow x = \frac{6 - 2 \sqrt{3} }{ {3}^{2} - {( \sqrt{3}) }^{2} } \\ \\ \sf \longrightarrow x = \frac{6 - 2(1.732)}{9 - 3} \\ \\ \sf \longrightarrow x = \frac{2.536}{6} \\ \\ \leadsto \underline{\boxed{\sf{\pink{x \approx 0.4226}}}}[/tex]
Please help with this coin problem, include an explanation pleaasee! Thank you
Answers
Answer:
uf
iydit s6jdkyditsk6o
8 dimes and 15 nickels
50 POINTS SOLVE !! ::
pls actually solve it thank you <3
k-4 /9 =3
8+b /-4 = -5
Answers
Answer:
k = 31/9b = 12Step-by-step explanation:
k - 4 = 3
9
k/9 = 3(9) + 4
k = 31/9
k = 31/9
8 + b = -5
-4
8 + b = -5 (-4)
8 + b = 20
b = 20 - 8
b = 12
Solve.
X-9 = 12
.....
Answers
Answer:
x=21
Step-by-step explanation:
x=9+12 x=21
Answer:
Step-by-step explanation:
X-9=12
Reverse the operation into
9+12=x
9+12=21
Now check
21-9=12
If the length is 9 inches the width is 8 in and the height is 27 in what is the surface area of the rectangle box
Answers
Answer:
1944
Step-by-step explanation:
you times height by width by depth 9×8×27=1944
Solve for the value of V. (9v-3)° (8v+8)°
Answers
Answer: the answer is -5 subtract 9 and 4 you get 5 then add 8v to -9v you get -1v then you divide it from 5 and v= -5
Step-by-step explanation:
100 random samples were taken from a large population. A particular numerical characteristic of sampled items was measured. The results of the measurements were as follows: 45 measurements were between 0.859 and 0.900 0.901 was observed once 0.902 was observed three times 0.903 was observed twice 0.904 was observed four times The smallest value was 0.859, and the largest value was 0.958. The sum of all 100 measurements was 91.170. Except those noted, no measurements occurred more than twice. What is the median of the measurements
Answers
Answer:
The median is [tex]Median = 0.903[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The [tex]1^{st} \to 45^{th}[/tex] measurements is [tex]= 0.859 \to 0.900[/tex]
Generally since that after 0.900 we have 0.901 , then the
[tex]46^{th} \ measurement \ is \ 0.901[/tex]
in the same manner the [tex]47^{th} \ measurement \ is \ 0.902[/tex],
Given that 0.902 was observed three times it means that
[tex]47^{th},48^{th},49^{th} \ measurement \ is \ 0.902[/tex],
Given that 0.903 was observed two times it means that
[tex]50^{th},51^{th} \ measurement \ is \ 0.903[/tex],
Given that 0.903 was observed four times it means that
[tex]52^{nd},53^{rd},54^{th},55^{th} \ measurement \ is \ 0.904[/tex],
Given that the highest measurement is 0.958 then then the [tex]56^{th} \to 100^{th} \ measurement \ is \ between \ 0.905 \to 0.958[/tex]
Generally the median is is mathematically represented as
[tex]Median = \frac{ [\frac{n^{th}}{2}] + [(\frac{n}{2})^{th} + 1 ]}{2}[/tex]
=> [tex]Median = \frac{ [\frac{100^{th}}{2}] + [(\frac{100}{2})^{th} + 1 ]}{2}[/tex]
=> [tex]Median = \frac{ [50^{th}] + [51^{th} ]}{2}[/tex]
=> [tex]Median = \frac{ 0.903 + 0.903}{2}[/tex]
=> [tex]Median = 0.903[/tex]
Elijah's father is 47. He is 17 years older than twice Elijah's age. How old is Elijah?
Answers
Answer:
let Elijah age be a
Then
2*a + 17 =47
2a=47-17
2a=30
a=15
Step-by-step explanation:
That’s correct !!!! BELIEVEEEE!!!!dhxhx
What's the Constant of Proportianlity/Unit Rate?
Answers
Answer:
1/3 cup of juice per cup of berries
Step-by-step explanation:
The table shows that if we go from 0 to 4 cups (a "run" of 4 cups), the juice output is 1 1/3 (or 4/3) (a "rise" of 4/3 cups), and so the desired constant of proportionality is the unit rate
(4/3) cups
------------------------ = 1/3 cup of juice per cup of berries
4 cups berries
The graph a linear function if passes through the point (3, -8) and has a slope of -2
Answers
Answer:
It's not 0 I got it wrong.
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
i just took the test
A team has won 51 out of 68 games explain how to use the bar diagram to find the percent of games the team has won
Answers
you would divide -> 51/68 and you would get .75. move the 2 first numbers after the dot to the front and you get 75%
Answer:
I the diagram, 17 represents 25% of the total games. Since 17 times 3 equals 51, you use the first 3 columns to find the answer of 75%.
Just took test that was the answer they gave.
Step-by-step explanation:
At one point the average price of regular unleaded gasoline was $3.39 per gallon. Assume that the standard deviation price per gallon is $ per gallon and use Chebyshev's inequality to answer the following. (a) What percentage of gasoline stations had prices within standard deviations of the mean? (b) What percentage of gasoline stations had prices within standard deviations of the mean? What are the gasoline prices that are within standard deviations of the mean? (c) What is the minimum percentage of gasoline stations that had prices between $ and $?
Answers
This question was not written completely
Complete Question
At one point the average price of regular unleaded gasoline was $3.39 per gallon. Assume that the standard deviation price per gallon is $0.07 per gallon and use Chebyshev's inequality to answer the following.
(a) What percentage of gasoline stations had prices within 3 standard deviations of the mean?
(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the mean? What are the gasoline prices that are within 2.5 standard deviations of the mean?
(c) What is the minimum percentage of gasoline stations that had prices between $3.11 and $3.67?
Answer:
a) 88.89% lies with 3 standard deviations of the mean
b) i) 84% lies within 2.5 standard deviations of the mean
ii) the gasoline prices that are within 2.5 standard deviations of the mean is $3.215 and $3.565
c) 93.75%
Step-by-step explanation:
Chebyshev's theorem is shown below.
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.
3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.
4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.
(a) What percentage of gasoline stations had prices within 3 standard deviations of the mean?
We solve using the first rule of the theorem
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
Hence, k = 3
1 - 1/k²
= 1 - 1/3²
= 1 - 1/9
= 9 - 1/ 9
= 8/9
Therefore, the percentage of gasoline stations had prices within 3 standard deviations of the mean is 88.89%
(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the mean?
We solve using the first rule of the theorem
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
Hence, k = 3
1 - 1/k²
= 1 - 1/2.5²
= 1 - 1/6.25
= 6.25 - 1/ 6.25
= 5.25/6.25
We convert to percentage
= 5.25/6.25 × 100%
= 0.84 × 100%
= 84 %
Therefore, the percentage of gasoline stations had prices within 2.5 standard deviations of the mean is 84%
What are the gasoline prices that are within 2.5 standard deviations of the mean?
We have from the question, the mean =$3.39
Standard deviation = 0.07
μ - 2.5σ
$3.39 - 2.5 × 0.07
= $3.215
μ + 2.5σ
$3.39 + 2.5 × 0.07
= $3.565
Therefore, the gasoline prices that are within 2.5 standard deviations of the mean is $3.215 and $3.565
(c) What is the minimum percentage of gasoline stations that had prices between $3.11 and $3.67?
the mean =$3.39
Standard deviation = 0.07
Applying the 2nd rule
2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.
the mean =$3.39
Standard deviation = 0.07
μ - 2σ and μ + 2σ.
$3.39 - 2 × 0.07 = $3.25
$3.39 + 2× 0.07 = $3.53
Applying the third rule
3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.
$3.39 - 3 × 0.07 = $3.18
$3.39 + 3 × 0.07 = $3.6
Applying the 4th rule
4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.
$3.39 - 4 × 0.07 = $3.11
$3.39 + 4 × 0.07 = $3.67
Therefore, from the above calculation we can see that the minimum percentage of gasoline stations that had prices between $3.11 and $3.67 corresponds to at least 93.75% of a data set because it lies within 4 standard deviations of the mean.
What is the expected value of the spinner? And is the game fair? Correct answer gets brainiest!
Answers
Answer:
This game is not fair
Step-by-step explanation:
This game is not fair because there is a 25 percent chance of 8 and about 37 percent chance for 24 and 6
Given: m
1. Find x if the angles are vertical.
2. Find x if the angles are linear pair.
(Imagine included)
Answers
Answer:
Something!
Step-by-step explanation:
Do something then do something and thats it!
How do you do this question?
Answers
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Rewrite, using the distributive
property.
-3(5x – 10) = [?]x +[ ]
Answers
Answer:
-15x + 30
Step-by-step explanation:
Using the distributive property, distribute -3 to the parentheses:
-3(5x) = -15x
-3(-10) = 30
Add these terms together:
-15x + 30 is the rewritten expression
Answer:
-15x + 30
Step-by-step explanation:
-3*5 = -15 and -3 * -10 equals 30 also negative times a negative is always a positive number
High Hopes ^^
Barrys
Explain how rates and ratios are related. Be sure to include examples to support you response.
Answers
Answer:
Both rates and ratios are a comparison of two numbers. A rate is simply a specific type of ratio. The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit. For example, in a room full of students, there are 10 boys and 5 girls. This means the ratio of boys to girls is 10:5.
Y= 3x+4, what is y when x is 1 2, and 3?
Answers
Answer:
e7gevey2u2veveve wheheveveg
Step-by-step explanation:
I took the quiz please give me five stars for the memes.pls. I know u will so there is no reason to ask.
Answer:
if x = 12; y = 40
if x = 3; y= 13
Step-by-step explanation:
if x = 12 then,
y = 3(12) + 4
y = 36 + 4
y = 40
if x = 3 then,
y = 3(3) + 4
y = 9 + 4
y = 13
What is 1/10 of 1 3.027
Answers
Answer:
1.3027
Step-by-step explanation:
The area of a square porch is 81 square feet. Find the dimensions of the porch.
Answers
Answer:
9 feet
Step-by-step explanation:
Square root 81 as all the sides of the porch are the same length
I just need to know what's Nine sixty-eight thousand one hundred twenty-three
is in numbers bc
idk my brain is kind of jumbled rn
Answers
Identify the slope and intercept of the following linear equation.
y=3/7x-5
A. Slope: 3/7; intercept: 5
B. Slope: 3/7; intercept: -5
C. Slope: 5; intercept: 3/7
D. Slope: -5; intercept: 3/7
Answers
Answer:
3/7 is the slope and -5 is the y intercept
Step-by-step explanation:
y=3/7x-5
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
3/7 is the slope and -5 is the y intercept
Answer:
B
Step-by-step explanation:
The slope is always the coefficient of the x value in the linear equation. And the y intercept is the constant in the equation.
If the quotient of a number and 16 is added to 1/4 the result is 5/16
Answers
Answer:
if youre trying to find the number then the number is 1
Step-by-step explanation:
the equation would be x/16+1/4=5/16
well we want to make everything have the same denominator and 16 is the LCD ( least common denominator ) so you would multiply 1/4 by 4/4 to get 4/16.
this means x/16+4/16=5/16 and and 4+1=5 so 1 is the answer
Solve the following and explain your steps. Leave your answer in base-exponent form. (3^-2*4^-5*5^0)^-3*(4^-4/3^3)*3^3 please step by step!!!!
Answers
Answer:
[tex]\boxed{2^{\frac{802}{27}} \cdot 3^9}[/tex]
Step-by-step explanation:
I will try to give as many details as possible.
First of all, I just would like to say:
[tex]\text{Use } \LaTeX ![/tex]
Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! （＊＾Ｕ＾）人（≧Ｖ≦＊）/
[tex]$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$[/tex]
Note that
[tex]\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }[/tex]
The denominator can't be 0 because it would be undefined.
So, we can solve the expression inside both parentheses.
[tex]\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3[/tex]
Also,
[tex]\boxed{a^{0} = 1, a\neq 0 }[/tex]
[tex]\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]
Note
[tex]\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}[/tex]
[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]
[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]
[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]
[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]
Note
[tex]\boxed{\dfrac{1}{\dfrac{1}{a} } = a}[/tex]
[tex]9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]
[tex]\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)[/tex]
Once
[tex]9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6[/tex]
[tex]\boxed{(a \cdot b)^n=a^n \cdot b^n}[/tex]
And
[tex]$4^{\frac{4}{27}} = 2^{\frac{8}{27} $[/tex]
We have
[tex]\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)[/tex]
Also, once
[tex]\boxed{\dfrac{c^a}{c^b}=c^{a-b}}[/tex]
[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27[/tex]
As
[tex]30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}[/tex]
[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3[/tex]
[tex]2^{\frac{802}{27}} \cdot 3^9[/tex]
Corresponding value of Powers of 10
Answers
Answer: A power of 10 is as many number 10s as indicated by the exponent multiplied together. Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000.
Step-by-step explanation:
HELPPPPPPP MEEEEEEEEEEEE
Answers
Answer:
your answer is b 32/4=8
Step-by-step explanation:
if you take the groups of 4 and count them up it is 32 and then you divide them in to equal groups and it is 8 groups of 4
hope this helped
:)
helllllpp pleaseeeeeee
Answers
x = 1 loaf of bread
y = eggs
Dwayne buys a loaf of bread ( x ) and 6 eggs ( 6y ) for $4.45
x + 6y = 4.45
Sheila buys 1 loaf of bread ( x ) and and 1 dozen eggs ( 12y ) - dozen is 12 for $5.65
x + 12y = 5.65
B. x + 6y = 4.45
x + 12y = 5.65
9514 1404 393
Answer:
B. x +6y = 4.45; x +12y = 5.65
Step-by-step explanation:
The problem statement defines the variables for you. Using x and y for the cost of a loaf and the cost of an egg, respectively, each purchase can be represented by an equation of the form ...
(number of loaves)x + (number of eggs)y = (amount spent)
The first purchase is described as
number of loaves = 1number of eggs = 6amount spent = 4.45equation: x +6y = 4.45The second purchase is of a dozen eggs, which is 12 eggs. The description of this purchase can be ...
number of loaves = 1number of eggs = 12amount spent = 5.65equation: x +12y = 5.65The situation can be represented by the equations shown in the attachment.
what is the distance between 1/3 and 1/2
Answers
Answer
1/3
Step-by-step explanation:
Answer:
1/2 is bigger than 1/3 by a little bit