The volume of a cube with sides of length s is given by v = s3. find the rate of change of the volume with respect to s when s = 3 centimeters.
Answers
Final answer:
The rate of change of the volume of a cube with respect to its side length s, when s = 3 cm, is 27 cubic centimeters per centimeter.
Explanation:
The volume V of a cube with sides of length s is given by V = s³. To find the rate of change of the volume with respect to s when s = 3 cm, we need to differentiate the volume function V(s) with respect to s. The derivative of V with respect to s is [tex]\frac{dV}{ds}[/tex] = 3s². When s = 3 cm, [tex]\frac{dV}{ds}[/tex] = 3(3)² = 3(9) = 27. The rate of change of the volume when s = 3 cm is 27 cubic centimeters per centimeter.
Related Questions
The area of a rectangle is 45 square inches. The rectangle is 9 inches long. How wide is the rectangle?
A. 5 inches
B. 36 inches
C. 27 inches
D. 3 inches
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area equals length times width
Given a right cone with base area b and height h, what is the formula for the volume?
Answers
Hope this helps
V = πr^2(h/3)
V: Volume
r: radius
h: height
πr^2 = base area of a cone
Answer
The formula for the volume in terms of base area b and height h is: V = b(h/3)
Linear Programming HELP!! must answer both questions for brainliest and explain your answer.
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A salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?
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i am not sure what to substitite for a or w
Sorry but hopes this gives a hint
Please help thank you very much.
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For the first picture, the correct answer is option B
They say that AB = BC = CD and they want us to find JM.
Well, since the right side are equal, the left side must equal to.
So, all we have to do is add them.
JK = KL = LM
7 + 7 + 7 = 21
------------------------------
The answer is 720
Sum = (6-2) * 180
Sum= 4 * 180
Sum = 720
For the last one, the correct answer is 99
This is too complicated to explain :)
I hope this helps!
Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality 7.2b + 6.5 > 4.8b – 8.1. Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1. Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1. Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6. Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b. Which student’s first step was incorrect, and why? Amelia’s, because the variable term must be isolated on the left side Luis’s, because he flipped the inequality sign when he subtracted Shauna’s, because she did not apply the subtraction property of equality properly Clarence’s, because the terms he added together were not like terms
Answers
Answer: Luis’s, because he flipped the inequality sign when he subtracted
Step-by-step explanation:
what is 10 1/2 divided by 2 1/4
Answers
The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The mathematical expression is;
'' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] ''
Now, Solve the mathematical expression by using division method as;
The mathematical expression is,
[tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] = [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
Change the mixed fraction into improper fraction as;
⇒ [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
⇒ [tex]\frac{21}{2}[/tex] ÷ [tex]\frac{9}{4}[/tex]
It can be solve as;
⇒ 21/2 ÷ 9/4
⇒ 21/2 × 4/9
⇒ 14/3
Change into mixed fraction as;
⇒ [tex]\frac{14}{3} = 4 \frac{2}{3}[/tex]
So, [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex] = [tex]4 \frac{2}{3}[/tex].
Therefore,
The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].
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4.25 × 0.6 = 2.04 × 1.25
True
False
Answers
Answer:
false
Step-by-step explanation:
its not
Answer:
false
Step-by-step explanation:
4.25 x 0.6 doesn't equal 2.04 it equals 2.55
If Log 4 (x) = 12, then log 2 (x / 4) is equal to
A. 11
B. 48
C. -12
D. 22
Answers
The answer to your problem is D. 22. Hope this helps and have a wonderful day!
The easiest way:
a) log₄ (x) = 12, re write it in exponential way : x = 4¹² = 16,777,216
b) Plug the value of x in log₂ (x / 4)
log₂ (16,777,216 / 4) → log₂(4,194,304)
and log₂(4,194,304) = 22
The tooth fairy brings jack $5 plus $1 for each tooth that he loses. After jack loses a few teeth, the tooth fairy decides that he is paying too much money for teeth. He is gives jack $5 plus $0.50 for each tooth lost. Which graph shows the new function?
Answers
Answer:
The new function is [tex]y=0.5x+5[/tex] and its graph is shown below.
Step-by-step explanation:
Let the number of tooth = x and the cost of teeth = y (in dollars).
Tooth fairy charges $1 for each tooth with extra charge of $5.
So, the cost of the teeth is [tex]y=x+5[/tex].
Now, the tooth fairy charges $0.5 for each tooth with extra charge of $5.
Thus, the new cost of the teeth is given by.
[tex]y=0.5x+5[/tex]
So, the new function is [tex]y=0.5x+5[/tex] and its graph is shown below.
5.50
i think thats the anserw
Which angle is the included angle for MP¯¯¯¯¯¯ and MN¯¯¯¯¯¯¯ ?
∠M
∠N
∠P
Answers
Answer:
First one.
Step-by-step explanation:
M is in both angles.
we know that
An included angle is the angle between two sides of a triangle
so
in the triangle MNP
1) the included angle for MP and MN is the angle M
2) the included angle for PM and PN is the angle P
3) the included angle for NM and NP is the angle N
therefore
the answer is
the included angle for MP and MN is the angle M
Mr.Williams' physical education class lasts 7/8 hour.How many minutes are not spent on instructions . playing game:1/2 , instructions: 1/5 ,warm up and cool down:3/10
Answers
1/5 spent on instruction - 20%
Just find 80 percent of 52.5 and you will get 42 minutes not spent on instruction
You are taking part in a charity walk, and you have walked 12.5 miles so far. Your girl is to walk 20 miles. How many more miles do you need to walk to meet your goal?
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After walking 12.5 miles with a goal of 20 miles, you need to walk 7.5 more miles to meet your goal.
To meet your goal in the charity walk, you need to calculate how many more miles are left to walk after having walked 12.5 miles with a goal of 20 miles. The calculation is simple subtraction: 20 miles (goal) - 12.5 miles (distance already walked) = 7.5 miles remaining to be walked. So, you need to walk 7.5 more miles to meet your goal.
For the standard normal probability distribution, the area to the right of the mean is:
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Use geometry to evaluate (see attached) (calculus) the integral from 0 to 6 of the function f of x, dx for f of x equals 3 for x less than or equal to 3 and equals the quantity 6 minus x for x greater than 3.
27
13.5
12
10.5
Answers
notice the area is just a 3x3 square and a triangle with a base of 3 and a height of 3, simply get the area of both, add them up, and that's the area of the piece-wise on that range.
Answer:
13.5
Step-by-step explanation:
The geometric representation of an integral is the area below the curve. So, let's graphic the function.
[tex]f(x) = 3[/tex] is an horizontal line, (y = 3)
and [tex]f(x) = 6-x[/tex] is also a line, but it is decreasing.
We can see in the image that the area below the curve happens to be a polygon. In order to calculate the area we are going to separate it into simpler polygons: a square and a triangle.
The area of the square is [tex]3*3 = 9[/tex].
The area of the triangle is [tex]\frac{3*3}{2} = \frac{9}{2} = 4.5[/tex]
If we add them, we get
[tex]\int_0^6 f(x) dx =9 + 4.5 = 13.5[/tex]
Select a counter-example that makes the conclusion false.
7 - 3 = 4, 8 - 5 = 3, 9 - 8 = 1
Conclusion: the difference of two positive numbers is always positive.
Counterexample:
Answers
HOPE I HELP!!!!!!!!!!!!
Answer:
2 - 7 = -5Step-by-step explanation:
This means that two positive numbers have given a difference of -5, so the conclusion above can not be true. In fact, subtracting a larger number from a smaller number will always give a negative result, so this conclusion isn't even true in most cases.
I'm always happy to help :)Two angles are supplementary. one angle is 4 degrees° less than three times the other. find the measures of the angles.
Answers
and we have the sum a+b=180.
in addition 3b-4=a
So we have 3b-4+b=180
or 4b=184 and at the end we have b=46, a= 134
Nick can throw a baseball three more than 4 times the number of feet, f, that Jeff can throw the baseball. Which numbered expression can be used to find the number of feet that Nick can throw the ball?
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N=J*4+3
more than is +
4 times is multiplying by 4 (*4)
to my understanding this is the numerical equation
So let's write this out
Nick can throw a baseball 3>4 times than F. So to write an equation to find how many feet Nick can throw the ball we do 4F+3. Now this makes sense because he throws it +3 (three more) than 4F.
Hope this helps!
what is the curconfrrince
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Plz mark me brainliest!
Hope this helps!
The distance around a circle is called the circumference,while, the distance through the circle through the center is called the diameter. π is the ratio of the circumference to the diameter. Meaning, for any circle, if you divide the circumference by the diameter, you will always get π. This is expressed in the formula: C/d=π
Which shows the image of ΔRST after the rotation (x, y) → (y, –x)?
Answers
examples?
Step-by-step explanation:
Write 1.42 as a fraction or mixed number in simplest form.
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what is the area of rhombus ABCD? do not round any steps
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The length of AC = 4 (the base of ΔABC.
The height of ΔABC = 7 - 1 = 6
The area of ΔABC is
(1/2)*4*6 = 12
Therefore the area of ABCD = 2*12 = 24
Answer: 24
how many solutions does
25-x=15-(3x+10)
Answers
25-x=15-3x-10
25-x=15-10-3x
25-x=5-3x
25-5-x=5-5-3x
20-x=-3x
20-x+x=-3x+x
20=-2x
20/-2=-2/-2x
-10=x
Only one solution for this equation.
What is x and y. This is a geometry question
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Solve 5x - 20 = 3x for x as step 1.
Take it from here.
Find the percent change from 60 to 63. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent.
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[tex] \frac{3}{60}[/tex] = 0.05 ≈ 5%
5% increase
Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip? ANSWER ASAP
Answers
If Bryson purchased 40 raffle tickets. There were 500 raffle tickets sold. Then 2/25 is the theoretical probability of Bryson winning the trip
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Bryson hopes to win a three-day vacation in a drawing that is being held at his office.
Bryson purchased 40 raffle tickets
The number of raffle tickets sold were 500
We need to find the theoretical probability of Bryson winning the trip
P(win)=40/500
=4/50
=2/25
2/25 because he bought 40 out of the 500 tickets
Hence 2/25 is the theoretical probability of Bryson winning the trip
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The reference angle for an angle whose measure is 260° is
Answers
So your answer is 80 degrees.
Hope this helps,
Brian
Answer:
80 degrees
Step-by-step explanation:
It is known that the depth of a lake at a point with coordinates (x, y) is z = 200 + 0.02x2 − 0.001y3, where x, y, and z are measured in meters. a woman in a kayak starts at the point (80, 60) and moves toward another point located at (0, 0). (a) find du f(80, 60). (give your answer correct to at least two decimal places.)
Answers
[tex]z = 200 + 0.02x^2-0.001y^3[/tex]
[tex]0.04x-0.003y^2 \frac{dy}{dx} =0 \\ \\ \frac{dy}{dx} = \frac{0.04x}{0.003y^2} \\ \\ \left.\frac{dy}{dx} \right |_{(80, 60)}= \frac{0.04(80)}{0.003(60)^2} = \frac{3.2}{10.8} =0.2963[/tex]
Craig is training for a race. He bikes every 2 days and swims every 3 days. If he biked and swam today, how many days will pass before he bikes and swims on the same day again, the least common multiple of the numbers of days? Multiples of 2: 2, 4, 6, 8, 10, 12, . . . Multiples of 3: 3, 6, 9, 12, 15, 18, . . .
Answers:
1. 2 days
2. 3 days
3. 6 days
4. 12 days
Answers
Have a wonderful day.
What property justifies this statement? If segment A B is congruent to segment D E and segment D E is congruent to segment F G, then segment A B is congruent to segment F G.