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1 year ago

The edges of a cube increase at a rate of 3 cm/s. How fast is the volume changing when the length of each edge is 40 cm?

Mathematics

1 answer:

OLga [1]1 year ago

7 0

Answer:

14400 cm³/s

Step-by-step explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

<h3>Rate of change of volume</h3>

V = s³ . . . . volume in terms of edge length (s)

dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s

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Which of the following have both 2 and -5 as solutions.

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$x_1=2;\ x_2=-5\\\\(x-2)(x-(-5))=(x-2)(x+5)=x^2+5x-2x-10=x^2+3x-10\\\\Answer:a.$

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3 years ago

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. Suppose you plan to make a box that will hold exactly 40 one-inch cubes. Give the dimensions (ex: 1in x 1in x 40in) of 3 possi

stiks02 [169]

Answer:

The dimensions of the three possible boxes are;

Box 1: 2 inches length by 4 inches width by 5 inches height

Box 2: 2 inches length by 2 inches width by 10 inches height

Box 3: 8 inches length by 1 inch width by 5 inches height

Step-by-step explanation:

The dimensions of the required box = 40 in³

Therefore, a box that will hold all the cubes will have a dimension given as follows;

Length, l × Width, w × Height, h = 40 in.³

We therefore, look for possible dimensions of l, w, h, however to make is faster, we note that l × w = base area, BA, hence we look for the factors 40 thus;

BA × h ≡ l × w × h

8 × 5 = 40 ≡ 2 × 4 × 5 = 40

4 × 10 = 40 ≡ 2 × 2 × 10 = 40

8 × 5 = 40 ≡ 8 × 1 × 5 = 40

Hence we have our three possible boxes as follows;

Box 1: Length = 2 inches, width = 4 inches and height = 5 inches

Box 2: Length = 2 inches, width = 2 inches and height = 10 inches

Box 3: Length = 8 inches, width = 1 inches and height = 5 inches.

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2 years ago

What is the rational expression in simplest form? State any restrictions on the variables.

allochka39001 [22]

According to the question, the given rational expression can be simplified which is as shown below:

Rational expression = $\frac{12-4x}{x^{2} -9}=\frac{4(3-x)}{(x-3)(x+3)}$

For the simplification of the given expression, calculate the factors of the numerator as well as denominator terms and divide them from each other. In this change the sign of the expression before dividing with each other.

Rational expression = $\frac{-4}{(x+3)}$

The rational expression are also known as polynomial expression. The highest degree of these expression is two. And these expression uses concept of factor rule.

Therefore, the final expression is $\frac{-4}{(x+3)}$

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

To learn more about the polynomial expression from the given link:

<u>brainly.com/question/1280754</u>

#SPJ4

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1 year ago

Which expression can be used to find 32% of 130?

ser-zykov [4K]

Answer:

130 times .32

Step-by-step explanation:

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2 years ago

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Same question bc i cant find the one i posted earlier

lora16 [44]

Answer:

224 pi

703.36 either might be in your answer list.

Step-by-step explanation:

Givens

r = 8 inches

rotations = 14

Formula

D = 14*C where C = 2 pi r

Solution

D = 14 * (2 pi * 8)

D = 224 * pi One possible answer

D = 224 * 3.14 = 703.36 inches Another possible Answer

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3 years ago