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Elena-2011 [213]
3 years ago
7

The volume of a cube is given by s9 and the total surface area of a cube is given by 632, where s is the side length of the cube

.
If the side length of a cube is 5 inches, the volume of the cube is [ ]
cubic inches and its total surface area is[ ]
square inches

BROO HELP ME FAST
Mathematics
1 answer:
Mariana [72]3 years ago
3 0

Answer:

Surface area of a cube = side * side * 6

632 = side * side * 6

side^2 = 632/6

side^2 = 105.3333333333

side = 10.2632028789

********************************************

For a 5 inch side

volume = 5 * 5 * 5

= 125 cubic inches

surface area = 5 * 5 * 6

surface area = 150 square inches

Step-by-step explanation:

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rosijanka [135]
\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx

Notice that x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1). Decompose the integrand into partial fractions:

\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}
=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}

Integrating term-by-term, you get

\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx
=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C
5 0
4 years ago
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Only 1 try
vagabundo [1.1K]

Using the shell method, the volume is

\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx

Each cylindrical shell has radius 2-x (the horizontal distance from the axis of revolution to the curve y=8x^3); has height 8x^3 (the vertical distance between a point on the x-axis in 0\le x\le1 and the curve y=8x^3).

Compute the integral.

\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}

6 0
2 years ago
An angle measures 70° more than the measure of its supplementary angle. What is the measure of each angle
jekas [21]

Answer:

55° and 125°

Step-by-step explanation:

Formulate an equation x + (x+70) = 180

Combine like terms to get 2x + 70 = 180

Subtract 70 on both sides to get 2x = 110.

Divide both sides by 2 to get x = 55.

Add 70 to 55 to get 125.

Check your answer by adding 55 + 125. It equals 180, so the angles are equal to 55 and 125.

5 0
3 years ago
2. what is the value of x? Show your work
Mademuasel [1]

Write a full questions to understand. You have wrote half questions only

7 0
2 years ago
a sports store sells three different packs of tennis balls. which pack is the best to buy? 4 sleeves for 11.49, 6 sleeves for 16
PIT_PIT [208]

Answer:

9 sleeves for 22.99

Step-by-step explanation

The first pack has a unit rate of $11.49/ 4 balls

=$2.8725

The second pack has a unit rate of $16.79/6balls

=$2.798 per ball

the third pack has a unit rate of $22.99/9balls

=2.554

So, I would definitely go for the third pack since it has the least cost.

6 0
3 years ago
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