In the garden of the forking paths borges refers to various unfinished works of literature to convey the idea of____

What is the volume of a cube that has a side length of 5 centimeters?

Cerrena [4.2K]

Answer:

125 cm³

Step-by-step explanation:

The cube has a side length of 5 cm.

Volume of a cube is given by; side × side × side

Since all the sides are equal then the volume is:

5cm × 5cm × 5cm = 125 cm³

6 0

3 years ago

Avril types essays for students from her home. On average, she can type a page in about 10 2/3 minutes. she spends 54 1/2 minute

andreev551 [17]

Hi 0101sj,

Your Question:

Avril types essays for students from her home. On average, she can type a page in about 10 2/3 minutes. she spends 54 1/2 minutes typing on essay, how many pages if this essay?

Answer:

1 PAGE = 10 2/3 = 10.20

Essay = 54 1/2 = 54.50

54.50 / 10.20 = 5.34313...

She approximately wrote 5 pages.

4 0

3 years ago

Use integration by parts to find the integrals in Exercise.<br> ∫^3_0 3-x/3e^x dx.

Viefleur [7K]

Answer:

8.733046.

Step-by-step explanation:

We have been given a definite integral $\int _0^3\:3-\frac{x}{3e^x}dx$ . We are asked to find the value of the given integral using integration by parts.

Using sum rule of integrals, we will get:

$\int _0^3\:3dx-\int _0^3\frac{x}{3e^x}dx$

We will use Integration by parts formula to solve our given problem.

$\int\ vdv=uv-\int\ vdu$

Let $u=x$ and $v'=\frac{1}{e^x}$ .

Now, we need to find du and v using these values as shown below:

$\frac{du}{dx}=\frac{d}{dx}(x)$

$\frac{du}{dx}=1$

$du=1dx$

$du=dx$

$v'=\frac{1}{e^x}$

$v=-\frac{1}{e^x}$

Substituting our given values in integration by parts formula, we will get:

$\frac{1}{3}\int _0^3\frac{x}{e^x}dx=\frac{1}{3}(x*(-\frac{1}{e^x})-\int _0^3(-\frac{1}{e^x})dx)$

$\frac{1}{3}\int _0^3\frac{x}{e^x}dx=\frac{1}{3}(-\frac{x}{e^x}- (\frac{1}{e^x}))$

$\int _0^3\:3dx-\int _0^3\frac{x}{3e^x}dx=3x-\frac{1}{3}(-\frac{x}{e^x}- (\frac{1}{e^x}))$

Compute the boundaries:

$3(3)-\frac{1}{3}(-\frac{3}{e^3}- (\frac{1}{e^3}))=9+\frac{4}{3e^3}=9.06638$

$3(0)-\frac{1}{3}(-\frac{0}{e^0}- (\frac{1}{e^0}))=0-(-\frac{1}{3})=\frac{1}{3}$

$9.06638-\frac{1}{3}=8.733046$

Therefore, the value of the given integral would be 8.733046.

6 0

3 years ago

What kinds of functions can be integrated using partial fraction decomposition? Choose the correct answer below

zaharov [31]

Answer:

B. Rational functions

Step-by-step explanation:

The partial fraction decomposition is used for functions there are described by fractions, and for which the substitution method is not possible. These are rational functions, in which both the numerator and the denominator are polynomials.

So the correct answer is:

B. Rational functions

4 0

3 years ago

Georgie spent 15 hours doing her chores last week. This week

Oksana_A [137]

Answer:

Yes. Explanation: 120%=1.2. If Maxine is correct, then she spent 1.2 times the hours she did homework than last week. 15⋅1.2=18.0=18.

Yes Explanation: 120

3 0

3 years ago

In the garden of the forking paths borges refers to various unfinished works of literature to convey the idea of_____