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2 years ago

8

What type of number is 3/2

2 answers:

garri49 [273]2 years ago

6 0

Answer:

it is a mixed number the number is 1 1/2

Step-by-step explanation:

VARVARA [1.3K]2 years ago

5 0

:1 1/2 that’s answer

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Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t

Anika [276]

Answer:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

Step-by-step explanation:

Given

$\int\limits {\frac{x}{x^4 + 16}} \, dx$

Required

Solve

Let

$u = \frac{x^2}{4}$

Differentiate

$du = 2 * \frac{x^{2-1}}{4}\ dx$

$du = 2 * \frac{x}{4}\ dx$

$du = \frac{x}{2}\ dx$

Make dx the subject

$dx = \frac{2}{x}\ du$

The given integral becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

Recall that: $u = \frac{x^2}{4}$

Make $x^2$ the subject

$x^2= 4u$

Square both sides

$x^4= (4u)^2$

$x^4= 16u^2$

Substitute $16u^2$ for $x^4$ in $\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du$

Simplify

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

In standard integration

$\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)$

So, the expression becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)$

Recall that: $u = \frac{x^2}{4}$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

4 0

2 years ago

Obed's bike is twice as heavy as Elsa bike but only 3 pounds heavier than George bike if George bike weighs 15 pounds how much d

ratelena [41]

If George's bike weighs 15 pounds, then we can say that because Obed's bike is 3 pounds heavier than George's, Obed's bike weighs 18 pounds. If Obed's bike weighs 18 pounds, then we can say that because Elsa's bike is twice as heavy as Obed's, Elsa's bike weighs 9 pounds.

5 0

2 years ago

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What are the coordinates of the midpoint of GH with endpoints (-2,5) and<br> H(4,1)?

kozerog [31]

Answer:

(1, 3)

Step-by-step explanation:

Given coordinates of 2 endpoints, G(-2, 5) and H(4, 1), midpoint of AB is calculated as shown below:

Midpoint (M) of GH, for G(-2, 5) and H(4, 1) is given as:

$M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

Let $G(-2, 5) = (x_1, y_1)$

$H(4, 1) = (x_2, y_2)$

Thus:

$M(\frac{-2 + 4}{2}, \frac{5 + 1}{2})$

$M(\frac{2}{2}, \frac{6}{2})$

$M(1, 3)$

Coordinates of the midpoint of GH = (1, 3).

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2 years ago

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atroni [7]

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2 years ago

Write the prime factorization of 10. Use exponents when appropriate and order the factors from least to greatest (for example, 2

Goryan [66]

Answer:

1,2,5,10

Step-by-step explanation:

8 0

2 years ago

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