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3 years ago

Jacob Is Twice as old as Sue. The sum of their ages is 69 years. How old is Jacob?

Mathematics

1 answer:

NemiM [27]3 years ago

7 0

$x-Sue\\2x-Jacob\\\\x+2x=69\\\\3x=69\ \ /:3\\\\x=69:3\\\\x=23-Sue\\\\2x=2\cdot23=46-Jacob\\\\Answer:Jacob\ is\ 46.$

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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

3 years ago

11/98 x 2/99 = ???????

Nutka1998 [239]

All we have to do is multiply the numerator by the other numerator and the denominator by the other denominator.
11•2=22
98•99=9702
They are both even, so we can divide by two with both numbers.
11/4851
4851 can be divided by 11. So we can divide the top and bottom by 11.
1/441 is the product.

3 0

3 years ago

A team of 9 tennis players can order bags with their uniforms

jeka94

Answer:

Step-by-step explanation:

5 0

3 years ago

please help me with it and dont just put random letters cause i dont know why u do it its not like u can buy a house with these

BartSMP [9]

Answer:

v=432cm

sA=144cm

Step-by-step explanation:

1)))

v=w*d*h

v=3*9*16

v=432cm

2)))

sA=h*w

sA=16*9

sA=144cm

6 0

2 years ago

Read 2 more answers

Human blood has an approximate pH of 7.3. Which substance is more basic than human blood?

ratelena [41]

so, 7 is neutral anything past 7 is considered basic.

answer: <em>a water and ammonia solution with a pH of 11 (very basic).</em>

<em />any number under 7 is acidic and of course there are different degrees of acidic just like there are different degrees of basicity.

______________________________________________________________

- stomach's digestive juices, would be considered very acidic

-apple juice is also acidic but not as acidic like stomach juices.

- grape juice, is becoming less acidic.

________________________________________________________________

Hopefully this helped and good luck.

5 0

3 years ago