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2 years ago

The sum of a number and nine is 17. find the number

Mathematics

2 answers:

Arisa [49]2 years ago

8 0

Answer:

The number is 8

Step-by-step explanation:

Let n = number

n+9 = 17

Subtract 9 from each side

n+9-9 = 17-9

n = 8

slavikrds [6]2 years ago

7 0

17-9 = 8
8 is your answer.

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Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

6 0

2 years ago

64000 / blank equals 800

Irina18 [472]

Answer:

= 80

Step-by-step explanation:

64000/80 = 80

3 0

3 years ago

Read 2 more answers

Adult tickets for the school musical are sold for $3.50 and student tickets are sold for $2.50 on a given night 425 tickets were

miskamm [114]

Answer:

3.5x + 2.50y = 1237.50

425 = x + y

Step-by-step explanation:

number of adult tickets: x

number of student tickets: y

3.5x + 2.50y = 1237.50

( value of adult ticket [3.50]* number of adult tickets [x]) + (value of student ticket [2.50] * number of student tickets [y]) = total value (1237.50)

425 = x + y

(number of adult tickets [x]) + (number of student tickets [y]) = total (425)

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2 years ago

Each bucket holds 212

serg [7]

Answer:

5088

Step-by-step explanation:

212*24=5088

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2 years ago

Find the inequality represented by the graph.

Rainbow [258]

Answer:

y>-2/3x+3

Step-by-step explanation:

Looking at the line, we notice that the y-intercept is 3, and the slope is -2/3, so using that information, we find the slope intercept form of the inequality, which is y(?)-2/3x+3 (the question mark is where the inequality symbol will be).

Looking at the line again, we see that it is shaded above (not below), so y is greater than the other side of the inequality.

Looking at the line AGAIN, we see the graph has a dashed line (not solid), so we are not dealing with an "or equal to" inequality.

Therefore, we should use the greater than symbol, creating the answer y>-2/3x+3.

5 0

2 years ago