Translate each verbal description into an algebraic expression. Then simplify

Mathematics

1 answer:

gogolik [260]3 years ago

7 0

Answer:

(1/3)q - (4/3) p - 5/9

Step-by-step explanation:

Step one

Write the fractional form of the givens

(1/3)(q + p)

(5/9)(3p + 1)

Step Two

Write out the expression

(1/3)(q + p) - (5/9)(3p + 1) Remove the brackets

(1/3)q + (1/3)p - (5/9)*3p - 5/9 Combine the 2 p terms

(1/3)q + (1/3 - 15/9 )p - 5/9 Reduce 15/9 down to 5/3

(1/3)q + (1/3 - 5/3)p - 5/9 Combine what is inside the brackets

(1/3)q + ( - 4/3)p - 5/9 Bring out the minus sign

(1/3)q - (4/3) p - 5/9 This should be 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]

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

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

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3 years ago

Write the inequality that goes with the graph shown.

m_a_m_a [10]

Answer:

—1=<x<-3

Since

X<-3

X>=-1

Not shaded means including.

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