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3 years ago

What is 1(z) when z = -7/12

Mathematics

2 answers:

Firlakuza [10]3 years ago

8 0

It will just be -7/12 because anything times 1 stays the same

UkoKoshka [18]3 years ago

6 0

The answer will be -7/12. Hope it help!

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SOMEONE PLEASE HELP ASAP IM IN A TEXT NO EXPLANAION NEEDED JUST THE FUNCTION!!THANK YOU SO MUCH :)

Lynna [10]

Answer:

$\frac{-1}{4} x^{2}$

$\frac{-1}{4} g(x)$

Step-by-step explanation:

3 0

3 years ago

I'm having trouble with #2. I've got it down to the part where it would be the integral of 5cos^3(pheta)/sin(pheta). I'm not sur

Butoxors [25]

$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

Setting $x=5\sin\theta$ , you have $\mathrm dx=5\cos\theta\,\mathrm d\theta$ . Then the integral becomes

$\displaystyle\int\frac{\sqrt{25-(5\sin\theta)^2}}{5\sin\theta}5\cos\theta\,\mathrm d\theta$
$\displaystyle\int\sqrt{25-25\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{1-\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

Now, $\sqrt{x^2}=|x|$ in general. But since we want our substitution $x=5\sin\theta$ to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means $\theta=\sin^{-1}\dfrac x5$ , which implies that $\left|\dfrac x5\right|\le1$ , or equivalently that $|\theta|\le\dfrac\pi2$ . Over this domain, $\cos\theta\ge0$ , so $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

Long story short, this allows us to go from

$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

to

$\displaystyle5\int\cos\theta\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\dfrac{\cos^2\theta}{\sin\theta}\,\mathrm d\theta$

Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

$\dfrac{\cos^2\theta}{\sin\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}=\csc\theta-\sin\theta$

Then integrate term-by-term to get

$\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)$
$=-5\ln|\csc\theta+\cot\theta|+\cos\theta+C$

Now undo the substitution to get the antiderivative back in terms of $x$ .

$=-5\ln\left|\csc\left(\sin^{-1}\dfrac x5\right)+\cot\left(\sin^{-1}\dfrac x5\right)\right|+\cos\left(\sin^{-1}\dfrac x5\right)+C$

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

$=-5\ln\left|\dfrac{5+\sqrt{25-x^2}}x\right|+\sqrt{25-x^2}+C$

4 0

3 years ago

Read 2 more answers

HEELP please i dont under stand

DIA [1.3K]

The answer is A 3/10 because there is 3 blue marbles and all together there is 10

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3 years ago

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Please help!<br><br>4^x*5^y=20, 4^y*5^x=20^2, x+y=?

photoshop1234 [79]

Answer:

x + y are either 2 or 4

Step-by-step explanation:

conclusion x + y = 2 OR 4

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3 years ago

How do you find the y-intercept of a line?

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The equation of any straight line, called a linear equation, can be written as: y= mx+b, where my is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the lone crosses the y axis.

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3 years ago