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Neporo4naja [7]

2 years ago

6

--/: Lesson Quiz Why is subtracting an expression similar to distributing a -1?

1 answer:

o-na [289]2 years ago

3 0

Answer:

You increase each term inside the parentheses by -1 in order to subtract each term, since the subtraction is the additive inverse

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Verizon [17]

If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show

$\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx$

Let $f(x) = \sqrt{1 + x^3}$ . Compute the inverse:

$f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}$

and we immediately notice that $f^{-1}(x+1)=\sqrt[3]{x^2+2x}$ .

So, we can write the given integral as

$\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx$

Splitting up terms and replacing $x \to x-1$ in the first integral, we get

$\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}$

7 0

2 years ago

A UFO is coming in to pick up some test subjects. Their elevation above the ground is 60,000 feet. Their laser sights tell them

charle [14.2K]

Answer:

41.83°

Step-by-step explanation:

It is given that :

The vertical distance of the UFO from the ground = 60,000 feet

The diagonal distance of the landing area to the UFO = 90,000 feet

In order to find the angle of depression, we have to use the trigonometric ratios, i.e.,

$\sin \ \theta = \frac{\text{perpendicular distance}}{\text{hypotenus}}$

$\sin \ \theta = \frac{60,000}{90,000}$

$\sin \ \theta = \frac{2}{3}$

$\sin \ \theta = 0.667$

∴ $\theta = \sin^{-1 }(0.667)$

= 41.83°

3 0

3 years ago

Find the coefficient of correlation between and X and Y if covariance between X and Y is 15 and the variance of X and Y are resp

IRINA_888 [86]

Answer:

0.95

Step-by-step explanation:

$Correlation \ coefficient \ (r) = \dfrac{covaraince \ between \ X \ and \ Y }{SD_X \times SD_Y }$

$Correlation \ coefficient \ (r) = \dfrac{15 }{10^{1/2} \times 25^{1/2} }$

$Correlation \ coefficient \ (r) = \dfrac{15 }{3.162 \times 5 }$

$Correlation \ coefficient \ (r) = \dfrac{15 }{15.81 }$

$Correlation \ coefficient \ (r) \simeq 0.95$

5 0

3 years ago

What is the answer to |3x-4|=|3x-5|

Butoxors [25]

Answer:

i think this is the answer

4 0

3 years ago

Read 2 more answers

Two cars depart an intersection.

patriot [66]

Answer:

The distance between them after 1 hour and 30 minutes will be of 63.64 miles.

Step-by-step explanation:

This question can be solved using the Pythagorean Theorem.

Both cars travel at a constant speed of 30 miles per hour. So, after 1 hour and 30 minutes, which is 1 and a half hour, they will have traveled 30*1.5 = 45 miles.

The distance between them is the hypotenuse of a right triangle, in which the sides are 45. So

$d^2 = 45^2 + 45^2$

$d = \sqrt{45^2 + 45^2}$

$d = 63.64$

The distance between them after 1 hour and 30 minutes will be of 63.64 miles.

4 0

3 years ago