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3 years ago

Do you think the equation y=|x|+6 will be a function or not a function?

Mathematics

1 answer:

Lelechka [254]3 years ago

8 0

It is a function, so yes ig

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Geometric probability

Anna [14]

7+3+8+3=21 fishes in total
8/21 fishes are healthy
8/21 = 0.4 => 40%

3 0

2 years ago

Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

3 years ago

Plz Help ASAP!!!! Which of the following statements demonstrates the associative property of multiplication? a. 4 ∙ (3 ∙ 6) = (4

777dan777 [17]

Answer:

A is your answer

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Consider the system of linear equations and the matrix equations below.

gregori [183]

9514 1404 393

Answer:

x = 7

Step-by-step explanation:

Using Cramer's rule, the value of x is ...

$x=\dfrac{\left|\begin{array}{cc}2&3\\22&-2\end{array}\right|}{\left|\begin{array}{cc}-1&3\\4&-2\end{array}\right|}$

x = ((2)(-2) -(22)(3))/((-1)(-2) -(4)(3)) = (-4-66)/(2-12) = -70/-10

x = 7

4 0

3 years ago

Someone pls help me

Nat2105 [25]

The answer should be AC+BC

We can answer this by applying the rule called "Greater angle, greater side". This is where in any triangle, the opposite side of the larger angle is also longer.

So in this question, first we have to find the largest 2 angles, which is ∠ABC and ∠BAC with measures of 120° and 35° respectively. Therefore, from the diagram, the opposite sides of the angles are AC and BC.

Therefore, the answer should be AC+BC.

7 0

3 years ago