F(x) = -4x^2+ 10 Find f(-2)

Mathematics

2 answers:

sveticcg [70]2 years ago

6 0

-6 should be the correct answer

NISA [10]2 years ago

3 0

Answer:

-6

Step-by-step explanation:

plug -2 into x

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How to integrate 1/(1-y)^2

Akimi4 [234]

If you're using the app, try seeing this answer through your browser: brainly.com/question/866966

_______________

Evaluate the indefinite integral:

$\mathsf{\displaystyle\int\!\dfrac{1}{(1-y)^2}\,dy}\\\\\\ =\mathsf{\displaystyle\int\!\dfrac{-1}{(1-y)^2}\cdot (-1)\,dy}\\\\\\ =\mathsf{\displaystyle- \int\!(1-y)^{-2}\cdot (-1)\,dy\qquad\quad(i)}$

Substitution:

$\begin{array}{lcl} \mathsf{1-y=u}&\quad\Rightarrow\quad&\mathsf{y=1-u}\\\\ &&\mathsf{dy=-1\,du} \end{array}$

So the integral $\mathsf{(i)}$ becomes

$=\mathsf{\displaystyle -\int\! u^{-2}\,du}\\\\\\ =\mathsf{-\,\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\ =\mathsf{-\,\dfrac{u^{-1}}{-1}+C}\\\\\\ =\mathsf{u^{-1}+C}\\\\\\ =\mathsf{\dfrac{1}{u}+C}$

$=\mathsf{\dfrac{1}{1-y}+C}\\\\\\\ \therefore~~\boxed{\begin{array}{c}\mathsf{\displaystyle\int\!\dfrac{1}{(1-y)^2}\,dy=\dfrac{1}{1-y}+C} \end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: <em>indefinite integral fraction rational substitution power differential calculus</em>

3 0

2 years ago

Sketch the figure: Two different isosceles triangles with perimeter 4a + b

Nikitich [7]

The two triangles with the given perimeter is attached .

Perimeter is the sum of all sides.

For the first triangle , sies are 2a,2a and b.

So the perimeter is

$Perimeter = 2a+2a+b
\\
Perimeter = 4a+b$