What is the area of the rectangle?

Mathematics

2 answers:

almond37 [142]3 years ago

8 0

Take a look at the picture i sent you

NARA [144]3 years ago

5 0

Use the formula of length of the segment:
$A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

$A(-3;-7);\ B(5;-1)\\\\|AB|=\sqrt{(5-(-3))^2+(-1-(-7))^2}=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10\\\\A(-3;-7);\ D(-6;-3)\\\\|AD|=\sqrt{(-6-(-3))^2+(-3-(-7))^2}=\sqrt{(-3)^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$
$A_{\boxed{ . }}=|AB|\cdot|AD|\\\\A_{\boxed{ . }}=10\cdot5=50\ \text{units}^2$

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svetlana [45]

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3 years ago

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If f(x)=sinx 2x 1 and g is the inverse function of f

Bingel [31]

The value of the derivative of the function g(x) at x = 1 will be 1/3. Then the correct option is A.

<h3>What is an inverse function?</h3>

A function that may convert into another function is known as an inverse function or anti-function.

If the function is f(x) = sinx + 2x + 1.

Then the derivative of an inverse function g(x) of a function f(x) at a given value (a) will be

$\rm g'(a) = \dfrac{1}{f'(g(a))}$

The derivative of f(x) will be

f'(x) = cos x + 2

Then the given value of a will be

a = 1

g(x) = f⁻¹(x)

put x = 0, then we have

f(0) = sin 0 + 2(0) + 1

f(0) = 1

Put x = 1, in the function f⁻¹(x). Then we have

f⁻¹(1) = 0

and

g(1) = 0

Then put a = 1, then we have

$\rm g'(a) = \dfrac{1}{f'(g(a))}\\\\g'(1) = \dfrac{1}{f'(g(1))}\\\\g'(1) = \dfrac{1}{f'(0)}\\\\g'(1) = \dfrac{1}{\cos 0 + 2}\\\\g'(1) = \dfrac{1}{1+2}= \dfrac{1}{3}$