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2 years ago

Pls help ASAP!!!!! plss anyone!!!!

Mathematics

1 answer:

vfiekz [6]2 years ago

5 0

Answer:

a = 117°

c = 117°

d = 63°

c = 87°

a = 60°

b = 30°

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Y = x - 3 y = -7 solve the system of equations by subtraction

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Step-by-step explanation:

$y = \frac{4}{5} x - 3 \\ y = - 7 \\ - 7 = \frac{4}{5} x - 3$

$- 7 + 3 = \frac{4}{5} x \\ - 4 = \frac{4}{5} x \\ - 20 = 4x \\ x = - 5$

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2 years ago

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For the function f(x) = 1/4e^-x + e^x, prove that the arc length on any interval has the same value as the area under the curve.

faltersainse [42]

Take an arbitrary interval [a, b], where a < b.

Compute the arc length L of y = f(x) over [a, b] :

$L=\displaystyle\int_a^b\sqrt{1+\left(f'(x)\right)^2}\,\mathrm dx$

Now comptue the area A under the curve y = f(x) over [a, b] :

$A=\displaystyle\int_a^bf(x)\,\mathrm dx$

We have

f (x) = 1/4 e ⁻ˣ + e ˣ → f ' (x) = -1/4 e ⁻ˣ + e ˣ

Then

√(1 + (f ' (x))²) = √(1 + (-1/4 e ⁻ˣ + e ˣ)²)

… = √(1 + 1/16 e ⁻²ˣ - 1/2 + e ²ˣ)

… = √(1/16 e ⁻²ˣ + 1/2 + e ²ˣ)

… = 1/4 √(e ⁻²ˣ + 8 + 16e ²ˣ)

… = 1/4 √((e ⁻ˣ + 4 e ˣ)²)

… = 1/4 (e ⁻ˣ + 4 e ˣ)

… = 1/4 e ⁻ˣ + e ˣ

… = f (x)

so both A = L for any choice of interval [a, b].

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3 years ago