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3 years ago

PLEASE HELP ASAP

Mathematics

1 answer:

sineoko [7]3 years ago

8 0

Answer-

Tyler must be more than 7 years old, so that the ratio of his sister's age to his brother's age is less than 2.

Solution-

Let's assume that,

Age of Tyler = x years, then

Age of his sister = (x+3) years and Age of his brother = (x-2) years

As given that the ratio of his sister's age to his brother's age must be less than 2, so

$\Rightarrow \dfrac{x+3}{x-2}$

$\Rightarrow x+3$

$\Rightarrow 3+4$

$\Rightarrow 7$

$\Rightarrow x>7$

Therefore, Tyler's age must be more than 7, in order to satisfy the condition.

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Read 2 more answers

Find the value of the integral that converges. ∫^-5_-[infinity] x^-2 dx.

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Answer:

$\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}$

Because the $\lim_{x\to -\infty} \frac{1}{x} =0$

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Step-by-step explanation:

For this case we want to find the following integral:

$\int_{-\infty}^{-5} x^{-2}dx$

And we can solve the integral on this way:

$\int_{-\infty}^{-5} x^{-2}dx= \frac{x^{-2+1}}{-2+1} \Big|_{-\infty}^{-5}$

$\int_{-\infty}^{-5} x^{-2}dx= -\frac{1}{x} \Big|_{-\infty}^{-5}$

And if we evaluate the integral using the fundamental theorem of calculus we got:

$\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}$

Because the $\lim_{x\to -\infty} \frac{1}{x} =0$

The integral converges to $\frac{1}{5}$

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Area of triangle is 9.88 units^2

Step-by-step explanation:

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