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3 years ago

Solve the following question

Mathematics

1 answer:

nydimaria [60]3 years ago

5 0

9514 1404 393

Answer:

π/3

Step-by-step explanation:

The given integral does not exist. We assume there is a typo in the upper limit, and that you want the integral whose upper limit is (√3)/2.

It is convenient to make the substitution ...

x = sin(y) . . . . so, y = arcsin(x)

dx = cos(y)·dy

Then the integral is ...

$\displaystyle\int_0^{\sqrt{3}/2}{\dfrac{\cos{y}}{\sqrt{1-\sin^2{y}}}}\,dy=\int_0^{\sqrt{3}/2}{dy}=\left.\arcsin{x}\right|\limits_0^{\sqrt{3}/2}\\\\=\arcsin{(\sqrt{3}/2)}=\boxed{\dfrac{\pi}{3}}$

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Answer:

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Explanation

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Therefore...3 gal

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3 years ago

What is the value of d? Round your answer to the nearest tenth.

Sergeeva-Olga [200]

Answer:

11.9 mm

Step-by-step explanation:

We can find d by applying the cosine rules.

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3 years ago

Apopulation grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.a) Write a function to model the

solong [7]

Answer:

a) $P(t) = 22000(1.071)^{t}$

b) The population increases 7.1% each year.

Step-by-step explanation:

The continuous population growth model is given by:

$P(t) = P_{0}(1+r)^{t}$

In which $P(t)$ is the population after t years, $P_{0}$ is the initial population and r is the growth rate.

In this problem, we have that:

A population grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.

This means that $P_{0} = 22000, r = 0.071$

a) Write a function to model the population increase.

$P(t) = 22000(1 + 0.071)~{t}$

$P(t) = 22000(1.071)^{t}$

b) By what percent does the populaiion increase each year?

$r = 0.071$

So the population increases 7.1% each year.

6 0

3 years ago

Help please! my teacher wants us to show how we got our answer

Mila [183]

Direct variation is when $\dfrac{y}{x}$ is the same for each coordinate.

Indirect variation is when x · y is the same for each coordinate.

11. Answer: Direct Variation

Step-by-step explanation:

$\begin {array}{c||c|c|c|c|c}x&12&18&23&29&34\\y&132&198&253&319&374\\\\\dfrac{y}{x}&\dfrac{132}{12}=11&\dfrac{198}{18}=11&\dfrac{253}{23}=11&\dfrac{319}{29}=11&\dfrac{374}{34}=11\\\end{array} \\\\\\\text{The coordinates x and y show a direct variation.}$

12. Answer: Indirect Variation

Step-by-step explanation:

$\begin {array}{c||c|c|c|c|c}x&4&6&8&8.4&12\\y&21&14&10.5&10&7\\x\cdot y&4\cdot 21=84&6\cdot 14=84&8\cdot 10.5=84&8.4\cdot 10=84&12\cdot 7=84\\\end{array} \\\\\\\text{The coordinates x and y show an indirect variation.}$

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3 years ago

4x3= So ? what's the division

MrRa [10]

Answer:

12/4=3 or 12/3=4

Step-by-step explanation:

because multiplication is the opposite of division

8 0

3 years ago

Solve the following question ​

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