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3 years ago

A square sandbox has sides that are 10 feet long. What is the sandbox's area?

Mathematics

1 answer:

Ainat [17]3 years ago

4 0

Answer:

0.0929

Step-by-step explanation:

thats the answer

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4sin²<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D" id="TexFormula1" title="\frac{x}{2}" alt="\frac{x}{2}" align="absm

raketka [301]

Answer:

$\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}$

Step-by-step explanation:

Hi there!

We want to solve for $x$ in:

$4\sin^2(\frac{x}{2})=3$

Since $x$ is in the argument of $\sin^2$ , let's first isolate $\sin^2$ by dividing both sides by 4:

$\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}$

Next, recall that $\sin^2x$ is just shorthand notation for $(\sin x)^2$ . Therefore, take the square root of both sides:

$\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}$

Simplify using $\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ :

$\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}$

Let $\phi = \frac{x}{2}$ .

<h3><u>Case 1 (positive root):</u></h3>

$\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}$

Therefore, we have:

$\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

<h3><u>Case 2 (negative root):</u></h3>

$\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

8 0

3 years ago

What is the answer to<br> -12 + 7 = __

bixtya [17]

Answer:

-5

Step-by-step explanation:

an easy way to do it is to flip it so its 7-12 or you can do 12-7 and you get 5 then just add a - sign but thats my way and its weird lol

6 0

4 years ago

Read 2 more answers

Help me please help me please

Olegator [25]

2=10
3 =15
7=35
1=5
Constant of 1 is 5

3 0

3 years ago

Read 2 more answers

Find a polynomial f(x) of degree 4 that has the following zeros.

34kurt

Answer:

The answer to your question is (x₁ - 4)(x₂ - 9)(x₃)(x₄ +4)

Step-by-step explanation:

Data

zeros of a polynomial = 4, 9, 0, -1

Process

1.- Equal each root to zero

x₁ = 4 x₂ = 9 x₃ = 0 x₄ = -1

x₁ - 4 = 0 x₂ - 9 = 0 x₃ = 0 x₄ + 1 = 0

2.- Write the terms together

(x₁ - 4)(x₂ - 9)(x₃)(x₄ +4)

3.- Expand to check the answer

(x - 4)(x - 9) = x² -13x + 36

(x² -13x + 36)(x) = x³ - 13x² + 36x

(x³ - 13x² + 36x)(x + 4) = x⁴ - 13x³ + 36x² + 4x³ - 52x² + 144x

= x⁴ - 9x³ - 16x² + 144

3 0

3 years ago

Can someone help me with this question please?

erma4kov [3.2K]

Answer:

the answer will be 4/3 in slope form

Step-by-step explanation:

the answer will be 4/3 in slope form

3 0

3 years ago