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3 years ago

14

(15pts) just about area don't have to show work

1 answer:

Kazeer [188]3 years ago

6 0

Good luck with ur quiz I hope u pass

You might be interested in

Eight less than four times a number is less then 56. What are the possible values of that number?

Mashutka [201]

Answer: B. X<12

Step-by-step explanation:

First we need to find out what number multipled by 4 is less than 56

4 x 12 = 48

56-48 = 8

And 4 is lower/less than 12 so that's why it's B

5 0

3 years ago

Read 2 more answers

I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).

Aleksandr-060686 [28]

Answer:

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

Step-by-step explanation:

$\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$

Let's first isolate the trig function.

Add 1 one on both sides:

$\sqrt{3} \tan(x-\frac{\pi}{8})=1$

Divide both sides by $\sqrt{3}$ :

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

Now recall $\tan(u)=\frac{\sin(u)}{\cos(u)}$ .

$\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

or

$\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

The first ratio I have can be found using $\frac{\pi}{6}$ in the first rotation of the unit circle.

The second ratio I have can be found using $\frac{7\pi}{6}$ you can see this is on the same line as the $\frac{\pi}{6}$ so you could write $\frac{7\pi}{6}$ as $\frac{\pi}{6}+\pi$ .

So this means the following:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

is true when $x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

where $n$ is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

$x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

Add $\frac{\pi}{8}$ on both sides:

$x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi$

Find common denominator between the first two terms on the right.

That is 24.

$x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi$

$x=\frac{7\pi}{24}+n \pi$ (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval $[0,2\pi)$ .

So if $\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$ and we let $u=x-\frac{\pi}{8}$ , then solving for $x$ gives us:

$u+\frac{\pi}{8}=x$ ( I just added $\frac{\pi}{8}$ on both sides.)

So recall $0\le x$ .

Then $0 \le u+\frac{\pi}{8}$ .

Subtract $\frac{\pi}{8}$ on both sides:

$-\frac{\pi}{8}\le u$

Simplify:

$-\frac{\pi}{8}\le u$

$-\frac{\pi}{8}\le u$

So we want to find solutions to:

$\tan(u)=\frac{1}{\sqrt{3}}$ with the condition:

$-\frac{\pi}{8}\le u$

That's just at $\frac{\pi}{6}$ and $\frac{7\pi}{6}$

So now adding $\frac{\pi}{8}$ to both gives us the solutions to:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$ in the interval:

$0\le x$ .

The solutions we are looking for are:

$\frac{\pi}{6}+\frac{\pi}{8}$ and $\frac{7\pi}{6}+\frac{\pi}{8}$

Let's simplifying:

$(\frac{1}{6}+\frac{1}{8})\pi$ and $(\frac{7}{6}+\frac{1}{8})\pi$

$\frac{7}{24}\pi$ and $\frac{31}{24}\pi$

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

5 0

3 years ago

a garden plot is to contain 240 sq. ft. if its length is to be 3 times its width,what should its dimensions be?

SOVA2 [1]

240 ft^2 = L X W
240 = 3W x W
240 = 3W^2
W = 8.94427 ft
L = 3W = 3(8.94427)
L = 26.8328 FT

8 0

3 years ago

Is the following shape a rectangle? How do you know?

pogonyaev

I would think it’s a square

7 0

2 years ago

Drag and drop each expression into the box to correctly classify it as having a positive or negative product

AfilCa [17]

Following expressions will have negative product

$(\frac{1}{2})(-\frac{1}{2})\ and\ (-\frac{1}{2})(\frac{1}{2})$

Following expressions will have positive product

$(-\frac{1}{2})(-\frac{1}{2})\ and\ (\frac{1}{2})(\frac{1}{2})$

Further explanation:

We will see at each expression one by one

First expression is:

$(-\frac{1}{2})(\frac{1}{2})$

In the given expression one term is positive and one term is negative. The product of negative and positive terms is negative.

Second Expression is:

$(-\frac{1}{2})(-\frac{1}{2})$

Both terms are negative and the product of two negative terms is positive.

Third Expression is:

$(\frac{1}{2})(-\frac{1}{2})$

The expression has one positive and one negative term so the product will be negative

Fourth Expression is:

$(\frac{1}{2})(\frac{1}{2})$

Both terms are positive so the product will also be positive

Keywords: Product, Expressions

Learn more about expressions at:

#LearnwithBrainly

5 0

3 years ago