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nikitadnepr [17]

3 years ago

13

Im doing integers ? what is -80*-31

2 answers:

Evgen [1.6K]3 years ago

7 0

2,480 is the answer, since there are two negative signs they get canceled out and replaced with a positive.

ira [324]3 years ago

6 0

-80*-31 is actually -80×31
so the answer is 2480
hope this helps feel free to ask

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4 days = 96 hours.......

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3 years ago

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

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3 years ago

What is the result when the number 35 is increased by 20%?<br> Show me your work!

nirvana33 [79]

Answer:

42

Step-by-step explanation:

first we calculate what is 20% of 35 is then we add it to 35 to find the increased number

35 ÷ 100 = 0.35 this multipled by 20 = 7

35 + 7 = 42

3 0

4 years ago

Jimmy's cedar trunk is in the shape of a rectangular prism and has a volume of 3/4 cubic yard. How many cubic blocks with a side

gizmo_the_mogwai [7]

Answer: 6 blocks

Step-by-step explanation:

Given

Volume of the rectangular prism is $V=\dfrac{3}{4}\ yd^3$

Length of the cubic block is $a=\dfrac{1}{2}\ yd$

Volume of each cubic block is

$\Rightarrow V_o=\left (\dfrac{1}{2}\right)^3\\\\\Rightarrow V_o=\dfrac{1}{8}\ yd^3$

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Thus, 6 blocks are required to measure the volume of prism.

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3 years ago

The two figures shown are congruent. which statement is true?

Masteriza [31]

Answer:

1st Option

Step-by-step explanation:

Hope it helps

4 0

3 years ago

Read 2 more answers