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2 years ago

Evaluate 1 2/3 x 2 5/8

Mathematics

1 answer:

sergiy2304 [10]2 years ago

5 0

Answer:

the answer to your question is 4 3/8 , hope this helps have a good rest of your day :)

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How does a number line represent equivalent fractions and decimals?

kogti [31]

Dododkdldlldlflffosjdididkdkdkdkd

8 0

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

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

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

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:

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

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

2 years ago

Question

AlekseyPX

Answer:

The population mean is 5 volts

Step-by-step explanation:

Output voltage is assumed to be normally distributed, with standard deviation 0.25 Volts

s=0.25

n = 8

$H_0:\mu = 5\\H_a:\mu \neq 5$

Sample mean = $\bar{x}=4.85$

Since n < 30 and population standard deviation is unknown

So, we will use t test

Formula : $t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{4.85-5}{\frac{0.25}{\sqrt{8}}}$

t=-1.69

Refer the t table for p value

Degree of freedom = n-1 = 8-1 = 7

So, $t_{(df,\alpha)}=t_{7,0.05}=2.365$

P value >α

So, We are failed to reject null hypothesis

Hence The population mean is 5 volts

7 0

3 years ago

A square pool has a side length of x feet.A uniform border around pool is 1 footwide.The total area of the pool and the border o

lions [1.4K]

The total area of pool and border = 361 square feet.

Length of square pool = x

Length of square pool plus border = (x + 1 +1 ) = x + 2

There is 1 foot length on each side on the x length.

The other length of the square pool and border = (x + 2)

Area = (x+2)(x+2)

   (x + 2)(x +2) = 361.    Let A = x +2

A*A = 361
    A² = 361    Take square root of both sides
   A = √361
   A = 19

A = x + 2 = 19
   x = 19 - 2
   x = 17

Area of square pool = x*x = 17*17 = 289

Area of the pool = 289 square feet.

8 0

2 years ago

Solve for b. 4b-3b+7= 10

Morgarella [4.7K]

b = 3

Step-by-step explanation:

$4b - 3b + 7 = 10$