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3 years ago

The pair of figures is similar , find x

Mathematics

1 answer:

Andrei [34K]3 years ago

8 0

Create equivalent fractions:

23/x = 40/17

Cross multiply and divide:

x = 9.8

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Which of the following is a third root of the given complex number.

Leokris [45]

Answer:

The correct option is C.

Step-by-step explanation:

The given complex number is

$z=64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])$

We need to find the third root of the given complex number.

$z^{\frac{1}{3}}=(64(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}]))^{\frac{1}{3}}$

$z^{\frac{1}{3}}=64^{\frac{1}{3}}(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}$

$z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}]-i\sin[\frac{\pi}{7}])^{\frac{1}{3}}$

De moivre's theorem:

$(\cos\theta+i\sin\theta)^n=\cos n\theta+i\sin n\theta$

where, n is an integer.

Using de moivre's theorem, we get

$z^{\frac{1}{3}}=4(\cos[\frac{\pi}{7}\times \frac{1}{3}]-i\sin[\frac{\pi}{7}\times \frac{1}{3}])$

$z^{\frac{1}{3}}=4(\cos[\frac{\pi}{21}]-i\sin[\frac{\pi}{21}])$

Therefore the correct option is C.

6 0

3 years ago

Read 2 more answers

Summer has an offer to buy an item with a sticker price of $13,200 by paying $460 a month for 36 months. What interest rate is S

AysviL [449]

Answer:

the annual interest rate is 7.583%

Step-by-step explanation:

We are given

Summer has an offer to buy an item with a sticker price of $13,200

so, we have

P=13200

paying $460 a month for 36 months

so, we can find total amount

$A=460\times 36$

$A=16560$

Let's assume

annual interest is r

total time =36 months

so, total number of years =3

Since, it is compounded monthly

so, n=12

now, we can use formula

$A=P(1+\frac{r}{n} )^{nt}$

now, we can plug values

$16560=13200(1+\frac{r}{12} )^{36}$

now, we can solve solve for r

$(1+\frac{r}{12} )^{36}=\frac{16560}{13200}$

$r=0.07583$

So, the annual interest rate is 7.583%

6 0

3 years ago

Read 2 more answers

Non example of ratio

Thepotemich [5.8K]

A non example of a ratio would be 5 or 3 or 6 or 8 or 1 a ratio is 2:1

7 0

3 years ago

Which equation is of a line is parallel to -2x + 3y = 15

Marta_Voda [28]

$y=\frac{2}{3} x$ is the required equation.

<u>Step-by-step explanation:</u>

Equation of line is given as, -2x + 3y = 15

Now we have to write the equation in y = mx+ b form, where m is the slope and b is the y- intercept.

So the above line can be written as,

3y = 2x+ 15

Dividing both sides by 3 we will get,

$y=\frac{2}{3} x+\frac{15}{3}$

$y=\frac{2}{3} x+5$ is the equation of the given line

If a line is parallel to the given line then its slope must be the same, so the equation of line parallel to the given line is,

$y=\frac{2}{3} x$ is the required equation.

8 0

4 years ago

the value of y varies directly with x, and when x = 1/4 , y = 25. What is the value of y when x is 2 1/3 need help ASAP

Grace [21]

Answer:

$y=233\frac{1}{3}$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In this problem we have

For $x=1/4, y=25$

Find the value of k (constant of proportionality)

$y/x=k$ -----> $k=25/(1/4)=100$

The linear equation is

$y=100x$

Find the value of y when the value of $x=2\frac{1}{3}$

substitute the value of x in the equation but first convert to an improper fraction

$x=2\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}$

$y=100(\frac{7}{3})=\frac{700}{3}$

convert the result in mixed number

$\frac{700}{3}=\frac{699}{3}+\frac{1}{3}=233\frac{1}{3}$

3 0

4 years ago