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3 years ago

On a line graph, time is usually represented on the vertical axis.

1 answer:

3 0

False. Time is usually represented on the horizontal axis.

This is because the independent variable usually goes on the horizontal/x axis and the dependent variable goes on the vertical/y axis. The independent variable is what you're changing and usually time is what affects whatever outcome (aka dependent variable value) you get.

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Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

____ [38]

Let $z=-\sqrt3+i$ . Then

$|z|=\sqrt{(-\sqrt3)^2+1^2}=2$

$z$ lies in the second quadrant, so

$\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6$

So we have

$z=2e^{i5\pi/6}$

and the fourth roots of $z$ are

$2^{1/4}e^{i(5\pi/6+k\pi)/4}$

where $k\in\{0,1,2,3\}$ . In particular, they are

$2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}$

$2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}$

$2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}$

$2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}$

7 0

3 years ago

3 pieces of wood have a total length of 32 m. The second piece is twice the size of the first and the third piece is 2 more mete

andreev551 [17]

Answer:

X + Y + Z = 32

X2 = Y

X3 + 2 = Z

X + X2 + X3 + 2 = 32

Make X alone

There is a 2 so we subtract 2 from both sides

X + X2 + X3 = 30

Add the X's up

X + X2 + X3 = X6

X6 = 30

Divide by 6

30 / 6 = 5

You are left with X=5

The first piece of wood has a length of 5

5 x 2 = 10

The second piece has a value of 10

5 x 3 + 2 = 17

The third piece is 17

Hope this helps. If you have any questions you may ask.

Step-by-step explanation:

5 0

3 years ago

John went to an electronics store to purchase a new computer. The electronics store allowed John to make payments on the compute

gavmur [86]

Answer:

The monthly payment is $210

Step-by-step explanation:

The computation of the monthly payment is shown below:

Given that

The cost of the computer i.e. purchased is $1,260

And, there are 6 equal monthly payments

So, the monthly payment is

= Computer cost ÷ number of equal monthly payments made

= $1,260 ÷ 6 payments

= 210

hence, the monthly payment is $210 and the same is to be considered

6 0

3 years ago

You want to put a 5 inch thick layer of topsoil for a new 23 ft by 17 ft garden. the dirt store sells by the cubic yards. how ma

Oksanka [162]

1 yard = 3 feet = 36 in

so 1 in = 1/36 yard, 1 ft = 1/3 yard.

The volume of the layer of the topsoil, is:

5 in * 23 ft * 17 ft = 5 *(1/36)*23*(1/3)*17*(1/3) yard cubed =

(5*23*17)/(36*3*3)= 1955/324=6.034 yard cubed.

The store only sells increments of 1/4 = 0.25 cubic yards.

we need 6.034/0.25=24.136

So we need to buy 25 (24 will not be enough) increments of 1/4 cubic yards.

Answer: 25 increments of 1/4 cubic yard, that is 25*0.25=6.25 cubic yards.

5 0

4 years ago

What is the y-intercept of the line given by the equation below ? Y=8x + 7

docker41 [41]

The answer is B (0,7)

5 0

3 years ago