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3 years ago

11

Darius is going home from college for the weekend. He checked google maps and found that his house is 480 miles away. If he want

s to drive at a constant speed, and drive in exactly 8 hours, then what should his speed be?

1 answer:

Vesnalui [34]3 years ago

8 0

Answer:

60.

Step-by-step explanation:

You might be interested in

Delvig [45]

Answer:

Q1: $\frac{3}{4}$

Q2: $\frac{83}{100}$

Step-by-step explanation:

Q1: 12 : 16 = 3 : 4 = $\frac{3}{4}$

Q2: 8.3 : 10 = $\frac{83}{100}$

3 0

3 years ago

Line 1 passes through the points A(-15,-8) and B(-3,0). Line 2 has

Katyanochek1 [597]

Answer:

The equation of line 3 is;

y = $\frac{2}{3} x$ + 6

Step-by-step explanation:

Line 1 passes through the points A(-15,-8) andn B(-3,0)

Line 2 has equation shown below;

5x - 3y + 18 = 0

Line 3 is parallel to line 1 and has the same y-intercept as line 2.

We are to determine the equation of line 3.

<u>Equation of line 1:</u>

<u />

Slope = change in y-axis ÷ change in x-axis

The slope of line 1 = $\frac{0 - -8}{-3 - -15} = \frac{8}{12} = \frac{2}{3}$

Picking another point (x,y) on the line;

Slope = $\frac{y - 0}{x - -3} = \frac{2}{3}$

y = $\frac{2}{3} x$ + 2 (this is the equation of line 1)

<u>Equation of line 2:</u>

<u />

We put the equation given, of line 2, in the cartesian plane format;

3y = 5x + 18

y = $\frac{5}{3} x$ + 6

Finally, the equation of line 2 is;

y = 1 $\frac{2}{3} x$ + 6

<u>Equation of line 3:</u>

<u />

Given: Line 3 is parallel to line 1

The slopes of two parallel lines are the same so line 3 has a slope of $\frac{2}{3}$

Given: Line 3 has the same y-intercept as line 2

The y-intecept of line 2 is 6 (y-intercept is the value of y when x = 0)

So the equation of line 3 is;

y = $\frac{2}{3} x$ + 6

3 0

3 years ago

Which of the following is not one of the 8th roots of unity?

Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1. Since $z=1=1+0\cdot i,$ then

$Rez=1,\\ \\Im z=0$

and

$|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.$

This gives you $\varphi=0.$

Thus,

$z=1\cdot(\cos 0+i\sin 0).$

2. The 8th roots can be calculated using following formula:

$\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.$

Now

at k=0, $z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;$

at k=1, $z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=2, $z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;$

at k=3, $z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=4, $z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;$

at k=5, $z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

at k=6, $z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;$

at k=7, $z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

The 8th roots are

$\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.$

Option C is icncorrect.

5 0

3 years ago

Which statement correctly describes order of operations (PEMDAS)?

Serjik [45]

Answer:

B

Step-by-step explanation:

parentheses exponents multiplication division addition subtraction

4 0

3 years ago

Read 2 more answers

A company deposits $5,000 into an account that earns interest. The rate at which the value changes is given by dA/dt=0.0225A, wh

xxMikexx [17]

Answer:

$6261.61

Step-by-step explanation:

The solution to the differential equation is the exponential function ...

A(t) = 5000e^(0.0225t)

We want the account value after 10 years:

A(10) = 5000e^(0.225) = 6261.61

The value of the account after 10 years will be $6,261.61.

_____

The rate of change equation basically tells you that interest is compounded continuously. After working interest problems for a while you know the formula for that is the exponential formula A = A0·e^(rt).

Or, you can solve the differential equation using separation of variables:

dA/A = 0.0225dt

ln(A) = 0.0225t +C . . . . integrate

A(t) = A0·e^(0.0225t) = 5000·e^(0.0225t) . . . . solution for A(0) = 5000

7 0

3 years ago