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3 years ago

You create 15 centerpieces for a party in 5 hours. what is the unit rate?

Mathematics

1 answer:

Tema [17]3 years ago

8 0

15 in 5 hours would mean you are making 3 an hour, or one every 20 minutes.

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Complex numbers & DeMoivre's theory<br> If z=-1-√3 i and z^6=a+bi, a=_____ and b=_____

Mice21 [21]

Convert $z$ to exponential/polar/trigonometric form:

$r=|z|=\sqrt{(-1)^2+(-\sqrt 3)^2}=2$

$\tan\theta=\dfrac{-\sqrt3}{-1}\implies\theta=\dfrac{4\pi}3$

$\implies z=-1-\sqrt3\,i=2e^{4\pi/3\,i}=2\left(\cos\dfrac{4\pi}3+i\sin\dfrac{4\pi}3\right)$

By DeMoivre's theorem,

$z^6=\left(2e^{4\pi/3\,i}\right)^6=2^6e^{24\pi/3\,i}=64e^{8\pi\,i}$

$z^6=64\left(\cos8\pi+i\sin8\pi)=64$

so that $a=64$ and $b=0$ .

8 0

3 years ago

Which step could be used to help isolate the variable in the following equation

makvit [3.9K]

The subtraction of 4 on both sides would isolate the term 1.1j, then the division of 1.1 on both sides would isolate j.

8 0

3 years ago

Read 2 more answers

Sophie sprays 200 fluid ounces of water on the window plants in her house every day. How much water does she spray each day?

lutik1710 [3]

I think it is A not sure though

5 0

3 years ago

Solve 3x+k= c for x.

Debora [2.8K]

Answer:

x = $\frac{c-k}{3}$

Step-by-step explanation:

Given

3x + k = c ( isolate the term 3x by subtracting k from both sides )

3x = c - k ( divide both sides by 3 )

x = $\frac{c-k}{3}$

5 0

3 years ago

Consider h(x)=x^2+8+15. identify its vertex and y-intercept.

OleMash [197]

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ .

<h3>Use the equation: $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ </h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

$x = \frac{-b}{2a}$

$x = \frac{-8}{2(1)}$

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

5 0

2 years ago