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3 years ago

14

A group of students were competing to raise money for a charity; their goal was to raise a total of $300. Philip raised 40% of t

he total goal by himself. How much money did Philip raise?

1 answer:

Anna11 [10]3 years ago

3 0

$120 because you multiply 300*40 and get 1200 then divide it to 100 and get $120

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Which is a valid prediction about the continuous

kumpel [21]

33333333333333333333333333333333333

4 0

1 year ago

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using <span>De Moivre's theorem:
</span>
If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
</span>

Part (A) <span>find the modulus for all of the fourth roots
</span>
<span>∴ The modulus of the given complex number = l z l = 81
</span>
∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

7 0

3 years ago

Find the factorization of each of the following number:<br> A.18 B.24 C.38 D.81

const2013 [10]

Answer:

A: (3^2)*2

B: (2^3)*3

C: 2*19

D: (3^2)*9

Step-by-step explanation:

We have:

A) 18= 3*3*2= (3^2)*2

B) 24=2*2*2*3=(2^3)*3

C) 38 = 2*19

D) 81 =3*3*9=(3^2)*9

6 0

3 years ago

What is the slope of a line of best fit if its equation is y = −2x + 3?

serg [7]

-2. or otherwise put as -2/1

8 0

3 years ago

Read 2 more answers

11. Find the product of (3x+5) with (2x - 3) in simplest form.

STatiana [176]

Answer:

(3x + 5)(2x - 3) = 6x² + x - 15

Step-by-step explanation:

To find the product of two binomials, we could use the FOIL method.

First

Outer (Outside)

Inner (Inside)

Last

(3x + 5)(2x - 3) = (3x)(2x) + (3x)(-3) + (5)(2x) + (5)(-3) = 6x² - 9x + 10x - 15 = 6x² + x - 15

So the product of the two binomials would be 6x² + x - 15.

I hope you find my answer and explanation to be helpful. Happy studying.

3 0

3 years ago