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3 years ago

Hey! Can someone please help me with this question? Really appreciate it

Mathematics

1 answer:

Olin [163]3 years ago

3 0

Answer:

$d = 0.112* 10^3$

Step-by-step explanation:

Given

$h = 8.4 * 10^3$

$d = \sqrt{\frac{3h}{2}}$

Required

Find d

We have:

$d = \sqrt{\frac{3h}{2}}$

Substitute: $h = 8.4 * 10^3$

$d = \sqrt{\frac{3*8.4 * 10^3}{2}}$

$d = \sqrt{\frac{25.2 * 10^3}{2}}$

$d = \sqrt{12.6 * 10^3}$

Express as:

$d = \sqrt{1.26 *10* 10^3}$

$d = \sqrt{1.26 *10^4}$

Split

$d = \sqrt{1.26} *\sqrt{10^4}$

$d = 1.122* 10^2$

To write in form of: $a * 10^b$

The value of a must be: $0 \le a \le 1$

So, we have:

$d = 0.1122* 10 * 10^2$

$d = 0.1122* 10^3$

Approximate

$d = 0.112* 10^3$

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A figure has an area of 64 unit square which describes the area of the figure after a dilation with a scale factor of 3/2

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Step-by-step explanation:

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2 years ago

Find all the complex roots. Write the answer in exponential form.

dezoksy [38]

We have to calculate the fourth roots of this complex number:

$z=9+9\sqrt[]{3}i$

We start by writing this number in exponential form:

$\begin{gathered} r=\sqrt[]{9^2+(9\sqrt[]{3})^2} \\ r=\sqrt[]{81+81\cdot3} \\ r=\sqrt[]{81+243} \\ r=\sqrt[]{324} \\ r=18 \end{gathered}$ $\theta=\arctan (\frac{9\sqrt[]{3}}{9})=\arctan (\sqrt[]{3})=\frac{\pi}{3}$

Then, the exponential form is:

$z=18e^{\frac{\pi}{3}i}$

The formula for the roots of a complex number can be written (in polar form) as:

$z^{\frac{1}{n}}=r^{\frac{1}{n}}\cdot\lbrack\cos (\frac{\theta+2\pi k}{n})+i\cdot\sin (\frac{\theta+2\pi k}{n})\rbrack\text{ for }k=0,1,\ldots,n-1$

Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.

To simplify the calculations, we start by calculating the fourth root of r:

$r^{\frac{1}{4}}=18^{\frac{1}{4}}=\sqrt[4]{18}$

<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>

Then, we calculate the arguments of the trigonometric functions:

$\frac{\theta+2\pi k}{n}=\frac{\frac{\pi}{2}+2\pi k}{4}=\frac{\pi}{8}+\frac{\pi}{2}k=\pi(\frac{1}{8}+\frac{k}{2})$

We can now calculate for each value of k:

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Answer:

The four roots in exponential form are

z0 = 18^(1/4)*e^(i*π/8)

z1 = 18^(1/4)*e^(i*5π/8)

z2 = 18^(1/4)*e^(i*9π/8)

z3 = 18^(1/4)*e^(i*13π/8)

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STatiana [176]

Hey there!
Let's break this expression into two parts:
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To solve the first part, we need to use the distributive property which states:
a(b+c) = ab+ac

Applying that to this problem, we have:
6(3x) + 6(-1) =
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Now, we can take that -10x and put it right back in:

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Combine like terms and subtract the 10x from the 18x to get:
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Hope this helps!

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3 years ago

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lubasha [3.4K]

X^2-14x+49=0

Factor
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Check
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Use ZPP
x-7=0
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Final answer: x=7

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3 years ago

Read 2 more answers