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3 years ago

State the name of the property illustrated. -6(4 + 6) = -24 + (-36)

Mathematics

1 answer:

Mice21 [21]3 years ago

3 0

Answer:

It's distributive property.

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How to solve 45 45 90 triangle given hypotenuse?

statuscvo [17]

From the Special Triangle Theorem, the hypotenuse is equal to the side lengtht times the Sqrt(2).
So hypotenuse H = xSqrt(2), x=H/Sqrt(2).
Using numbers, if H = 7, then x = 7/Sqrt(2) = 7Sqrt(2)/2 to rationalize it.

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4 years ago

How many wholes are in 11/3?

lesantik [10]

There are 3 holes because if you do 4 thats to high cuz you would get 12 hope this is what you mean

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2 years ago

Convert the following sum into a product. cosx + cos3x + cos5x + cos7x

kvv77 [185]

Answer:

$4\cos x\cos (4x)\cos (2x)$

Step-by-step explanation:

Given: $cosx + cos3x + cos5x + cos7x$

To convert: the given sum into product

Solution:

Use formula: $\cos A+\cos B=2\cos \left ( \frac{A+B}{2} \right )\cos \left ( \frac{A-B}{2} \right )$

$cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos (2x)\cos (-x)+2\cos (6x)\cos (-x)\\=2\cos (2x)\cos (x)+2\cos (6x)\cos (x)\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]$

$cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]\\=2\cos x\left [2 \cos \left ( \frac{2x+6x}{2} \right )\cos \left ( \frac{2x-6x}{2} \right ) \right ]\\=2\cos x\left [ 2\cos (4x) \cos (-2x) \right ]\\=4\cos x\cos (4x)\cos (2x)$

4 0

3 years ago

Solve using demoivres theorem

pashok25 [27]

It's difficult to make out, but I think the task is to expand

$(\sqrt3-i)^4$

Write the number in polar form first:

$\sqrt3-i=2e^{-i\pi/6}$

By DeMoivre's theorem, you have

$(\sqrt3-i)^4=\left(2e^{-i\pi/6}\right)^4=2^4e^{-i4\pi/6}=16e^{-i2\pi/3}$

and converting back to Cartesian form, this number is equivalent to

$16\left(\cos\dfrac{2\pi}3-i\sin\dfrac{2\pi}3\right)=16\left(-\dfrac12+-\dfrac{\sqrt3}2\right)=-8(1+i\sqrt3)$

3 0

3 years ago

I need help on all of this too

Dmitriy789 [7]

Here’s a picture of the answer

5 0

3 years ago