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2 years ago

Two times one number added to three times a second number is 21.

Mathematics

1 answer:

il63 [147K]2 years ago

5 0

Answer:

$x = - \frac{9}{17} \: \: y = \frac{125}{17 }$

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Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

2 years ago

Use the area model to find the product of 28×32

Rudiy27

When u times 28 by 32 you will get 896..I'm not sure if this is what u were asking for but if so here you go :)

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2 years ago

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What are the restrictions on the domain of g o h?

umka21 [38]

$g(x) = \sqrt{x-4}$ and h(x)= 2x-8

g o h is a composition function

First we find g o h

g o h is g(h(x))

We plug in h(x) in g(x)

We replace x with 2x-8 in g(x)

$g(h(x)) = g (2x-8) = \sqrt{2x-8-4} = \sqrt{2x-12}$

$g(h(x)) = \sqrt{2x-12}$

To find domain we look at the domain of h(x) first

Domain of h(x) is set of all real numbers

now we look at the domain of g(h(x))

Negative number inside the square root is imaginary. so we ignore negative number inside the square root

So to find domain we set 2x - 12 >=0 and solve for x

2x - 12 >=0

add both sides by 12

2x >= 12

divide both sides by 2

x > = 6

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2 years ago

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Find the distance between 13/3 and the square root of 16/9

Ainat [17]

Answer:

Root 16=4

Root 9=3

Therefore it becomes 4/3

Now distance between the two= 13/3-4/3 which is equal to 9/3 and 9 divided by 3 is 3.

Therefore the distance between the two on a number line is 3

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2 years ago

List all the factor pairs for the number 56

maks197457 [2]

1, 2, 4, 7, 8, 14, 28, and 56

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2 years ago

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