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icang [17]
1 year ago
12

Convert the polar equation∅=45° to a Cartesian equation.Choices:y=xy=√2xy=2x

Mathematics
1 answer:
GrogVix [38]1 year ago
8 0

Explanation

Step 1:

Given data

\theta\text{ = 45}

Step 2:

Write the equations relating polar to rectangular coordinates are

\theta\text{= arc}\tan (\frac{y}{x})\text{ or }\tan (\theta)\text{ = }\frac{y}{x}\text{ and r = }\sqrt[]{x^2+y^2}

Since your polar equation has no "r" we will not need the last equation.

Step 3:

\text{Substitute the value of }\theta\text{ = 45}

Therefore

\begin{gathered} \tan 45\text{ = }\frac{y}{x} \\ \tan \text{ 45 = 1} \\ 1\text{ = }\frac{y}{x} \\ \text{Cross multiply} \\ y\text{ = x} \end{gathered}

Final answer

y = x

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Area of triangle = 1/2 x base x height

so old triangle we have  1/2 x b x h = 48

new triangle has base 3 times as long and height is half as long
 so we would get:

1/2 x (3B) x (1/2H) = area

rewrite as 1/2 x 3/2 x b x H = area

divide by original are os 1/2 x b x h and you end up with 3/2

so new area = 3/2 x old area

new area = 3/2 * 48 = 72 square inches
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Answer:

1 st expression is used in this

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What is the area of a quadrilateral with vertices at (-2, - 6),
svet-max [94.6K]

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18 sq. unit

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2 years ago
What is the value of x in the equation 2x+3y=36 when y is 6​
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2x + 3*6 = 36

2x = 36-18

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Solve for a: 5(a+5)-3=3(2-a)
ivann1987 [24]

Simplify:

5(a + 5) + -3 = 3(2 + -1a)

Reorder the terms:

5(5 + a) + -3 = 3(2 + -1a)

(5 * 5 + a * 5) + -3 = 3(2 + -1a)

(25 + 5a) + -3 = 3(2 + -1a)

Reorder the terms again:

25 + -3 + 5a = 3(2 + -1a)

Combine like terms:

]25 + -3 = 22

22 + 5a = 3(2 + -1a)

22 + 5a = (2 * 3 + -1a * 3)

22 + 5a = (6 + -3a)

Solve:

22 + 5a = 6 + -3a

To solve for variable 'a':

You have to move all terms containing A to the left, all other terms to the right.

Then add '3a' to each side of the equation:

22 + 5a + 3a = 6 + -3a + 3a

Combine like terms:

5a + 3a = 8a

22 + 8a = 6 + -3a + 3a

Combine like terms again:

-3a + 3a = 0

22 + 8a = 6 + 0

22 + 8a = 6

Add '-22' to each side of the equation.:

22 + -22 + 8a = 6 + -22

Combine like terms:

22 + -22 = 0

0 + 8a = 6 + -22

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Combine like terms once more:

6 + -22 = -16

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Divide each side by '8'.

a = -2

Simplify:

a = -2

Answer: a=-2

Hope I could help! :)

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