2 years ago

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Mathematics

1 answer:

fiasKO [112]2 years ago

4 0

Answer:

the answer is option (B)

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Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

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

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

3 years ago

M∠GHI = 3x° and m∠LMN = 17x°. If ∠GHI and ∠LMN are supplementary, find the measure of each angle.

Savatey [412]

If they are supplementary then 3x + 17x = 180

20x = 180

x = 9
m<GHI = 27 degrees
m < LMN = 153 degrees

3 0

2 years ago

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What is the value of x

sergey [27]

X = 7 / sin(45)

x = 7 / sqrt(2)/2

x = 7 sqrt(2)

4 0

3 years ago

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What is 243=m+108.27?

KATRIN_1 [288]

Answer:

134.73

Step-by-step explanation:

Solving for m:

243 = m + 108.27

243 - 108.27 = m + 108.27 - 108.27

134.73 = m

7 0

3 years ago

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Caleb has driven 820 miles of his road trip. He has 20% of his trip left to go. How many miles does he have left to go? Need asp

Neporo4naja [7]

He has 164 miles left

5 0

3 years ago