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Tom [10]
3 years ago
8

Line p passes through A(-2, -4) and has a slope of - 1/2

Mathematics
1 answer:
Alenkasestr [34]3 years ago
8 0
M = -1/2
(x₁, y₁) = (-2,-4)

Find the equation
y - y₁ = m(x - x₁)
y - (-4) = -1/2 (x - (-2))
y + 4 = -1/2 (x + 2)
2(y + 4) = -1 (x + 2)
2y + 8 = -x - 2
x + 2y = -10
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Step-by-step explanation:

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The formula for the volume sphere is V=4/3pie r^3 what is the formula solved for r?
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Answer:

r = \sqrt[3]{\frac{3V}{4 \pi}}

Step-by-step explanation:

From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.

V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r

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A hot air balloon is flying at an altitude of 800 feet. A passenger takes a picture of the top of a tree and estimates that the
nalin [4]

The height of the tree given the depression angle to the top and the base

is given by the tangent relationship of the two given angles.

Correct response:

  • The height of the tree is approximately <u>79.58 feet</u>
<h3 /><h3>Methods used for the calculation of the height of the tree</h3>

Given:

Altitude of the hot air balloon = 800 feet

Angle of depression to top of tree = 43°

Angle of depression to base of tree = 46°

Required:

Height of tree

Solution:

The horizontal distance of the balloon from the tree is given as follows;

  • \displaystyle tan(46^{\circ}) = \frac{Altitude \ of \ balloon}{Horizontal \ distance \ from \ tree} = \mathbf{\frac{800 \, feet}{Horizontal \ distance \ from \ tree}}

Therefore;

\displaystyle Horizontal \ distance \ of \ balloon \  from \ tree = \frac{800 \ feet}{tan(46^{\circ})}

  • \displaystyle tan(43^{\circ})  = \mathbf{\frac{Height \ of \ balloon \ above \ tree}{\dfrac{800 \, feet}{tan(46^{\circ})} }}

Therefore;

\displaystyle Height \ of \ balloon \ above \ tree = tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})}

  • Height of tree = Altitude of balloon - Height of balloon above tree

Therefore;

  • \displaystyle Height \ of \ tree = 800 \, feet - tan(43^{\circ}) \times \frac{800 \, feet}{tan(46^{\circ})} \approx \underline{  79.58 \, feet}

Learn more about angle of elevation and depression here:

brainly.com/question/1978238

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