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vova2212 [387]
2 years ago
8

A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by t

he x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 16 feet tall. The other tree is 11 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth. Need answer ASAP.
Mathematics
1 answer:
statuscvo [17]2 years ago
7 0

The distance from the base of the tree to the tallest would be 14.21 cm

<h3>We have the following data points in this question</h3>

X1 = 8 feet

y1 = 16 feet

x2 = 11 feet

y2 = 9 feet

To proceed with the solution we have to

We have to solve for the shorter tree

\sqrt{(y2 -y1)^2 + (x2-x1)^2} \\\\= \sqrt{9-0^2 + 11-0^2}

<em>= </em>9² + 11²

= √81 +121

= 14.21

<h3>For the taller tree we would have</h3>

√8² + 16²

= √64 +256

= 17.89

Read more on distance here:

brainly.com/question/2854969

#SPJ1

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3 years ago
How to solve this?<br> Please explain step by step
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Step-by-step explanation:

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8 0
3 years ago
(a) Find the equation of the normal to the hyperbola x = 4t, y = 4/t at the point (8,2).
gtnhenbr [62]

The slope of the tangent line to the curve at (8, 2) is given by the derivative \frac{dy}{dx} at that point. By the chain rule,

\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}

Differentiate the given parametric equations with respect to t :

x = 4t \implies \dfrac{dx}{dt} = 4

y = \dfrac4t \implies \dfrac{dy}{dt} = -\dfrac4{t^2}

Then

\dfrac{dy}{dx} = \dfrac{-\frac4{t^2}}4 = -\dfrac1{t^2}

We have x=8 and y=2 when t=2, so the slope at the given point is \frac{dy}{dx} = -\frac14.

The normal line to the same point is perpendicular to the tangent line, so its slope is +4. Then using the point-slope formula for a line, the normal line has equation

y - 2 = 4 (x - 8) \implies \boxed{y = 4x - 30}

Alternatively, we can eliminate the parameter and express y explicitly in terms of x :

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2 years ago
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6 0
3 years ago
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Lerola and her younger sister Kiara are jogging around a circular track. Lerola jogs far enough from the center of the circle th
xxTIMURxx [149]

Circumference of circular track, C = 0.5 miles = 0.5×5280 feet = 2640 feet.

We know, circumference in circle is given by :

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Therefore, distance between centre and track is 420.38 feet .

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3 years ago
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