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Marta_Voda [28]
3 years ago
8

A straight road rises at an inclination of 0.3 radian from horizontal. Find the slope and change in elevation over a one mile se

ction of the road.
Mathematics
1 answer:
zimovet [89]3 years ago
3 0

Answer:

As per the given statement: A straight road rises at an inclination of 0.3 radian from horizontal.

⇒Inclination\theta = 0.3 \text{radian}.

The slope is given by:

m =\tan \theta

Substitute the given value we have;

m = \tan (0.3)

m = 0.30933624961

Let Δx represents the change in horizontal distance and  Δy represents the change in vertical distance.

Slope is also defined as the change in vertical distance to the change in horizontal distance.

i.,e  m = \frac{\triangle y}{\triangle x}                     .....[1]

It is given that change in elevation over a one mile section of the road

⇒Δx = 1

Substitute the  value of Δx = 1 and m = 0.30933624961  in [1] we have;

0.30933624961 = \frac{\triangle y}{1}

or

\triangle y = 0.30933624961 mile.

Therefor, the slope is, 0.30933624961 and change in elevation over a one mile section of the road is, 0.30933624961 mile





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If the volume of the popcorn box is 74 cubic inches. Then the length of the popcorn box in inches will be 0.3 inches.

<h3>What is a rectangular prism?</h3>

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

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Its width is 3 and 1/2 in and its height is 77 in.

Then the width of the prism will be

\rm W  = 3 + \dfrac{1}{2}\\\\W = \dfrac{7}{2}

Then the length of the popcorn box in inches will be

\rm V  \ = LWH\\\\\\74= L \times \dfrac{7}{2} \times 77\\\\\\L\ = 0.2745 \approx 0.3

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F(1)=-12, f(n)=2f(n-1) <br> find first 4 terms
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<h3>First four terms are:   -12, -24, -48, -96</h3>

============================================

Explanation:

The notation f(1) = -12 tells us that the first term is -12.

The equation f(n) = 2*f(n-1) indicates that we're multiplying the (n-1)th term by 2 to get the nth term. Basically we multiply each term by 2 to get the next term.

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So the first four terms are -12, -24, -48, -96.

-----------------------------------

Alternative Approach

f(1) = -12 .... first term

f(n) = 2*f(n-1) ... nth term recursive formula

f(2) = 2*f(2-1) ... plug in n = 2

f(2) = 2*f(1)

f(2) = 2*(-12) ... plug in f(1) = -12

f(2) = -24 ... second term

f(n) = 2*f(n-1) .... resetting for the next computation

f(3) = 2*f(3-1) ... plug in n = 3

f(3) = 2*f(2)

f(3) = 2*(-24)  ... plug in f(2) = -24

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f(n) = 2*f(n-1) ... one more reset

f(4) = 2*f(4-1) .... plug in n = 4

f(4) = 2*f(3)

f(4) = 2*(-48) ... plug in f(3) = -48

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