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jek_recluse [69]
3 years ago
8

What would be the angle of elevation of a tree from the ground, if the height of the

Mathematics
1 answer:
garri49 [273]3 years ago
7 0

Answer:

45°

Step-by-step explanation:

The diagram for this question has been attached to this response. Please check.

<em>The angle of elevation is the angle between a horizontal line from a viewer and the line of sight to an object being viewed which is above the horizontal line.</em>

From the diagram;

θ is the angle of elevation

x = height of the tree

y = length of the shadow of the tree = x

Therefore,

tanθ = \frac{x}{y}           [Remember that y = x? Then substitute into the equation]

tanθ = \frac{x}{x}

tanθ = 1

θ = tan⁻¹(1)

θ = 45°

Therefore, the angle of elevation is 45°

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Consider the force field and circle defined below.
grin007 [14]

By Green's theorem,

\displaystyle\int_{x^2+y^2=9}\vec F(x,y)\cdot\mathrm d\vec r=\iint_D\left(\frac{\partial(xy)}{\partial x}-\frac{\partial(x^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_Dy\,\mathrm dx\,\mathrm dy

where C is the circle x^2+y^2=9 and D is the interior of C, or the disk x^2+y^2\le1.

Convert to polar coordinates, taking

\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta

Then the work done by \vec F on the particle is

\displaystyle\iint_Dy\,\mathrm dx\,\mathrm dy=\int_0^{2\pi}\int_0^3(r\sin\theta)r\,\mathrm dr\,\mathrm d\theta=\left(\int_0^{2\pi}\sin\theta\,\mathrm d\theta\right)\left(\int_0^3r^2\,\mathrm dr\right)=\boxed0

4 0
3 years ago
How do u subtract 4/8 from 5/8
Westkost [7]
1/8 is the answer when you subtract 4/8from 5/8
3 0
3 years ago
Sum 2 5/8 + 4 1/8 = ?
Lostsunrise [7]

Answer:

6 6/8 OR 6 3/4

Step-by-step explanation:

2 5/8 +4 1/8

6 6/8

SImplify= 6 3/4

4 0
3 years ago
Read 2 more answers
Alex invests $2,000 in a company's stock. After a year, the value of Alex's stock has increased to $2,500. What rate of return h
Kay [80]

The rate of interest is 25%

<u>Explanation:</u>

Given:

Principal, P = $2,000

Amount, A = $2500

Time, t = 1 year

Rate of Interest, r = ?

We know:

Amount = P(1+\frac{r}{100})^t

On substituting the value we get:

2500 = 2000 (1 + \frac{r}{100})^1\\ \\\frac{25}{20}= (1+\frac{r}{100})\\

\frac{5}{20} = \frac{r}{100}\\  \\r = \frac{100 X 5}{20} \\\\r = 25

Therefore, the rate of interest is 25%

5 0
3 years ago
Read 2 more answers
In triangle ABC, a = 9, c = 5, and angle B = 120°. Find the measure of angle A to the nearest degree. Show your work.
slamgirl [31]

<u>Answer:</u>

Angle A = 39°

<u>Step-by-step explanation:</u>

We are given that there is a triangle ABC where a = 9, c = 5 and angle B = 120° and we are to find the measure of angle A.

But first we need to find the side b using the law of cosine:

b^2 = a^2 + c^2- 2a*c*cos(120)

b^2 = 81 + 25 - 2*9*5*(-0.5)

b=\sqrt{151}

Now finding angle A using law of cosine:

cos(A) = \frac{b^2+c^2-a^2}{2b*c}

cos(A) = \frac{151+25-81}{2*12.29*5}

cos A=0.7730

A=39.38

Therefore, the measure of angle A = 39°.

7 0
3 years ago
Read 2 more answers
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