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zalisa [80]
3 years ago
15

To measure the height of a tree, a surveyor walked a short distance from the tree and found the angle of elevation was 43.9°, th

en walked 20 feet farther and measured the angle of elevation to be 37.6°. Find the height of the tree.

Mathematics
1 answer:
padilas [110]3 years ago
4 0

Answer:

The height of the tree is H = 77.06 m

Step-by-step explanation:

From Δ ABC

AB = height of the tree

\tan 43.9 = \frac{AB}{BC}

\tan 43.9 = \frac{h}{x}

h = 0.9623 x ------- (1)

From Δ ABD

\tan 37.6 = \frac{h}{20+ x}

h = 0.77 (x + 20) ----- (2)

Equating Equation  1 & 2 we get

0.9623 x =  0.77 (x + 20)

0.9623 x = 0.77 x + 15.4

x (0.1923) = 15.4

x = 80.08 m

Thus the height of the tree is given by

H = 0.9623 x

H = 0.9623 × 80.08

H = 77.06 m

Therefore the height of the tree is H = 77.06 m

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Luda [366]
EQUATION 1: x-y=12
EQUATION 2: 3x+y=4

STEP 1:
solve for one variable in equation 1

x - y= 12
add y to both sides

x= 12 + y


STEP 2:
use x value from step 1 and substitute in equation 2

3x + y= 4

3(12 + y) + y= 4
multiply 3 by parentheses

(3*12) + (3*y) + y= 4
multiply inside parentheses

36 + 3y + y= 4
combine like terms

36 + 4y= 4
subtract 36 from both sides

4y= -32
divide both sides by 4

y= -8


STEP 3:
substitute y value from step 2 into either equation

x - y= 12
x - (-8)= 12
x + 8= 12
subtract 8 from both sides
x= 4


CHECK:
x= 4, y= -8

3x + y= 4
3(4) + (-8)= 4
12 - 8= 4
4= 4


ANSWER: The x value is 4 and the y value is -8.

Hope this helps! :)
5 0
3 years ago
Sid had $42 he owned $10 to his brother .Choose the correct expression to show this
Dafna11 [192]

Answer:

B. 42-10

Step-by-step explanation:

It is the amount that Sid has minus what he ows

7 0
3 years ago
Read 2 more answers
Can someone check whether its correct or no? this is supposed to be the steps in integration by parts​
Gwar [14]

Answer:

\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}

Step-by-step explanation:

\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}

Given integral:

\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x

\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:

\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x

Using <u>integration by parts</u>:

\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)

\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}

Therefore:

\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}

\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:

\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)

\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}

\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}

Therefore:

\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x

\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:

\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}

Divide both sides by 2:

\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}

Rewrite in the same format as the given integral:

\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}

5 0
2 years ago
Please help me this is a study island question!
algol13

Answer:

It's C

Step-by-step explanation:

I believe my calculations are correct

7 0
3 years ago
Given:<br> A6, 4), M(8, 1)<br> Find: B
777dan777 [17]

Answer:

Coordinates for B= (10,-2)

Step-by-step explanation:

The solution is shown in the image provided step by step, as it was not possible typing it on this given space here. Hope it helps :)

3 0
3 years ago
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