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3 years ago

Find the angle of elevation of a kite on a 50m string flying 40m vertically above the ground.

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

6 0

Sin(x)=40/50
x= sin^-1(40/50)
x= 53.1301023542—>53.1 rounded to the nearest tenth
angle of elevation is 53.1

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Special Triangles

Ugo [173]

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = $\frac{\sqrt{3} }{2}$ and tan30° = $\frac{1}{\sqrt{3} }$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{6}{m}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

$\sqrt{3}$ × m = 12 ( divide both sides by $\sqrt{3}$ )

m = $\frac{12}{\sqrt{3} }$ ← rationalise by multiplying numerator/ denominator by $\sqrt{3}$ )

m = $\frac{12}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{12\sqrt{3} }{3}$ = 4 $\sqrt{3}$

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tan30° = $\frac{opposite}{adjacent}$ = $\frac{n}{6}$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

$\sqrt{3}$ × n = 6 ( divide both sides by $\sqrt{3}$ )

n = $\frac{6}{\sqrt{3} }$ ← rationalise the denominator

n = $\frac{6}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{6\sqrt{3} }{3}$ = 2 $\sqrt{3}$

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7 0

3 years ago

What is the average rate of change in f(x) over the interval [4,13]?

mestny [16]

we know that

Average Rate of Change. is the change in the y-value divided by the change in the x-value for two distinct points on the graph

$A=\frac{(f(b)-f(a))}{(b-a)}$

in this problem

$a=4\\ b=13\\ f(a)=f(4)=8\\ f(b)=f(13)=11$

substitute the values in the formula above

$A=\frac{(11-8)}{(13-4)} \\ \\ A=\frac{3}{9}$

Divide by $3$ both numerator and denominator

$A=\frac{1}{3}$

therefore

the answer is

$\frac{1}{3}$

8 0

3 years ago

Read 2 more answers

Abi had 20 cents. She bought x pencils for 3 cents each. If y equals the number of cents left, write an equation that shows the

Vladimir [108]

An equation that shows the dependence of $y$ on $x$ is $y=20-3x$ and the domain of the function is $x=[0,6], x \in N$ .

Total number of cents $= 20$ .

She bought $x$ pencils for $3$ cents each.

Let $y$ equals the number of cents left.

So, $3x+y=20$ .

$y=20-3x$

Here $y$ must be positive

So, $20-3x>0$

$20>3x$

$\frac{20}{3}>x$

Domain of a function is the set of values for which the function is defined.

So, $x$ can get values from $0$ to $6$ .

Therefore, the domain is:

$x=[0,6], x \in N$ .

Learn more about domain here:

brainly.com/question/17440903?referrer=searchResults

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3 years ago

The general equation of the plane that contains the points (1, 0, 2), (−1, 1, −2), and the origin is of the form ax + by + cz =

ICE Princess25 [194]

Answer:

2x-z=0 is the equation of the plane.

Step-by-step explanation:

Given that the plane passes through the points (1,0,2) and (-1,1,-2)

and also origin.

Hence equation of the plane passing through three points we can use

Any plane passing through 3 given points is given as

$\left[\begin{array}{ccc}x-x_1&y-y_1&z-z_1\\x_2-x_1&y_2-y_1&z_2-z_1\\x_3-x_1&y_3-y_1&z_3-z_1\end{array}\right] =0$

Substitute the three points to get

$\left[\begin{array}{ccc}x-1&y&z-2\\-1-1&1&-2-2\\0-1&0&0-2\end{array}\right] \\=0\\(x-1)(-2) -y(4-4)+(z-2)(1) =0\\-2x+z=0\\2x-z-=0$

2x-z=0 is the equation of the plane.

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4 years ago

Riley bought 50 foot or rope. He cut off pieces that total 34’8” so far. How much rope does he have left

Vedmedyk [2.9K]

Answer:

the answer is 15'2" of the rope that is left

Step-by-step explanation:

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3 years ago