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3 years ago

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The angle of elevation from ground level to the top of a water tower that is 280 feet away measures 27 degrees. What is the heig

ht of the tower? Round the answer to the nearest foot. (Hint: Draw a picture to determine the trig function that will solve this problem.)

1 answer:

viva [34]3 years ago

6 0

1663is the height to the nearest foot

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At what x-values do the graphs of the functions y=cos 2x and y = cos^2 x-1 intersect over the interval 0 ≤ x ≤ pi. There must be

baherus [9]

Answer:

$x=\frac{\pi}{2}$ and $x=\frac{3\pi}{2}$

Step-by-step explanation:

We need to solve the 2 equations to figure out the x-values (intersecting points).

<em>Note: </em>The identity $cos^{2}x=\frac{1}{2}+\frac{1}{2}cos(2x)$

$cos(2x)=cos^{2}(x)-1\\cos(2x)=(\frac{1}{2}+\frac{1}{2}cos(2x))-1\\cos(2x)=\frac{1}{2}cos(2x)-\frac{1}{2}\\\frac{1}{2}cos(2x)=-\frac{1}{2}\\cos(2x)=-1\\2x=cos^{-1}(-1)\\2x=\pi, 3\pi\\x=\frac{\pi}{2}, \frac{3\pi}{2}$

So they intersect at $x=\frac{\pi}{2}, \frac{3\pi}{2}$

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The coordinates of ∆ABC are A(-3, 2), B(5, 8) & C(11, 0). Which type of triangle is ∆ABC? Select All that apply.

stepan [7]

Given:

The coordinates of ∆ABC are A(-3, 2), B(5, 8) & C(11, 0).

To find:

The type of the given triangle.

Solution:

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the distance formula, we get

$AB=\sqrt{(5-(-3))^2+(8-2)^2}$

$AB=\sqrt{(8)^2+(6)^2}$

$AB=\sqrt{64+36}$

$AB=\sqrt{100}$

$AB=10$

Similarly,

$BC=\sqrt{(11-5)^2+(0-8)^2}$

$BC=\sqrt{(6)^2+(8)^2}$

$BC=\sqrt{36+64}$

$BC=\sqrt{100}$

$BC=10$

And,

$AC=\sqrt{(11-(-3))^2+(0-2)^2}$

$AC=\sqrt{(14)^2+(-2)^2}$

$AC=\sqrt{196+4}$

$AC=\sqrt{200}$

$AC=10\sqrt{2}$

Two sides of the triangle are equal, i.e., $AB=BC$ . So, the triangle is an isosceles triangle.

Sum of square of two smaller side is

$AB^2+BC^2=10^2+10^2$

$AB^2+BC^2=100+100$

$AB^2+BC^2=200$

$AB^2+BC^2=AC^2$

Using the Pythagoras theorem, we can say that the given triangle is a right triangle.

Therefore, the correct options are B and F.

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A CD tower is shaped like a cylinder and holds CDs with a diameter of 4.75 inches. If the CD tower is 12 inches tall, what is it

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The height of a man is 1.7 meters. what is his height in centimeters.

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The prefix centi means 100. If you want to convert meters to centimeters, simply multiply by 100! For converting centimeters into meters, just divide by 100. Good luck, hope this helps!

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Step-by-step explanation:

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