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3 years ago

If 5 miles = 8 km, about how many miles would be equal to 66km?

Mathematics

2 answers:

kondor19780726 [428]3 years ago

8 0

Answer:

41.25 miles

Step-by-step explanation:

What you first want to do is to divide 66 by 8, and you would recieve 8.25.

Next Multiply 8.25 by 5 and the would be the amount of miles that is equal to 66km

Aneli [31]3 years ago

6 0

Answer:

41.25

Step-by-step explanation:

5 miles = 8 km

$\frac{66}{8}$ = 8.25km

5 x 8.25 = 41.25 miles

41.25 miles = 66km

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A camera is mounted at a point 4000 feet away from a geyser. If the water is rising vertically at 900 ft/s when it is 3000 feet

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Answer:

$\dot \theta = 0.144\,\frac{rad}{s}$ , $\dot \theta = 8.251\,\frac{deg}{s}$ (Option B)

Step-by-step explanation:

The trigonometric diagram is included herein as attachment. The expression is presented below:

$\tan \theta = \frac{y}{x}$

Where:

$x$ - Horizontal distance between the geyser and the camera.

$y$ - Vertical distance between the geyser and the camera.

The rate of change in terms of time is:

$\dot \theta \cdot \sec^{2}\theta = \frac{\dot y\cdot x-y\cdot \dot x}{x^{2}}$

$\dot \theta \cdot \left(\frac{1}{\cos^{2}\theta} \right) = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}}$

$\dot \theta = \left(\frac{\dot y \cdot x - y \cdot \dot x}{x^{2}} \right)\cdot \cos^{2}\theta$

$\dot \theta = \left(\frac{\dot y \cdot x - y\cdot \dot x}{x^{2}} \right)\cdot \left(\frac{x^{2}}{x^{2}+y^{2}} \right)$

$\dot \theta = \frac{\dot y \cdot x - y\cdot \dot x}{x^{2}+y^{2}}$

Finally,

$\dot \theta = \frac{\left(900\,\frac{ft}{s} \right)\cdot (4000\,ft)-(3000\,ft)\cdot \left(0\,\frac{ft}{s} \right)}{(4000\,ft)^{2}+(3000\,ft)^{2}}$

$\dot \theta = 0.144\,\frac{rad}{s}$

$\dot \theta = 8.251\,\frac{deg}{s}$

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