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3 years ago

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1 answer:

UNO [17]3 years ago

7 0

What do you don’t get

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A horse trot in a circle around it's trainer at the end of a 31 foot long rope. Find the area of the circle that is swept out. R

Mnenie [13.5K]

So, imagine the trainer is in the very middle of the circle and he is holding out a rope that's attached to the horse. The rope here from the trainer to the horse represents the radius of the circle. The horse trots around the trainer (middle point) in a circle.
The formula to find area of a circle is A = pi*r^2 (pi times r squared where r is radius)
We know that the radius of the "circle" here formed as the horse trots around the trainer is 31 (the 31 foot long rope).
So let r = 31 & plug the value into the formula to find circle area.
A = pi*31^2 = 3019.07054
The area is therefore 3019.07 square feet. (rounded)

3 0

2 years ago

(-2, 11) & (5,6)<br> What is the slope of the equation between these two points?

ololo11 [35]

Answer:

$m =\dfrac{-5}{7}$

Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

Two points (-2,11) and (5,6) .

And we need to find out the slope of the equation between the two points. The slope of the line passing through two points , is given by ,

$\implies Slope (m) =\dfrac{ y_2-y_1}{x_2-x_1}$

Here the two points are (-2,11) and (5,6) .So put on the respective values ,

$\implies Slope (m) =\dfrac{ 11 - 6}{-2-5}\\\\\implies Slope = \dfrac{5}{-7} \\\\\implies Slope = \dfrac{-5}{7}$

<u>Hence</u><u> the</u><u> </u><u>slope</u><u> of</u><u> the</u><u> line</u><u> is</u><u> </u><u>-</u><u>5</u><u>/</u><u>7</u><u> </u><u>.</u>

8 0

2 years ago

A hemispherical tank is filled with water and has a diameter of 14 feet. If water

tigry1 [53]

Answer:

$44,826.72\ \text{pounds}$

Step-by-step explanation:

Given that,

The diameter of a hemispherical tank= 14 feet

Radius, r = 7 feet

water

Water weighs 62.4 pounds per cubic foot.

We need to find the total weight of the water in a full tank to the nearest pound.

The volume of the hemisphere is given by :

$V=\dfrac{2}{3}\pi r^3\\\\V=\dfrac{2}{3}\pi \times (7)^3\\\\V=718.377\ \text{feet}^3$

If water weighs 62.4 pounds per cubic foot, it means

$V=718.377\times 62.4\\\\V=44,826.72\ \text{pounds}$

So, the total weight of the water is $44,826.72\ \text{pounds}$ .

3 0

2 years ago

Jason and Alison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of

Shalnov [3]

Answer:

$Owl= 67.14ft$

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

$22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}$

$22^{\circ} 8'6'' = 22.135^{\circ}$

$30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}$

$30^{\circ} 40'30'' = 30.675^{\circ}$

Considering Jason's position:

$tan(22.135^{\circ}) = \frac{H}{x + 48}$

Where x = distance between the tree and Alison

Make H the subject

$H = (x + 48)tan(22.135^{\circ})$

Considering Alison's position

$tan(30.675^{\circ}) = \frac{H}{x}$

Make H the subject

$H = xtan(30.675^{\circ})$

$H = H$

$(x + 48)tan(22.135^{\circ}) = xtan(30.675^{\circ})$

$(x + 48) *0.4068 = x* 0.5932$

Open bracket

$x *0.4068 + 48 *0.4068 = 0.5932x$

$0.4068x + 19.5264 = 0.5932x$

Collect Like Terms

$-0.5932x+0.4068x = -19.5264$

$-0.1864x = -19.5264$

$0.1864x = 19.5264$

Make x the subject

$x = \frac{19.5264}{0.1864}$

$x = 104.76$

Substitute 104.76 for x in $H = xtan(30.675^{\circ})$

$H = 104.76 * tan(30.675^{\circ})$

$H = 104.76 * 0.5932$

$H = 62.14$

The above represents the height of the tree.

The height of the owl is:

$Owl= H + 5$

$Owl= 62.14 + 5$

$Owl= 67.14ft$

7 0

2 years ago

Please help me.

mart [117]

Since they are similar both dimensions would have the same ratio. The ratio of 5 and 15 is 3. 15 is 3 times larger than 5, so the unknown dimension is 3 times larger than the known dimension.

3 x 10 = 30

The unknown dimension is 30

5 0

2 years ago