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3 years ago

6

A circus tent is supported by a rope that is staked to the ground. The tent makes a 90 angle with the ground. The following visu

al depicts the arrangement. Solve for the length of rope supporting the tent as well as the distance between the stake and the tent, if the tent is 40 feet tall Round to the nearest hundredth.

1 answer:

Crazy boy [7]3 years ago

3 0

The value of x is 34.64 feet

<h3>Right-angled triangle</h3>

Find the diagram attached

The height of the tent = 40 ft
length of the rope = x

Get the value of x using the SOH CAH TOA identity

$sin 60 = \frac{x}{40}\\0.8660 = \frac{x}{40}\\x = 40(0.8660)\\x = 34.64feet$

Hence the value of x is 34.64 feet

Learn more on SOH CAH TOA here: brainly.com/question/20734777

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A cylinder has a diameter of 6 feet. the volume of the cylinder is 36/5π cubic feet.

Anton [14]

Answer:

Height of cylinder is $\frac{4}{5}\ ft$ .

Step-by-step explanation:

Diameter of cylinder, D = 6 feet

Relation between Radius, R and diameter, D is given by:

$R = \dfrac{D}{2}$

So, radius, R = $\frac{6}{2} \Rightarrow 3$ feet

Let height of cylinder be $h$ feet.

Formula for volume of cylinder is given by:

$V = \pi R^{2} H$

Where, R is the radius of base of cylinder

and H is the height of cylinder

We are given that,

$V = \dfrac{36 \pi}{5} ft^{3}$

Using formula for volume, $V = \pi R^{2} H$

$\dfrac{36\pi}{5} = \pi \times 3^{2} \times h\\\Rightarrow \dfrac{36\pi}{5} = \pi \times 9 \times h\\\Rightarrow h = \dfrac{4}{5} ft$

Hence, Height of cylinder is $\frac{4}{5}\ ft$ .

7 0

3 years ago

Please help me. I have an idea of what the answer might be but I’m not sure so I need you to help me clarify if I was correct so

Gemiola [76]

Hello!

<em>According to the diagram, your answer is</em> <em>D.) Some Elephants have tusks</em>

If the entire circle labeled "Elephants" was inside the circle labeled "Animals With Tusks," it would be A, but that is not the case. only part of it is inside. so D is the correct answer.

I hope this helps, and have a nice day!

8 0

3 years ago

Read 2 more answers

In which number is the digit 5 one hundred times larger than it is in the number 253?

Paraphin [41]

The answer is B.
I timesed 50 by 100 and 1,000. So 5 would be in the thousands place.

7 0

3 years ago

Read 2 more answers

A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t

frosja888 [35]

The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y

since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

$\mathbf{L = 3x - 2( \dfrac{1000000}{x})}$

$\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}$

$\mathbf{ x^2= \dfrac{2000000}{3} }$

$\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }$

$\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}$

Now, if we replace the value with equation (1), then y will be:

$\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\ \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}$

$\mathbf{x =500\sqrt{6}}$

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

$\mathbf{L = 3( \dfrac{1000 \sqrt{6}}{3}) + 2(500 \sqrt{6})}$

$\mathbf{L =1000 \sqrt{6} + 1000 \sqrt{6}}$

$\mathbf{L =2000 \sqrt{6} }$

$\mathbf{L \simeq 4899 \ ft}$

Learn more about the area of a rectangle here:

brainly.com/question/25292087

6 0

2 years ago

Apply the properties of exponents to rewrite each expression in the form kxn, where nn is an integer and x ≠0

professor190 [17]

Answer:

The expression will be $0.333x^{-2}$

Step-by-step explanation:

We have given expression $\frac{x^{-3}x^5}{3x^4}$

We know the property of exponent that when two function are divided then the power of exponent is subtracted and when there is multiplication of two function then exponent is added

So $\frac{x^{-3}x^5}{3x^4}=\frac{x^{2}}{3x^4}=0.333x^{-2}$

So the expression will be $0.333x^{-2}$

4 0

3 years ago