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Rama09 [41]
3 years ago
8

Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 4000/3*π in^3. One day, her sink clogged. Sh

e has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping. Hint: you may need to find the volume for both.
(A) One cup has a diameter of 4 in. and a height of 8 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work.

(B) One cup has a diameter of 8 in. and a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number, and make certain to show your work.
Mathematics
1 answer:
In-s [12.5K]3 years ago
6 0

Answer:

  (A)  125 scoops

  (B)  31 scoops

Step-by-step explanation:

The volume of a cup in terms of radius and height is ...

  V = (1/3)πr²h

The radius is half the diameter, so the volume in terms of diameter is ...

  V = (1/3)π(d/2)²h = (π/12)d²h

The number of cups it takes to empty the sink will be the sink volume divided by the cup volume, so will be ...

  n = (4000π/3)/((π/12)d²h)

  n = 16000/(d²h)

__

(A) The number of cups required of diameter 4 and height 8 is ...

  n = 16000/(4²·8) = 125

  125 scoops are required to empty the sink

__

(B) The number of cups required of diameter 8 and height 8 is ...

  n = 16000/(8²·8) = 31.25 ≈ 31

  31 scoops are required to empty the sink

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Can you please help me find the area? Thank you. :)))
Phoenix [80]

The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.

The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:

A=w\cdot l

For our rectangle w=12 in and l=20 in, the area is:

\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}

The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.

The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.

You can determine the value of x as follows:

\begin{gathered} 20=8+8+x \\ 20=16+x \\ 20-16=x \\ 4=x \end{gathered}

x=4 in → this means that the base of the triangle is 4in long.

The area of the triangle is equal to half the product of the base by the height, following the formula:

A=\frac{b\cdot h}{2}

For our triangle, the base is b=4in and the height is h=6in, then the area is:

\begin{gathered} A_{\text{triangle}}=\frac{4\cdot6}{2} \\ A_{\text{triangle}}=\frac{24}{2} \\ A_{\text{triangle}}=12in^2 \end{gathered}

Finally, to determine the area of the shape you have to subtract the area of the triangle from the area of the rectangle:

\begin{gathered} A_{\text{total}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{\text{total}}=240-12 \\ A_{\text{total}}=228in^2 \end{gathered}

The area of the figure is 228in²

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1 year ago
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Ksivusya [100]
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3 years ago
Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find
natka813 [3]

Answer:

The width of the football field is 160 feet.

The length of the football field is 360 feet.

Step-by-step explanation:

Let w represent width of the football field.

We have been given that the length is 200 ft more than the width, so the length of the field would be w+200.

We are also told that the perimeter is 1,040 ft. We know that football field is in form of rectangle, so perimeter of field would be 1 times the sum of length and width. We can represent this information in an equation as:

2(w+w+200)=1040

Let us solve for w.

2(2w+200)=1040

4w+400=1040

4w+400-400=1040-400

4w=640

\frac{4w}{4}=\frac{640}{4}

w=160

Therefore, the width of the football field is 160 feet.

Upon substituting w=160 in expression w+200, we will get length of field as:

w+200\Rightarrow 160+200=360

Therefore, the length of the football field is 360 feet.

7 0
3 years ago
The lengths of the legs of a right triangle are consecutive even integers. The hypotenuse is 58 inches. What is the sum of the l
miskamm [114]

Answer:

82 inches

Step-by-step explanation:

The difference between consecutive even integers is 2, thus

let the legs be n and n + 2

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

n² + (n + 2)² = 58² ← expand and simplify left side

n² + n² + 4n + 4 = 3364 ( subtract 3364 from both sides )

2n² + 4n - 3360 = 0 ( divide all terms by 2 )

n² + 2n - 1680 = 0 ← in standard form

(n + 42)(n - 40) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 42 = 0 ⇒ n = - 42

n - 40 = 0 ⇒ n = 40

But n > 0 ⇒ n = 40

and n + 2 = 40 + 2 = 42

Thus sum of legs = 40 + 42 = 82 inches

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3 years ago
If tan 0 = ½ then what is sin 0?
pav-90 [236]
I think its 1 right?
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3 years ago
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