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JulsSmile [24]
4 years ago
12

Can you help me find the answer and explain it to me?

Mathematics
1 answer:
Mashutka [201]4 years ago
7 0
To find the area of a RIGHT ANGLE triangle, you do base x height then divide it by two.

(we divide by two because a parallelogram can be split into two triangles so we’re basically finding the area of that triangle twice to make an imaginary parallelogram then halving it to get the area of just the triangle).

because you didn’t attach a photo, im not entirely sure which length you gave is the height and base but because a rule for right angle triangles is that the longest length (called the hypotenuse) is always opposite the angle so we’re gonna assume that 32. 5cm is the hypotenuse for this triangle.

this means that 31.2cm and 9.1cm are our base and height length (interchangeable).

so we do
— 31.2 x 9.1 = 283.92
— 283.92 / 2 = 141.96cm squared (because it’s an area!)

hope this helped~ :)
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Answer:

0.07

Step-by-step explanation:

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3 years ago
Water is being pumped into a conical tank that is 8 feet tall and has a diameter of 10 feet. If the water is being pumped in at
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The rate of change of the depth of water in the tank when the tank is half

filled can be found using chain rule of differentiation.

When the tank is half filled, the depth of the water is changing at  <u>1.213 × </u>

<u>10⁻² ft.³/hour</u>.

Reasons:

The given parameter are;

Height of the conical tank, h = 8 feet

Diameter of the conical tank, d = 10 feet

Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.

Required:

The rate at which the depth of the water in the tank is changing when the

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Solution:

The radius of the tank, r = d ÷ 2

∴ r = 10 ft. ÷ 2 = 5 ft.

Using similar triangles, we have;

\dfrac{r}{h} = \dfrac{5}{8}

The volume of the tank is therefore;

V = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}

r = \dfrac{5}{8} \times h

Therefore;

V = \dfrac{1}{3} \cdot \pi \cdot \left(  \dfrac{5}{8} \times h\right)^2 \cdot h = \dfrac{25 \cdot h^3 \cdot \pi}{192}

By chain rule of differentiation, we have;

\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \cdot \dfrac{dh}{dt}}

\dfrac{dV}{dh}=\dfrac{d}{h} \left(  \dfrac{25 \cdot h^3 \cdot \pi}{192} \right) = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64}}

\dfrac{dV}{dt} = \dfrac{3}{5}  \ ft.^3/hour

Which gives;

\dfrac{3}{5} =  \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64} \times \dfrac{dh}{dt}}

When the tank is half filled, we have;

V_{1/2} = \dfrac{1}{2} \times  \dfrac{1}{3} \times \pi \times 5^2 \times 8 =\mathbf{ \dfrac{25 \cdot h^3 \cdot \pi}{ 192}}

Solving gives;

h³ = 256

h = ∛256

\dfrac{3}{5} \times \dfrac{64}{25 \cdot h^2 \cdot \pi} = \dfrac{dh}{dt}

Which gives;

\dfrac{dh}{dt} = \dfrac{3}{5} \times \dfrac{64}{25 \cdot (\sqrt[3]{256}) ^2 \cdot \pi} \approx \mathbf{1.213\times 10^{-2}}

When the tank is half filled, the depth of the water is changing at  <u>1.213 × 10⁻² ft.³/hour</u>.

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