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3 years ago

Translate the following statement into a mathematical equation:

Mathematics

1 answer:

steposvetlana [31]3 years ago

8 0

The answer is the first choice, 3(w-4)=5.

3 times = 3
a number minus four = (w-4)
is five = 5

I hope this helps.

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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

Deffense [45]

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 1.213 ×

10⁻² ft.³/hour.

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

tank is half full.

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 1.213 × 10⁻² ft.³/hour.

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6 0

3 years ago

4k-(3+3k)>2 solving inequalities, help please

nikdorinn [45]

4k-3-3k>2
1k-3>2
1k>5
k>5

6 0

4 years ago

Show that the equation Y -2= 4(3x+5) is a liner and then tell if it represents a proportional or nonproportional relationship be

Grace [21]

Answer:

y=12x+22 is linear but not proportional

Step-by-step explanation:

$y-2=4(3x+5)$

This is a linear equation because it has an x and y within the expression without exponents or other complex operators. We can rearrange and simplify the equation into slope-intercept form.

$y-2=4(3x+5)\\y-2=12x+20\\y-2+2=12x+20+2\\y=12x+22$

This linear equation follows the form y=mx+b where m is the slope and b is the y-intercept. For this function, m=12 and b=22. This is not a proportional relationship because the function's y-intercept is something other than 0.

4 0

4 years ago

13/26= x/24 solve for x

Serga [27]

Answer: x = 12

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Of the 800 sweaters at a certain store, 150 are red. How many of the red sweaters at the store are made of pure wool? (1) 320 of

vitfil [10]

Answer:

Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

Step-by-step explanation:

Judging by the first sentence, there are 800 sweaters, 150 of which are red. Hence 800 - 150 = 650 sweaters are not red.

Statement (1) mentions that 320 of the sweaters at the store are neither red nor made of pure wool. This implies that of the remaining 650 non-red sweaters, 320 of them are not made of pure wool. It tells us then that there are 650 - 320 = 330 sweaters that are not red and that are not pure wool. So, it does not give information about red sweaters at all, whether pure wool or not.

Statement (2) says 100 of the red sweaters at the store are not made of pure wool. This means out of all 150 red sweaters, 100 of them are not made of pure wool. Then we have that 150 - 100 = 50 red sweaters are made of pure wool. This is the response to the question asked.

Hence, we see that statement (2) alone is enough, while statement (1) alone is not.

8 0

3 years ago