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2 years ago

A circle with a radius of 15 yards contains a sector with an area of 609 yde. Find the measure of

Mathematics

1 answer:

kondaur [170]2 years ago

4 0

Answer: 310.3° or 5.41 radians.

Step-by-step explanation:

The area of a circle of radius R is calculated as:

A = pi*R^2

Now, if we have a sector of an angle θ degrees, the area of that sector is:

A = (θ/360°)*pi*R^2

In this case, we know that:

R = 15yd

And the area of the sector is 609 yd^2

Then we can replace these two values in the equation to get:

609yd^2 =(θ/360°)*3.14*(15yd)^2

(609yd^2)*360°/(3.14*(15yd)^2) = θ = 310.3°

And we want the angle also in radians.

We know that:

3.14 rad = 180°

(3.14 rad/180°) = 1

Then:

310.3° = 310.3°*(3.14 rad/180°) = (310.3°/180°)*3.14 rad = 5.41 radians.

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A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

What number is 54% of 125 type an integer or a decimal round to the nearest tenth

eimsori [14]

Answer is 67.5

To get this you must first turn 54% into a decimal.
54%---> .54
125*.54= 67.5
So 54% of 125 is 67.5 <span />

4 0

3 years ago

Read 2 more answers

Help me plz. I dont get this

Ulleksa [173]

Thats easy. figure it out

7 0

2 years ago

Which of the following describes how the margin of error is calculated?

Vika [28.1K]

The following option best describes how the margin of error is calculated: D. It is equal to the inverse of the square root of the sample size.
The small amount that is granted for in case of miscalculation or change of circumstances.

7 0

2 years ago

The base of a triangular prism is an isosceles right triangle with a hypotenuse of 32−−√ centimeters. The height of the prism is

Roman55 [17]

Isosceles triangle: two equal sides.
We have the following relationship:
root (32) = root (L ^ 2 + L ^ 2)
root (32) = root (2L ^ 2)
root (32) = Lraiz (2)
root (32) / root (2) = L
The surface area is:
Area of the base and top:
A1 = (1/2) * (root (32) / root (2)) * (root (32) / root (2))
A1 = (1/2) * (32/2)
A1 = (1/2) * (16)
A1 = 8
Area of the rectangles of equal sides:
A2 = (root (32) / root (2)) * (6)
A2 = 24
Rectangle area of different side:
A3 = (root (32)) * (6)
A3 = 33.9411255
The area is:
A = 2 * A1 + 2 * A2 + A3
A = 2 * (8) + 2 * (24) + (33.9411255)
A = 97.9411255
Round to the nearest tenth:
A = 97.9 cm
Answer:
The surface area of the triangular prism is:
A = 97.9 cm

3 0

3 years ago