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2 years ago

If the radius of the circle is 12 inches, the area of the sector contained by the minor arc and two radii is what?

Mathematics

1 answer:

earnstyle [38]2 years ago

8 0

Answer:

113.14 Inches²

Step-by-step explanation:

The area of a sector A contain by the minor arc of a circle is given as

A = Ф°/360 * πr²

Where Ф is the angle formed in the arc, π is a constant given as 22/7 and r is the radius of the circle.

Given that the minor arc is contained by two radii, the angel between them is 90° hence, the area of the arc

= 90/360 * 22/7 * 12²

= 113.14 Inches²

You might be interested in

A candy company claims that 25% of the candies in its bags are colored green. Steve buys 32 bags of 32 candies, randomly selects

Luden [163]

Answer:

45.88%

Step-by-step explanation:

We have in this case a binomial distribution when p = 0.25, since the probability is 25%

. The formula that we will use in excel is BINOM.DIST, separated by commas we must put the value of x, n, p and also if it is true or false. We know that n equals 32.

In this case we need to know when x = 7, 8 and 9 and add this, and thus we will obtain the probability:

P (X = 7) + P (X = 8) + P (X = 9)

Excel formulas: = BINOM.DIST (7,32,0.25, FALSE) + BINOM.DIST (8,32,0.25, FALSE) + BINOM.DIST (9,32,0.25, FALSE)

P = 0.1546 + 0.1610 + 0.1431

P = 0.4588

Probability that steve agrees with the company's claim 45.88%

4 0

2 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

2 years ago

Suppose that – in any given time period – a certain stock is equally likely to go up 1 unit or down 1 unit, and that the outcome

Scorpion4ik [409]

Answer:

Step-by-step explanation:

From the given information:

Let X represent the amount of the stock that goes up in the first period; &

Let Y denote the cumulative amount that goes up in the first three periods.

Then,

$X= X_1 + X_2 \\ \\ \\EX= EX_1 +EX_2\\ \\\\Now ; EX = 0 \\ \\ EX = \dfrac{1}{2}\times 1 + \dfrac{1}{2}\times -1 \\ \\ EX = \dfrac{1}{2}-\dfrac{1}{2} \\ \\ EX = 0$

$Cov(x,y) = Var(X_1) +Var(X_2) \\ \\ =\dfrac{1}{2}(1+1) + \dfrac{1}{2}(1+1) \\ \\ = \dfrac{1}{2}(2)+ \dfrac{1}{2}(2) \\ \\ = 1+1 \\ \\ =2$

$Var (X) = Var (X_1+X_2)\\ \\ = 2 \ Var(X_1) \\ \\ = 2 \times (1) \\ \\ = 2$

$Var (Y) = Var (X_1 +X_2+X_3) \\ \\ = 3 \times Var(X_1) = \\ \\ = 3 \times 1\\ \\ = 3$

∴

$Corr(x,y) = \dfrac{2}{\sqrt{6}} \\ \\ = \dfrac{2}{\sqrt{2\times 3}} \\ \\= \sqrt{\dfrac{2}{3}}$

3 0

1 year ago

The price of a math book after a discount of 25% is $36. What is the original price of the math book?

UNO [17]

If $36=75%,
That means we can divide both sides by three to get $12=25%,
And because 25x4 is 100, we multiply both sides of the equation by 4 to get $48=100%,
So the answer is $48 dollars.

This also worked for me but I’m not sure it’s the most reliable way:
36 ÷ 0.75 = 48
(amount after discount ÷ percentage that is remaining)

3 0

2 years ago

Pam bought 50 kg of sugar. She used 10 kg of sugar. What percentage of sugar was left? (step by step answer would be appreciated

galben [10]

Answer:

80%

Step-by-step explanation:

50 x 50 would be 100 and 50kg=100% and 10 x 2 = 20 so you used 20% therefore you have 80% left.

8 0

2 years ago

Read 2 more answers