Ask question

Ask question

All categories

2 years ago

9

The area of a sector of a circle is given by the equation uppercase A = StartFraction pi r squared uppercase S Over 360 EndFract

ion, where r is the radius of the circle and S is the angle measure of the sector.

1 answer:

Ganezh [65]2 years ago

8 0

Answer:360A/pi ^2

Step-by-step explanation:

You might be interested in

A rental car agency charges $200.00 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $3

Setler79 [48]

Equation: 0.25x + 200
0.25x + 200 = 345
0.25x = 145
140/0.25 = 580 miles
Answer: 580 miles

3 0

3 years ago

Roll two dice what are the chances you roll atleast one six

Lesechka [4]

It is not very likely you would roll one six.

5 0

3 years ago

Elimination Method: 6x - 4y = -24 and 4x + 5y = -2

nirvana33 [79]

Answer:

$(-2;-6)$

Step-by-step explanation:

First of all, let's rewrite the first one after dividing both sides by 2.

$\left \{ {{3x-2y=-12\atop {4x+5y=-2}} \right.$

Now, let's pick one you want to eliminate.

<u>Eliminating x:</u> Let's multiply the first one by 4, the second by 3, and subtract one from the other. Rest is simply solving an equation in one variable

$4I-3II : 12x-8y-12x+15y = -48 - (-6)\\7y = -42 \rightarrow y= -6$

<u>Eliminating y:</u> Let's multiply the first by 5, the second by 2, and add them together. Rest is simply solving an equation in one variable

$5I+2II: 15x -10y +8x +10y = -60 +4\\23x = -56 \rightarrow x=-2$

4 0

2 years ago

You use a garden hose to fill a wading pool. If the water level rises 16 centimeters every 7 minutes

Sergeeva-Olga [200]

Rise=16, run=7. Slope is rise/run, and therefore is 16/7. The run is considered to be the x coordinate. Since the x coordinate on the point is 21, we know it has moved 3 exact points away from the origin (21/7=3). We can use this movement of 3 exact points to determine the y coordinate as well. Since the rise (y) is 16 for every exact point on a graph, we know the graph has risen 48 units (16x3=48). So, the point ends up being (21,48). The rate of change is 16cm per 7 minutes, or 2.28cm/minute. The equation is Y=(16/7)X (no y intercept because the graph starts at the origin). The equation gives you the y value of 48 when x is equal to 21.

3 0

2 years ago

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

Novosadov [1.4K]

Answer:

$A(t)=240-220e^{-\frac{t}{40}}$

Step-by-step explanation:

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved.

Volume of the tank = 240 liters
Initial Amount of Salt in the tank, A(0)=20 grams

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

$R_{in}=$ (concentration of salt in inflow)(input rate of fluid)

$R_{in}=(1\frac{gram}{liter})( 6\frac{Liter}{min})=6\frac{gram}{min}$

$R_{out}=$ (concentration of salt in outflow)(output rate of fluid)

$R_{out}=(\frac{A(t)}{240})( 6\frac{Liter}{min})\\R_{out}=\frac{A}{40}$

Rate of change of the amount of salt in the tank:

$\dfrac{dA}{dt}=R_{in}-R_{out}$

$\dfrac{dA}{dt}=6-\dfrac{A}{40}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{40}=6\\$The integrating factor: e^{\int \frac{1}{40}dt} =e^{\frac{t}{40}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{40}}+\dfrac{A}{40}e^{\frac{t}{40}}=6e^{\frac{t}{40}}\\(Ae^{\frac{t}{40}})'=6e^{\frac{t}{40}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{40}})'=\int 6e^{\frac{t}{40}} dt\\Ae^{\frac{t}{40}}=6*40e^{\frac{t}{40}}+C, $(C a constant of integration)\\Ae^{\frac{t}{40}}=240e^{\frac{t}{40}}+C\\$Divide all through by e^{\frac{t}{40}}\\A(t)=240+Ce^{-\frac{t}{40}}$

Recall that when t=0, A(t)=20 (our initial condition)

$20=240+Ce^{-\frac{0}{40}}\\20-240=C\\C=-220\\$Therefore, the number A(t) of grams of salt in the tank at time t\\A(t)=240-220e^{-\frac{t}{40}}$

3 0

2 years ago