Consider the following function.

Use this image to answer questions 5 & 6. < BAC = 44° and < BCD = 131°

sashaice [31]

There are 2 angle measurements not identified.

Angle ACB and angle ABC.

To find angle ACB you need to know that a straight line is 180 degrees, so if the angle to the right is 131, the angle to the left (Angle ACB) must be 49 degrees.

To find angle ABC, you need to know that the sum of all 3 angles in a triangle equal 180 degrees, so 180 - (49 + 44) = 87 degrees. Angle ABC is 87 degrees.

8 0

3 years ago

Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

aliya0001 [1]

Answer:

$A=1500-1450e^{-\dfrac{t}{250}}$

Step-by-step explanation:

The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.

Volume = 500 gallons

Initial Amount of Salt, A(0)=50 pounds

Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min

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

$=(2\frac{lbs}{gal})( 3\frac{gal}{min})\\R_{in}=6\frac{lbs}{min}$

When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

Concentration c(t) of the salt in the tank at time t

Concentration, $C(t)=\dfrac{Amount}{Volume}=\dfrac{A(t)}{500}$

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

$=(\frac{A(t)}{500})( 2\frac{gal}{min})\\R_{out}=\dfrac{A}{250}$

Now, the rate of change of the amount of salt in the tank

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

$\dfrac{dA}{dt}=6-\dfrac{A}{250}$

We solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{250}=6\\$The integrating factor: e^{\int \frac{1}{250}dt} =e^{\frac{t}{250}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{250}}+\dfrac{A}{250}e^{\frac{t}{250}}=6e^{\frac{t}{250}}\\(Ae^{\frac{t}{250}})'=6e^{\frac{t}{250}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{250}})'=\int 6e^{\frac{t}{250}} dt\\Ae^{\frac{t}{250}}=6*250e^{\frac{t}{250}}+C, $(C a constant of integration)\\Ae^{\frac{t}{250}}=1500e^{\frac{t}{250}}+C\\$Divide all through by e^{\frac{t}{250}}\\A(t)=1500+Ce^{-\frac{t}{250}}$

Recall that when t=0, A(t)=50 (our initial condition)

$50=1500+Ce^{-\frac{0}{250}}50=1500+Ce^{0}\\C=-1450\\$Therefore the amount of salt in the tank at any time t is:\\A=1500-1450e^{-\dfrac{t}{250}}$

4 0

4 years ago

Help please ill give brainliest

nadezda [96]

Answer:

I'm pretty sure triangle 6 is similar to triangle 1

Step-by-step explanation:

7 0

3 years ago

What are all the digits of pie?

Artemon [7]

'Pi' is an irrational number. It can never be completely written with digits.

Here are the first 15 decimal places: 3.14159 26535 89792

A supercomputer lab in Japan has calculated <u>4 trillion</u> digits of pi,
and it still doesn't end.

With higher mathematics, it's possible to <u>prove</u> that pi never ends.
So, no matter how many digits somebody gives you for pi, there are
still an infinite number more after those.

8 0

3 years ago

Read 2 more answers

Please help! if anybody is good at equivalent polynomial expressions please help!!

scoundrel [369]

The one you have highlighted is correct

7 0

3 years ago