Find the average velocity of the function over the given interval 2+tan x[-pi/4

3(4a + 2) = 2(a - 2)?

Likurg_2 [28]

Answer:

A= -1

Step-by-step explanation:

8 0

2 years ago

Which is the best linear model for the data shown in the scatter plot?

Studentka2010 [4]

The best linear model for the data that's illustrated will be y = 10x + 5

<h3>What is a linear model?</h3>

It should be noted that a linear model simply means model where the terms are added. It should be noted that this can be used in connection with the regression model.

Here, the best linear model for the data will be:

= (10 × x) + 5

= 10x + 5

Therefore, the best linear model for the data that's illustrated will be y = 10x + 5.

Learn more about model on:

brainly.com/question/25987747

#SPJ1

3 0

1 year ago

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

2 years ago

Which of the following expressions is equal to -4x^2-36

liubo4ka [24]

Answer:

Step-by-step explanation:

-4x^2-36 can be rewritten as -4(x^2 + 9). The quantity in parentheses does not have real roots, but does have the imaginary roots ±3i.

Next time, please share the possible answer choices.

6 0

2 years ago

At Bill’s Burger Barn, every time you buy a burger there is a one in eight chance of winning a free burger. Nicholas bought a ha

guapka [62]

Answer:

im not sure about this one but my answer is 0.025.

Step-by-step explanation:

if there is a 1 out of 8 chance of getting a free burger, convert that into 1/8. divide that by 5 and you get 0.025.

6 0

3 years ago