MATHEMATICS
HIGH SCHOOL

where t is the time in months

(a) Find the avg. value of S(t) during the first year.

(b) During what month does S'(t) equal the avg value during the first year? ...?

Answer: (a) The "average value" of a function over an interval [a,b] is defined to be

(1/(b-a)) times the integral of f from the limits x= a to x = b.

Now S = 200(5 - 9/(2+t))

The average value of S during the first year (from t = 0 months to t = 12 months) is then:

(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12

or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12

This equals 200/12 * (5t -9ln(2+t))

Evaluating this with the limits t= 0 to t = 12 gives:

708.113 units., which is the average value of S(t) during the first year.

(b). We need to find S'(t), and then equate this with the average value.

Now S'(t) = 1800/(t+2)^2

So you're left with solving 1800/(t+2)^2 = 708.113

I'll leave that to you

(1/(b-a)) times the integral of f from the limits x= a to x = b.

Now S = 200(5 - 9/(2+t))

The average value of S during the first year (from t = 0 months to t = 12 months) is then:

(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12

or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12

This equals 200/12 * (5t -9ln(2+t))

Evaluating this with the limits t= 0 to t = 12 gives:

708.113 units., which is the average value of S(t) during the first year.

(b). We need to find S'(t), and then equate this with the average value.

Now S'(t) = 1800/(t+2)^2

So you're left with solving 1800/(t+2)^2 = 708.113

I'll leave that to you

HIGH SCHOOL

Which of the following is equivalent to (p3)(2p2 - 4p)(3p2 - 1)? A) (p3)(6p4 - 12p3 - 2p2 + 4p)

B) (p3)(6p4 + 4p)

C) (2p6 - 4p3)(3p2 - 1)

D) (2p5 - 4p4)(3p5 - p3)

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Now, we will solve the last two terms using "Product of polynomials":

So, at last it becomes:

Hence, Option 'A' is correct.

(p³)(2p² - 4p)(3p² - 1) = (p³)(2p²*3p² - 4p*3p² - 1*2p² - 4p*(-1)) =

= (p³)(6p⁴ - 12p³ - 2p² + 4p)

Answer: A)

= (p³)(6p⁴ - 12p³ - 2p² + 4p)

Answer: A)

MIDDLE SCHOOL

Solve for tye given variable: b = fjn for f

f=______

Answer:

f =

Step-by-step explanation:

Given

b = fjn ( isolate f by dividing both sides by jn )

= f

MIDDLE SCHOOL

6 times blank equals 24

6 blanks = 24

Divide each side by 6 : 1 blank = 4

6 times 4 equals 24 because you have to do 24/6 which is 4

HIGH SCHOOL

A population of fish in a lake is 14000 in 2010. The population decreases 6% annually. What is the population in 2019

Answer:

8022.

Step-by-step explanation:

Let x be the number of years after 2010.

We have been given a population of fish in a lake is 14000 in 2010. The population decreases 6% annually.

We can see that population of fish is the lake is decreasing exponentially as it is decreasing 6% annually.

Since we know that an exponential function is in form: , where,

a = Initial value,

b = For decrease or decay b is in form (1-r) where r represents decay rate in decimal form.

Let us convert our given decay rate in decimal form.

Upon substituting our given values in exponential form of function we will get the population of fish in the lake after x years as:

Let us find x by subtracting 2010 from 2019.

Upon substituting x=9 in our function we will get,

Therefore, the population of fish in 2019 will be 8022.

MIDDLE SCHOOL

Is 336 inches bigger than 18 ft

1 foot is 12 inches

336/12=28

yes it is bigger

336/12=28

yes it is bigger

18 ft = how many inches

12 in = 1 foot

18*12 = 216 in

336 in > 216 in

Answer: 336 in is bigger than 18 ft

12 in = 1 foot

18*12 = 216 in

336 in > 216 in

Answer: 336 in is bigger than 18 ft

HIGH SCHOOL

How many pieces of 4

inches of ribbon can get from a roll of 25 feet ribbon?

1 feet = 12 inches

25 feet= 25*12 inches

25 feet=300 inches

300inches/4inches=75 pieces of ribbon

25 feet= 25*12 inches

25 feet=300 inches

300inches/4inches=75 pieces of ribbon

25/4=6 1/4

since the questions say 4in. pieces we assume its whole 4in so you get 6 pieces

HIGH SCHOOL

Two angles that have the sum of 180 degrees

Two angles that have the sum of 180 degrees are supplementary angles. If you need to find angle A, you just need to subtract angle B from 180 degree to find out the degree of the particular angle. Hope I helped.

MIDDLE SCHOOL

What is the product?

(-2087+5) (50²-6s)

Answer:

-5205000 + 12492s

Step-by-step explanation:

used a tutorial to help you, yw ^^

HIGH SCHOOL

Identify and extend The pattern to find the next number in this sequence 22, 35, 48, 61,...

Each number is 13 more than the last. the next number should be 74