MATHEMATICS
HIGH SCHOOL

Answer: We are asked to determine the integral of sec 2x tan 2x dx

sec 2x is equivalent to 1/cos2x while tan 2x is equal to sin 2x/cos 2x

In this case, the expression becomes sin 2x/ cos^2 2x

We use cos 2x as u so the du is equal to -2 sin 2x dx

The equation then becomes

-1/2∫1/u^2 du

=0.5/cos 2x + c = 0.5 sec 2x + c, where c is a constant

sec 2x is equivalent to 1/cos2x while tan 2x is equal to sin 2x/cos 2x

In this case, the expression becomes sin 2x/ cos^2 2x

We use cos 2x as u so the du is equal to -2 sin 2x dx

The equation then becomes

-1/2∫1/u^2 du

=0.5/cos 2x + c = 0.5 sec 2x + c, where c is a constant

Answer:

MIDDLE SCHOOL

8 is what percent of 64

8 is equivalent to 12.5% of 64.

What is percentage?In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is one of the ways to represent a dimensionless relationship between two numbers.

Given is to find 8 is what percent of 64.

Let 8 is {x}% what percent of 64.

So, we can write -

8 = {x}% of 64

8 = {x/100} x 64

{x} = 800/64

{x} = 100/8

{x} = 25/2

{x} = 12.5%

Therefore, 8 is equivalent to 12.5% of 64.

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percent of 64 is 8 means number/100 * 64 = 8.n/100 * 64 = 8n/100 = 8/64n = 8*100/64 = 25/2 = 12.58 is 12.5% of 64

MIDDLE SCHOOL

Nisha won 121 lollipops playing basketball at her school’s game night. Later , she gave four to each of her friends. She only has 9 remaining. How many friends does she have?

Answer:she has 28 friends.

Step-by-step explanation:

121-9(the amount she had left) =112/4=28.

equation: 121-9=112/4=28.

Answer:

118

Step-by-step explanation:

MIDDLE SCHOOL

Adam Smith received a $875 discount loan to purchase an entertainment center. The loan was offered at 10.5% for 120 days. Find the interest in dollars and the proceeds for the following problem.

Answer:

Interest = $ 30.59

Proceedings = $ 844.41

Step-by-step explanation:

Principal = $875

Rate of Interest (r) = 10.5%

Time(t) = 120 days = 0.33 years

n = number of times the interest rate is compounded in one year

⇒ n = 12

Now, Interest = Compound Interest - Principal

⇒ Interest = 905.59 - 875

= $ 30.59

And the proceedings are = Principal - Interest

= 875 - 30.59

= $ 844.41

Answer:

interest - $30.63

proceeds-$844.37

MIDDLE SCHOOL

Function f(x) represents the population of bacteria x hours after 9 a.m. What does f(2)-f(1) represent?

x = number of hours after 9 am (eg: x = 1 means 1 hr after 9 am, so 10 am)

f(x) = population count x hours after 9 am

f(1) = population count at 10 am (1 hour later)

f(2) = population count at 11 am (2 hrs after 9 am)

f(2) - f(1) represents the difference in population counts from 10 am to 11 am, or put another way, how much the population increased during that time interval.