Please help me!

Lim x tends to π÷2 , then what is the value of (tanx + cotx) ÷ ( tanx - cotx)

KiRa [710]

(tan(x) + cot(x)) / (tan(x) - cot(x)) = (tan²(x) + 1) / (tan²(x) - 1)

… = (sin²(x) + cos²(x)) / (sin²(x) - cos²(x))

… = -1/cos(2x)

Then as x approaches π/2, the limit is -1/cos(2•π/2) = -sec(π) = 1.

8 0

2 years ago

On a multiple-choice test. Abby randomly guesses on all seven questions. Each question

Murrr4er [49]

Answer:

0.173 probability that she gets exactly three questions correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either she guesses the correct answer, or she does not. The probability of guessing the correct answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Seven questions:

This means that $n = 7$

Each question has four choices.

Abby guesses, which means that $p = \frac{1}[4} = 0.25$

Find the probability to the nearest thousandth, that Abby gets exactly three questions correct.

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{7,3}.(0.25)^{3}.(0.75)^{4} = 0.173$

8 0

3 years ago

The bar graph below shows the attendance at school dances. The ticket per price for each dance is $5 per student. Which two danc

topjm [15]

It's B because all the students that attended added together is 320 and 37.5 of 320 is 120

6 0

3 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!! Find the areas of the trapezoids.

Galina-37 [17]

Answer:

A = 12 units ^2

Step-by-step explanation:

The area of the trapezoid is found by

A = 1/2 (b1+b2)h

b1 = 2

b2 = 4

h = 4

I found these by looking at the graph

A = 1/2(2+4) 4

A = 1/2(6*4)

A = 12 units ^2

8 0

3 years ago

A person invest $10,000 into a bank the bank pays 4.75% interest compounded semi annually. To the nearest 10th of a year, how lo

Mama L [17]

Answer:

T is 13.9 years to the nearest 10th of a year

Step-by-step explanation:

In this question, we are to calculate the number of years at which someone who invests a particular amount will have a particular amount based on compound interest.

To calculate the number of years, what we do is to use the compound interest formula.

Mathematically,

A = P(1+ r/n) ^nt

Where A is the final amount after compounding all interests which is $19,200 according to the question

P is the initial amount invested which is $10,000 according to the question

r is the rate which is 4.75% according to the question = 4.75/100 = 0.0475

n is the number of times per year in which interest is compounded. This is 2 as interest is compounded semi-annually

t= ?

we plug these values;

19200 = 10,000(1+0.0475/2)^2t

divide through by 10,000

1.92 = (1+0.02375)^2t

1.92 = (1.02375)^2t

We find the log of both sides

log 1.92 = log [(1.02375)^2t)

log 1.92 = 2tlog 1.02375

2t = log 1.92/log 1.02375

2t = 27.79

t = 27.79/2

t = 13.89 years

The question asks to give answer to the nearest tenth of a year and thus t = 13.9 years

7 0

3 years ago