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4 years ago

Simplify the expression cos(x)cot(x)+sin(x) a. 0 b. csc(x) c. tan(x) d. sec(x)

Mathematics

1 answer:

Ilia_Sergeevich [38]4 years ago

6 0

Answer:

csc(x)

Step-by-step explanation:

cos(x)cot(x)+sin(x)

We know that cot(x) = cos(x)/ sin (x)

cos(x)cos(x)/ sin(x)+sin(x)

cos^2 (x)/ sin + sin (x)

Getting a common denominator

cos^2 (x)/ sin + sin (x)* sin (x)/ sin(x)

(cos^2(x) + sin^2(x)) /sin(x)

We know that (cos^2(x) + sin^2(x)) = 1

1/sin (x)

1/ sin (x) =csc(x)

csc(x)

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Please help me!

Alexandra [31]

In constructing the equation, you need to know the following:

1. What don't we know? How many minutes you must talk to have the same cost for both calling plans. So, let x be the number of minutes.
2. What do we know? Plan 1 charges $17.50 per month plus $0.17 per minute used and Plan 2 charges $32 per month plus $0.07 per minute used.

So the equation must look like this: 17.50 + .17x = 32 + 0.07x

Solving the equation:

1. Multiply both sides by 100
(100) 17.5 + .17x = 32 + 0.07x (100)
1750 + 17x = 3200 + 7x

2. Subtract 1750 from both sides
1750 + 17x - 1750 = 3200 + 7x - 1750
17x = 7x +1450

3. Subtract 7x from both sudes
17x - 7x = 7x + 1450 - 7x
10x = 1450

4. Divide both sides by 100
10x / 10 = 1450/10

x= 145 minutes

145 minutes is the number of minutes you must talk to have the same cost for both calling plans.

7 0

3 years ago

In 2014 the population of 1500 quail decreases at an annual rate of 3%. In writing an exponential function to model the quail po

Gelneren [198K]

Answer:

a = 1500

b = 0.97

Step-by-step explanation:

Let's define 2014 as our t = 0.

Then t = 1 will be 2015, and so on.

We know that in 2014 the population was 1500.

It decreases at an annual rate of 3% or 0.03 in decimal form.

Then in 2015, the population was: 1500 - 1500*0.03 = 1500*(0.97)

In 2016, the population was: 1500*(0.97) - 1500*(0.97)*0.03 = 1500*(0.97)^2

We already can see the pattern.

t years after 2014, the population will be:

f(t) = 1500*(0.97)^t

Now, answering the question:

using f(t)=a(b)^t what is the value of a and b?

a = 1500

b = 0.97

7 0

3 years ago

15% of 15 is what number? A. 2.25 B. 2.75 C. 1.5 D. 3.125

Dahasolnce [82]

Answer:

the answer is option A

Step-by-step explanation:

if 15 is 100

x is 15%

x= (15 * 15)/100 = 2.25

4 0

3 years ago

The product of a number and 9

Anna35 [415]

Answer:

Step-by-step explanation:

let's say that x is the number we don't know

the product means multiplication

9*x=9x

so the answer is 9x

4 0

4 years ago

Read 2 more answers

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

Lerok [7]

Answer:

Q1 - D. f(x) = $x^4-9x^2-50x-150$

Q13 - A. ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Q14 - A. $7x+6+4x^{2}$

Step-by-step explanation:

Question 1:

We know that rational roots always occurs in pairs. So, the zeros of the function will be 5, -3, -1+3i, -1-3i

So, the factored form is $(x-5)(x+3)(x+1-3i)(x+1+3i)=0$

i.e. $(x^2-2x-15)(x+1-3i)(x+1+3i)=0$

i.e. $(x^3-x^2-3ix^2-17x+6ix-15+45i)(x+1+3i)=0$

i.e. $x^4-9x^2-50x-150=0$

Hence, the polynomial function is $f(x)=x^4-9x^2-50x-150$ .

Question 13:

Rational Zeros Theorem states that 'If p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) = 0. Then, p is a factor of the constant term of p(x) and q is a factor of the leading coefficient of p(x)'.

Let, $\frac{p}{q}$ is a zero of $x^3-7x^2+9x-24=0$ . Then, p is a factor of -24 and q is a factor of 1.

Thus, possible values of p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 and q = ±1

This gives, possible values of $\frac{p}{q}$ are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Question 14:

We have, f(x) = 7x + 6 and g(x) = $4x^{2}$

Then, (f+g)(x) = f(x) + g(x) = 7x + 6 + $4x^{2}$

So, (f+g)(x) = $7x+6+4x^{2}$

6 0

4 years ago