Verify the identity. Show your work. cot θ ∙ sec θ = csc θ, assignment help

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1.Verify the identity. Show your work.

cot θ ∙ sec θ = csc θ

2.A gas company has the following rate schedule for natural gas usage in single-family residences:

Monthly service charge $8.80

Per therm service charge

1st 25 therms $0.6686/therm

Over 25 therms $0.85870/therm

What is the charge for using 25 therms in one month? Show your work.

What is the charge for using 45 therms in one month? Show your work.

Construct a function that gives the monthly charge C for x therms of gas.

3.Complete the following:

(a)
Use the Leading Coefficient Test to determine the graph’s end behavior.

(b)
Find the x-intercepts. State whether the graph crosses the x-axis or touches
the x-axis and turns around at each intercept. Show your work.

(c)
Find the y-intercept. Show your work.

f(x) = x²(x + 2)

(a).

(b).

(c).

4.Verify the identity. Show your work.

(1 + tan²u)(1 – sin²u)
= 1

5.Verify the identity. Show your work.

cot²x + csc²x = 2csc²x – 1

6.Verify the identity. Show your work.

1 + sec²xsin²x =
sec²x

7.Verify the identity. Show your work.

cos(α – β) – cos(α + β) = 2 sin α sin
β

8.Find the vertical asymptotes, if any, of the graph of the rational function. Show your work.

f(x) = x-4/x(x-4)

9.The formula A = 118e^0.024t
models the population of a particular city, in thousands, t years after 1998.
When will the population of the city reach 140 thousand? Show your work.

10.Find the specified vector or scalar.
Show your work.

u = -4i + 1j and v = 4i + 1j; Find .||u+v||.

11.Find the exact value of the trigonometric function. Do not use a calculator.
cot(-5π/4)

12.Find the x-intercepts (if any) for the
graph of the quadratic function.
6x² + 12x + 5 = 0
Give your answers in exact form. Show your work.

13.Use the compound interest formulas A =
Pe^rt and A = P(1+r/n)^nt to solve.

Suppose that you have $11,000 to invest. Which investment yields the greater return
over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?
Show your work.

14.Find functions f and g so that h(x) =
(f ∘ g)(x).

h(x) = (6x – 14)⁸

15.Begin by graphing the standard
absolute value function f(x) = | x |. Then use transformations of this graph to
describe the graph the given function.

h(x) = 2 | x | + 2

16.Find the reference angle for the given
angle. Show your work.

-404°

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