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3 years ago

Using trig identities, prove the equation shown below.

Mathematics

1 answer:

qaws [65]3 years ago

6 0

Answer:

Step-by-step explanation:

Prove that

sec(x) - sin(x)tan(x)=cosx

sec(x)=1/cos(x) tan(x)=sin(x)/cos(x)

1/cos(x) - sin(x) x sin(x)/cos(x)

(1-sin(x) x sin(x))/cos(x)

(1-sin^2(x))/cos(x) 1-sin^2(x)=cos^2(x)

Cos^2(x)/cos(x)

(Cos(x) x cos(x))/cos(x)

cos(x) proved

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Coffee beans worth $ 10.50 $10.50 per pound are to be mixed with coffee beans worth $ 13.00 $13.00 per pound to make 50 50 pound

MAVERICK [17]

Answer: 30 pounds of coffee beans worth $10.50 per pound was used.

20 pounds of coffee beans worth $13.00 per pound was used.

Step-by-step explanation:

Let x represent the number of coffee beans worth $10.50 per pound that should be mixed.

Let y represent the number of coffee beans worth $13.00 per pound that should be mixed.

50 pounds of beans worth $11.50 per pound is to be made. The total cost of the mixture would be

50 × 11.5 = 575

This means that

10.5x + 13y = 575 - - - - - - - 1

The total number of pounds of each type of coffee used is 50. This means that

x + y = 50

Substituting x = 50 - y into equation 1, it becomes.

10.5(50 - y) + 13y = 575

525 - 10.5y + 13y = 575

- 10.5y + 13y = 575 - 525

2.5y = 50

y = 50/2.5 = 20

x = 50 - 20= 30

6 0

3 years ago

Do rational expressions contain logarithmic functions? A. always B. sometimes C. never

bazaltina [42]

The right answer is C. never

The quotient of two algebraic expressions is a fractional expression. Moreover, the quotient of two polynomials such as:

$\frac{1}{x} \\ \\ \frac{3x-2}{1+x} \\ \\ \frac{x^2-4}{x^2+2}$

is called a rational expression. So according to this definition rational expressions does not contain logarithmic functions. In fact, a rational expression is an expression that is the ratio of two polynomials like this:

$f(x)=\frac{P(x)}{Q(x)} \\ \\ with \ Q(x) \neq 0$

3 0

3 years ago

Read 2 more answers

Pete's Plumbing charges a $150 inspection fee plus $60 per hour. Paul's Plumbing charges a $90 inspection fee plus $75 per hour.

Klio2033 [76]

Answer:

40+75 x = 125 + 25x

Step-by-step explanation:

5 0

3 years ago

F(x)=3x-3 g(x) 3x^3+5 Find F(-3) and g(-2)

astra-53 [7]

Answer:

f(-3) = -12

g(-2) = -19

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3x - 3

g(x) = 3x³ + 5

f(-3) is x = -3 for function f(x)

g(-2) is x = -2 for function g(x)

Step 2: Evaluate

f(-3)

Substitute in x [Function f(x)]: f(-3) = 3(-3) - 3
Multiply: f(-3) = -9 - 3
Subtract: f(-3) = -12

g(-2)

Substitute in x [Function g(x)]: g(-2) = 3(-2)³ + 5
Exponents: g(-2) = 3(-8) + 5
Multiply: g(-2) = -24 + 5
Add: g(-2) = -19

4 0

3 years ago

Read 2 more answers

Which of these is NOT an integer

Tema [17]

Hi there!

»»————-　★　————-««

I believe your answer is:

Option A

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

$\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}$

⸻⸻⸻⸻

$\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}$

⸻⸻⸻⸻

$\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}$

⸻⸻⸻⸻

$\text{Option \textbf{A} does not simplify into an integer.}$

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

7 0

2 years ago