linear graphing y= -2x
if tanx=-4/3 and x is in quadrant 2 then cos2x=?
A. 7/25
b. -3/5
c. -7/25
d. 3/5
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C, -7/25.
What are Trigonometric Identities?Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.
Given that the value of tan(x) = -4/3 and x is in quadrant 2.
In order to find the value of cos(2x), we can use the trigonometric identity of cos(2x), therefore, for cos(2x) we can write,
[tex]\cos(2x) = \dfrac{1-\tan^2(x)}{1+\tan^2(x)}[/tex]
Since the value of tan(x) is known, substitute the value in the identity,
[tex]\cos(2x) = \dfrac{1-(-\frac{4}{3})^2}{1+(-\frac{4}{3})^2}\\\\\cos(2x) = \dfrac{1-(\frac{16}{9})}{1+(\frac{16}{9})}\\\\[/tex]
cos(2x) = (-7/9) × (9/25)
Cancelling 9 from the numerator and the denominator,
cos(2x) = -7/25
Hence, if tanx=-4/3 and x are in quadrant 2 then cos2x=-7/25.
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The correct answer is c. [tex]$\cos(2x) = -\frac{7}{25}$[/tex].
First, we find [tex]$\sin(x)$[/tex] and [tex]$\cos(x)$[/tex] using the given value of [tex]$\tan(x)$[/tex]:
[tex]$\tan(x) = \frac{\sin(x)}{\cos(x)} = -\frac{4}{3}$.[/tex]
We can use the Pythagorean identity [tex]$\sin^2(x) + \cos^2(x) = 1$[/tex] to find [tex]$\sin(x)$[/tex] and [tex]$\cos(x)$[/tex]. Let's assume [tex]$\sin(x) = \frac{4}{5}$[/tex] (since [tex]$\tan(x) = -\frac{4}{3}$[/tex], and we are looking for a positive value of [tex]$\sin(x)$[/tex] in quadrant 2). Using the Pythagorean identity:
[tex]$\left(\frac{4}{5}\right)^2 + \cos^2(x) = 1$ \\ $\frac{16}{25} + \cos^2(x) = 1$ \\ $\cos^2(x) = 1 - \frac{16}{25}$ \\ $\cos^2(x) = \frac{25}{25} - \frac{16}{25}$ \\ $\cos^2(x) = \frac{9}{25}$. \\[/tex]
Since [tex]$\cos(x)$[/tex] is negative in quadrant 2, we have [tex]$\cos(x) = -\frac{3}{5}$[/tex].
Now, we can use the double-angle formula for cosine:
[tex]$\cos(2x) = 2\cos^2(x) - 1$ \\ $\cos(2x) = 2\left(-\frac{3}{5}\right)^2 - 1$ \\ $\cos(2x) = 2\left(\frac{9}{25}\right) - 1$ \\ $\cos(2x) = \frac{18}{25} - 1$ \\ $\cos(2x) = \frac{18}{25} - \frac{25}{25}$ \\ $\cos(2x) = -\frac{7}{25}$.[/tex]
Therefore, the value of [tex]$\cos(2x)$[/tex] = [tex]$ -\frac{7}{25}$[/tex].
what is the value of the 7 equal to (7×1/100)
A theater can seat 864 people. The number of rows is 5 less than the number of seats in each row. How many rows of seats are there?
Final answer:
To determine the number of rows in a theater that can seat 864 people, with the number of rows being 5 less than the number of seats per row, we set up the equation x(x-5)=864. Solving this quadratic equation, we find that there are 31 rows of seats.
Explanation:
To solve for the number of rows in the theater, let's denote the number of seats in each row as x and the number of rows as x - 5. Since the product of the number of seats in each row and the number of rows will give us the total seating capacity, we can write down the equation:
x(x - 5) = 864
Expanding the equation, we get:
x2 - 5x - 864 = 0
Using the quadratic formula or factoring, we find that x = 36. Therefore:
The number of rows is x - 5 = 36 - 5 = 31.
So, the theater has 31 rows of seats.
which number is greater 67.89 and 67.98
an equation is shown below. 3x-10x+5=5x+17 what is the value of x that makes the equation true?
collect like terms;
3x-10x=-7x
-7x+5=5x+17
move the variable to the left and change sign
-7x+5=5x+17
move the constant to the right and change sign
-7x-5x+17-5
collect the like terms
-12x=17-5
subtract the numbers
-12x=12
divide both sides by -12
your answer is: x= -1
If Mr. Khans buys 15 staplers, it would cost him $254.85. How would you write this using function notation?
Answer:
f(x) = don't spend more than 200 dollars on staplers
Step-by-step explanation:
Students can take MATH 080 between one and four times. The student's tuition for MATH 080 is $ 548.00 If the tuition is increased 6% AFTER 2 ATTEMPTS, what is the student's one semester tuition after the 2nd attempt? In this situation what is the total tuition for taking MATH 080 the allowed four times
What is the slope of the line represented by the equation y = 1/4x – 3?
Is the subset w = {(x, y, z) | z = 1} ⊂ r 3 a vector subspace of r 3 ? explain why or why not?
an airplane approaching its destination has begun it's final descent into the airport. if the plane descends at a rate of 300 feet per minute. what is the change in altitude of the plane after 4 minutes?
Your favorite football team has three games left to finish the season. the outcome of each game can be win, lose or tie. the number of possible outcomes is ____.
There are 27 possible outcomes for your favorite football team's remaining three games.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If each game can have one of three possible outcomes (win, lose, or tie), then the total number of possible outcomes for all three games can be calculated by multiplying the number of possible outcomes for each individual game.
Since each game has three possible outcomes, the total number of possible outcomes for all three games is:
3 x 3 x 3 = 27
So there are 27 possible outcomes for your favorite football team's remaining three games.
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Find the prime factorization of the follwing numbers: (write p0 if a prime does not appear in the given number.)
jake said he has 8/100 of a dollar in his pocket Margie said that the decimal for 8/100 is 0.8 what error did she make. what is the decimal form for 8/100?
Graph the line y+3=2(x-1) first identify the slope of the line
Kurt and Maria’s high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached. Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2. Maria estimated the number of pounds of newspapers collected by finding mc006-1.jpg of 3,600. Who is right, and why?
what is the answer ×-(-150)=200
At 1pm, there was 16 seagulls on the beach. At 3pm, there were 60 seagulls. What is the constant rate of change
Ignore the bottom...the top question is what I’m struggling with
Which equation has no solution?
A) 2.3y + 2 + 3.1y = 4.3y + 1.6 + 1.1y + 0.4
B) 32x + 25 - 21x = 10x
C) 5/8 x + 2.5 = 3/8 x + 1.5 + 1/4 x
D) 1/3 + 1/7 y = 3/7 y
PLEASE HELP!!
| THANK YOU SO MUCH |
Answer: c
Step-by-step explanation:
a few questions i need help with.
Carly is making 3 1/2 batches of biscuits. If one batch calls for 2 1/3 cups of floor, how much flour will she need?
Determine whether the variable is qualitative or quantitative. explain your reasoning. miles per gallon that a car gets for highway driving
the 4th and 13th terms of an AP are 5 and -1, find the 8th term of an AP
What type of solution does the system of linear equations have? 2x - 6y = 8 -x + 3y = 10
Answer:
No Solution
Step-by-step explanation:
Did the test and got this question correct :>
Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account. Determine the constant rate of change of the account.
Answer:
The constant rate of change of the account is $50 or Increasing by $50 per month.
Step-by-step explanation:
Consider the provided information.
Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account.
Rate of change is known as how one quantity change in relation to other.
The rate of change can be calculated as:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Now use the above formula to calculated the rate of change.
[tex]\frac{300-150}{6-3}[/tex]
[tex]\frac{150}{3}[/tex]
[tex]50[/tex]
Hence, the constant rate of change of the account is $50 or Increasing by $50 per month.
A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. the total of gas pumped at the station in a month is a random variable y (measured in 10,000 gallons) with a probability density function (p.d.f.) given by compute e(y)
The expected value E(y) cannot be computed without the given probability density function for the random variable y. The computation involves integrating the product of the variable and its probability density over its range. An example has been provided for how to compute the expected value with a hypothetical p.d.f.
Explanation:To answer the student's question, it appears there may be a missing probability density function (p.d.f.) for the random variable y, which represents the total amount of gas pumped at the station in a month. Without the actual function, we cannot compute E(y), which is the expected value (mean) of the random variable y. In general, if we had the p.d.f., we would compute the expected value by integrating the product of the variable and its probability density over its range.
An example of how to compute the expected value if we had a p.d.f. f(y) might look like this:
E(y) = ∫ y × f(y) dy
For instance, if the p.d.f. were f(y) = ay (a being a constant) over the interval [0, 1], then:
Integrate the product of y and the p.d.f. over the interval:E(y) = ∫01 y × ay dy = a × ∫01 y² dyAfter computing the integral you would find the expected value E(y).However, without the p.d.f. provided, we can only state the method, not the actual expected value.
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a pump is running at 6.4 quarts per minute. how many gallons per hour is this?
Suppose you buy a piece of office equipment for $17,000. After 3 years you sell it for a scrap value of $3,000. The equipment is depreciated linearly over 3 years. The rate of depreciation of the piece of equipment is
The rate of depreciation of the piece of equipment is 27.45%.
Given that,
The cost of office equipment is $17,000.The number of years is 3And, the scrap value is $3,000.Based on the above information, the depreciation should be
= (Office equipment cost - scrap value) ÷ (Office equipment cost × number of years)
= ($17,000 - $3,000) ÷ ($17,000 × 3)
= $14,000 ÷ $51,000
= 27.45%
Therefore we can conclude that the rate of depreciation of the piece of equipment is 27.45%.
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Use the chinese remainder theorem to solve the systems of congruences:
a. find x mod 77 if x ≡ 2 (mod 7) and x ≡ 4 (mod 11).
b. x ≡ 2 (mod 3), x ≡ 3 (mod 4), x ≡ 1 (mod 5).