Answers
I'll do the first problem to get you started.
In place of [tex]\sin^{-1}[/tex] I'll use arcsine
So [tex]\sin^{-1}(x) = \arcsin(x)[/tex]
-------------------------------------------------
Using that hint given, we can get the following
cos(arcsin(3x) - pi)
cos(arcsin(3x))*cos(pi) + sin(arcsin(3x))*sin(pi)
cos(arcsin(3x))*(-1) + sin(arcsin(3x))*(0)
-cos(arcsin(3x)) + 0
-cos(arcsin(3x))
Now the question is how to evaluate the cosine of an inverse trig function, especially when it's not inverse cosine.
The trick (often with many trig and geometry problems) is to draw out a triangle. Specifically we'll need a right triangle.
Check out the diagram below. I've drawn out a right triangle with reference angle theta, opposite leg of length 3x, and hypotenuse 1.
Note how sin(theta) = opposite/hypotenuse = 3x/1 = 3x
We can then go from sin(theta) = 3x to theta = arcsin(3x)
This ultimately means
cos(arcsin(3x)) = cos(theta)
cos(arcsin(3x)) = adjacent/hypotenuse
cos(arcsin(3x)) = sqrt(1-9x^2)/1
cos(arcsin(3x)) = sqrt(1-9x^2)
The sqrt(1-9x^2) is the result of using the pythagorean theorem.
---------------------------
So that means the final answer is [tex]-\sqrt{1-9x^2}[/tex]
Related Questions
A line passes through the point (0,1) and has a positive slope. Which of these points could that line NOT pass through?
Answers
Answer:
(-3, 1)
(5,-2)
Step-by-step explanation:
At Eastwood Middle School, 25% of the 60 students Mrs.Wade teaches buts their lunches in the cafeteria. How many students purchase their lunch in the cafeteria?
Giving out brainlist ❤️
Answers
Work: .25 x 60 = 15
HELP ASAP!! What’s the answer to this? (with steps)
Answers
Answer:
x = 13.5°
Step-by-step explanation:
Angles 2 + 3 = a straight line, so 180°
180 - 66 = 114 = angle 2
114 = 10x - 21
114 + 21 = 10x
135 = 10x
135 / 10 = x
13.5 = x
The sum of two numbers is 64 and the difference is 6. What are the numbers?
Answers
Solve A=nz + d for Z
Answers
Answer:
.A -d = nzn = (A - d)/z Hope that will help youMr. Brown wants to withdraw $1,000 from his bank in ten dollar bills. How many ten dollar bills should he receive?
Answers
Answer: 100
Step-by-step explanation:
1,000/10 equals 100
Answer:
100
Step-by-step explanation:
1,000 ÷ 10 = 100I hope this helps!
(Before you answer I am looking for how I do it. I have the answers but I need to know an equation to do this instead of using logic)
The sum of two consecutive even numbers is 30. How can you solve for the 2 numbers?
Answers
Answer:
14 and 16.
Step-by-step explanation:
We know that two consecutive even numbers is 30.
Let's let n be any number.
Then the first even number must be 2n.
This is because n can be any number, either even or odd. However, if we multiply it by 2, this ensures that 2n is even. Remember that any number multiplied by 2 yields an even number.
Therefore, the consecutive even number will be (2n+2). Not (2n+1), because that gives an odd number.
We know that they sum to 30. So, we can write the following equation.
[tex](2n)+(2n+2)=30[/tex]
And we solve from there:
[tex]4n+2=30\\\Rightarrow4n=28\\\Rightarrow n=7[/tex]
So, the value of n is 7.
Therefore, the first even number is 7(2)=14.
And the consecutive even number is 16.
Edit: Typo
how does y vary with x
Answers
Answer: y varies directly as x ", " y varies proportionally as x ", or " y is directly proportional to x . ") This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.
Step-by-step explanation:
please help me identify these!!!
Answers
2 Ukraine
3 Pakistan
4 Mexico
5 Saudi Arabia
6 Sudan
7 Algeria
8 China
9 Brazil
10 Russia
What is the slope-intercept form of the equation of the line that passes through the point (-6, 1) and is perpendicular to the graph of 2x + 3y = -5?
Answers
Answer:
3y=2x-5
Step-by-step explanation:
well y=mx+b
so you do the following
2x+3y=-5
-2x . -2x
3y=2x-5
is this what you need
SHOW YOUR WORK AS MUCH AS POSSIBLE 60 POINTS
A checking account is setup with an initial balance of $3,600 and $400 is removed from the count each month for rent no other transactions occur on the account
a. create an expression representing the amount in her account
b. write an equation whose solution is the number of months M it takes for the account balance to reach $2,000
c. what does each part of your equation represent
Answers
Answer:
see below
Step-by-step explanation:
The expression for the account is
a) 3600 -400M where m is the number of months
b) We want the expression to equal 2000
3600 -400M = 2000
c) 3600 is the initial amount in the account
400 is the amount that the account goes down each month
M is the number of months
2000 is the amount left in the account
Can you guys help me answer these two questions on percentage please ❤️❤️
Answers
Answer:
Question 2- 9
Question 3- 75%
Step-by-step explanation:
Jenna opens a savings account with $20 and each week after that she deposits $30. Write an equation that models the amount of money saved (m) as a function of the number of weeks (w) since she has been saving.
Answers
$20
+$30. $50answer corret yes
So what is my answer
What is the value of 3 minus (negative 2)?
A number line going from negative 5 to positive 5.
–5
–1
1
5
Answers
Answer:
5
Step-by-step explanation:
Answer:
The value of 3-(-2) is (with steps):
because it's subtracting a negative, we make the negative a positive and add, then solve----> 3+2=5.
A number line going from -5 to 5 is listed below:
•-5•-4•-3•-2•-1•0 •1 •2 •3 •4 •5
<---•---•---•---•---•---•---•---•---•---•---•--->
Step-by-step explanation:
Basically what I'm saying is that your answer is D.5 because you made the negative a positive and added.
Shia wants to purchase a pair of sneakers with an
original price of $25.00. The sneakers are on sale for
20% off and she had a coupon for $2.00 off any
purchase. Her mom wants her to determine the actual
price before they go to the store.
How much money would she save?
What is the new price of the sneakers?
Answers
Answer:
20% off of $25 is $20 , take away $2 with the coupon and that makes it $18
Step-by-step explanation:
Write y= -472 -167-14 in vertex form.
Answers
Answer: l used to know that
Step-by-step explanation:
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 42 states. What is the probability that she selects the route of three specific capitals?
Answers
Answer as a fraction = 1/68880 which is exact
Answer in decimal form = 0.0000145 which is approximate
=======================================================
Explanation:
Let's call these three cities A, B, and C
There is only one order ABC out of 42*41*40 = 68,880 different possible three city routes to pick from.
So the probability is 1/68880
If you want the answer in decimal form, then use your calculator to find
1/68880 = 0.0000145 approximately
Using the probability concept, it is found that there is a 0.000087 = 0.0087% probability that she selects the route of three specific capitals.
-------------------------
A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the capitals are chosen is not important, which means that the combination formula is used to find the number of total outcomes.Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
1 desired outcome.The total number of outcomes is a combination of 3 from a set of 42, thus:[tex]T = C_{42,3} = \frac{42!}{3!39!} = 11480[/tex]
The probability is:
[tex]p = \frac{1}{11480} = 0.000087[/tex]
0.000087 = 0.0087% probability that she selects the route of three specific capitals.
A similar problem is given at https://brainly.com/question/4037372
PLEASE HELP!!! Justify each step in solving the equation (WILL GIVE BRAINLIEST!)
Answers
3. Add variables
4. Subtraction of integers
5. Division of integer
Darius cuts out a square hole that is 6 inches long each side what is the area of the frame?
Answers
The area of the square hole having a side length of 6 inches is 36 inches².
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
Given, Darius cuts out a square hole that is 6 inches long each side.
We know the area of a square is (side×side).
Therefore, The area of the square hole having a side length of 6 inches is = (6×6) = 36 inch²
learn more about squares here :
https://brainly.com/question/28776767
#SPJ2
Evaluate sin 60° without using a calculator by using ratios in a reference triangle.
Answers
What additional information is needed to prove the triangles are congruent by SAS ?
EA¯¯¯¯¯≅CD¯¯¯¯¯
EB¯¯¯¯¯≅CB¯¯¯¯¯
∠BEA≅∠BCD
∠EAB≅∠CDB
Answers
Answer:
Answer choice B was correct
Step-by-step explanation:
Line segment EB is congruent to line segment CB. I took the test.
A worker uses 560 inches of steel wire to make 350 springs of the same size. At this rate how many inches of steel wire are needed to make 1 spring?
Answers
Answer:
1.5 inches of steel
Step-by-step explanation:
450/300
=1.5 in.
2. Trapezoid WXYZ is located at W(2.1) X[3.
5) Y(6.5) and Z[7. 1). After being translated 6
Units down, what are the new coordinates
of Point Y?
Answers
Point Y is (6, -1)
Subtract 6 from the y coordinate in point y since it is translated down. keep the x coordinate since it is only being translated up and down, or by the y axis
7. SOLVE THE EQUATION BELOW ASAP PLZ!
Answers
Answer:
15 = -3(2c + d), right?
So, 15 = -6c - 3d
If we're solving for c, then
-6c = 15 + 3d
c = -(15 + 3d) / 6
I'll keep on editing this answer solve for A, B, C, D, E, and F!
What is the product?
- 2
5
4 |
-1
이
22
18
○ [ 22 18]
6
119
0
[e 18]
Answers
Answer:
the answer is B
Step-by-step explanation:
^^
A sheet of paper measures 12 cm by 15 cm. Vince cuts the paper from one corner to the opposite corner,
making two congruent triangles. What is the area of one of the triangles?
Answers
Explanation: If the whole paper is 12 by 15 you have to divide them both by 2!
12 divide by 2=6
15 divide by 2=7.5
Then you have to multiply them together to find the area.
6x7.5=45
So therefore the answer is 45cm.
A food company produced 65 pounds of a new cereal. The marketing department wants to put the cereal into 4-ounce promotional boxes that will be given away for free. Assuming that the food company wants to use up all 65 pounds of the new cereal, will the marketing department need to order more than 260 4-ounce boxes? Defend your response.
Answers
Answer:
yes
Step-by-step explanation:
Graph the solution of this inequality
Answers
Answer:
4/9x-10>x/3-12
4/9x-x/3>-12+10
4/9x-3/9x>-2
1/9x>-2
x>-18
Step-by-step explanation:
Suppose that COP and TOD are vertical angles. MCOP = 11x-17 and mTOD =9x+11
Answers
Answer:
[tex]x = 14[/tex]
Step-by-step explanation:
Given
[tex]COP = 11x- 17[/tex]
[tex]TOD = 9x + 11[/tex]
Required
Determine x
Since COP and TOD are vertical angles, we have:
[tex]COP = TOD[/tex]
[tex]11x - 17 = 9x + 11[/tex]
Collect Like Terms
[tex]11x-9x = 11+17[/tex]
[tex]2x = 28[/tex]
[tex]x = 14[/tex]
17. You want to test a new athlete's-foot treatment. You test men and women separately, randomly dividing them into treatment and control groups. The treatment groups receive the new treatment and the control groups receive an inert powder that resembles the treatment. Neither the subjects nor the test administrators know which groups receive the treatment and which groups receive the inert powder. At the end of the experiment, all subjects are asked to rate their degree of relief from athlete's foot. These scores are compared between groups. Which of the following groups of elements were present in this study?
a. Randomization, blocking, placebo, comparative, double-blind
b. Comparative, randomization, placebo, blind
c. Double-blind, randomization, comparative, placebo
d. Randomization, stratified sample, placebo, blind, treatment
e. Double-blind, control, observational, blocking
Answers
Answer:
a. Randomization, blocking, placebo, comparative, double-blind
Step-by-step explanation:
1. Randomization is the process of assigning the subjects in an experiment to any of the treatment groups. This was applied in this experiment when the researcher randomly divided the men and the women into treatment and control groups.
2. Blocking is introduced in an experiment in order to remove nuisance factors. The researcher introduced blocking in this experiment when he divided the men and women on the basis of gender.
3. The Placebo is the inert powder that was given to a group. It has no effect on the participants who receive it.
4. Comparative research compares the result from two groups. This is seen in this research hen the researcher compares the scores between the groups.
5. A double-blind experiment is one where neither the subjects nor the test administrators know which groups receive a treatment. This factor is present in this test.
