Answer:
Proof in explanation
Step-by-step explanation:
Trigonometric Identities
The basic trigonometric identity is:
[tex]\sin^2\theta+\cos^2\theta=1[/tex]
We'll use it and some basic algebra to prove that, given:
[tex]a sin^3\theta+b cos^3\theta=sin\theta cos\theta[/tex]
And
[tex]a\sin\theta-b\cos\theta=0[/tex]
Then
[tex]a^2+b^2=1[/tex]
From the equation:
[tex]a\sin\theta-b\cos\theta=0[/tex]
We have:
[tex]a\sin\theta=b\cos\theta\qquad [1][/tex]
The equation
[tex]a sin^3\theta+b cos^3\theta=sin\theta cos\theta[/tex]
Can be rewritten as
[tex]a\sin\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta[/tex]
Replacing [1]:
[tex]b\cos\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta[/tex]
Taking the common factor:
[tex]b\cos\theta (\sin^2\theta+ \cos^2\theta)=\sin\theta \cos\theta[/tex]
The expression in parentheses is 1, thus:
[tex]b\cos\theta =\sin\theta \cos\theta[/tex]
Dividing by [tex]\cos\theta[/tex]
[tex]b=\sin\theta[/tex]
Replacing in
[tex]a\sin\theta=b\cos\theta[/tex]
We have
[tex]a\sin\theta=\sin\theta\cos\theta[/tex]
Dividing by [tex]\sin\theta[/tex]
[tex]a=\cos\theta[/tex]
Now:
[tex]a^2+b^2=(\cos\theta)^2+(\sin\theta)^2[/tex]
This expression is 1, thus it's proven:
[tex]\boxed{a^2+b^2=1}[/tex]
How do i write this quotient as a mixed number?
Answer:
32 2/98
Step-by-step explanation:
Answer:
32 2/98
Step-by-step explanation:
hope this helps
Assume LaTeX: \angle∠A and LaTeX: \angle∠B are complementary. Find mLaTeX: \angle∠A if it is 14 more than LaTeX: \angle∠B.
Answer:
[tex]A = 52[/tex]
Step-by-step explanation:
Given
[tex]A = 14 + B[/tex]
Required
Find A
Since both angles are complementary; then:
[tex]A + B = 90[/tex]
Solve for B in [tex]A = 14 + B[/tex]
[tex]B = A - 14[/tex]
Substitute [tex]B = A - 14[/tex] in [tex]A + B = 90[/tex]
[tex]A + A - 14 = 90[/tex]
[tex]2A - 14 = 90[/tex]
Solve for 2A
[tex]2A = 90 + 14[/tex]
[tex]2A = 104[/tex]
Solve for A
[tex]A = 104/2[/tex]
[tex]A = 52[/tex]
A survey of 100 people found that 35 people exercise in the morning, 45 people exercise in the afternoon, and 20 people exercise at night. Tara claims that 35:55, 45:80, and 20:65 are possible ratios from this data. Jim claims that 35:100, 45:100, and 20:100 are possible ratios from this data. Who is correct? Explain.
100 total people ... 35 exercise in the morning ... 45 in the afternoon ... and 20 at night
Jim is correct ...
35/100 is the ratio of people who exercise in the morning to total people.
45/100 is the ratio of afternoon exercisers to total people
20/100 is the ratio of night exercisers to total people
Answer: Jim is correct because 35:100, 45:100, and 20:100 are part-to-whole comparisons. There are other possible part-to-part ratios from the data.
Step-by-step explanation: sample response
formula for volume of rectangular prism? math terms.
Answer: V = whl
Step-by-step explanation:
V - Volume
w - width
h - height
l - length
multiply all of these and you’ll get the answer! good luck and hope this helps!
Answer:
V= W x L x H
Step-by-step explanation:
W= width
L= length
H= height
What idea did Alberti introduce in his famous work of art theory, On Painting?
A. Art should imitate nature.
B. Beauty is in the eye of the beholder.
C. Science and art are more similar than different.
D. Philosophers make the best artists.
Answer:
A
Step-by-step explanation:
Find the measures of
the missing angles.
Answer/Step-by-step explanation:
Ok, edited answer:
Angle A = 100 degrees
Angle B = 80 degrees
Angle C = 80 degrees
Angle D = 100 degrees
Angle E = 100 degrees
Angle F = 80 degrees
Angle G = 80 degrees
...and the give angle, of course, = 100 degrees!
Hope this helps, will gladly take brainliest!!!
A box of cereal states that there are 96 calories in a 3/4 cup serving. What is the unit rate. Of calories per cup? How many calorie are there in 3 cups.
Answer: 384 calories
Step-by-step explanation:
Answer:
7335
Step-by-step explanation:
5. Lela purchased 2 mechanical pencils and a notebook that costs $5. Her purchase totaled $11. How much was each pencil? Use p to represent the cost of each pencil.
Answer:
3 dollars per mechanical pencil
Step-by-step explanation:
11 minus 5 equals 6 and 6 divided by 2 equals 3 :)
Identify the intervals on which each quadratic function is positive. Part 2
4. y = -x^2 + 4x + 12
5. y = 2x^2 + 12x + 18
6. y = 5x^2 - 3x - 8
Answer: 4) (-2, 6)
5) (-∞, -3) U (-3, ∞)
6) (-∞, -1) U (8/5, ∞)
Step-by-step explanation:
Find the zeros.
When the a-value is positive, the curve will be positive to the left of the leftmost zero and to the right of the rightmost zero. + - +
←---|----|--→
When the a-value is negative, the curve will be positive between the zeros.
- + -
←---|----|--→
4) y = -x² + 4x + 12
y = -(x² - 4x - 12)
y = -(x + 2)(x - 6)
0 = -(x + 2)(x - 6)
0 = x + 2 0 = x - 6 -- + --
x = -2 x = 6 ←------|-----------|--------→
-2 6
Positive Interval: (-2, 6)
5) y = 2x² + 12x + 18
y = 2(x² + 6x + 9)
y = 2(x + 3)(x + 3)
0 = 2(x + 3)(x + 3)
0 = x + 3 0 = x + 3 + +
x = -3 x = -3 ←---------|----------→
-3
Positive Interval: (-∞, -3) U (-3, ∞)
6) y = 5x² - 3x - 8
y = 5x² + 5x - 8x - 8
y = 5x(x + 1) - 8(x + 1)
y = (5x - 8)(x + 1)
0 = (5x - 8)(x + 1)
0 = 5x - 8 0 = x + 1 + -- +
x = 8/5 x = -1 ←------|-----------|--------→
-1 8/5
Positive Interval: (-∞, -1) U (8/5, ∞)
Which is not a true statement about the transformation shown below?
1. The two figures are congruent.
2. The image was translated down then to the right
3. The orientation of the vertices did not change.
4. The shape was rotated about the origin
Evaluate the piece wise function
Answer:
Since x = -2
x satisfies the condition of x < 1
Hence, the output will be x + 3
-2 + 3
=1
Option C is the correct option
A cricketer's average score for 6 innings is 12 runs. what must he score in his next innings to make his average 13?
In an article about disinflation, various investments were examined. The investments included stocks, bonds, and real estate. Suppose that a random sample of 200 rates of return on real estate investments was computed and recorded. Assuming that the standard deviation of all rates of return on real estate investments is 2.25%, estimate an interval for the mean rate of return on all real estate investments with 95% confidence
Interpret the estimate.
Answer:
Step-by-step explanation:
Using the formula for calculating the confidence interval to estimate an interval for the mean rate of return on all real estate investments with 95% confidence;
Confidence Interval = xbar±(Z*S/√n)
xbar is the mean = 20%(assumed since we are not given)
n is the sample size = 200
S is the standard deviation = 2.25%
Z is the Z score at 95% confidence interval = 1.960
Confidence Interval = 20±(1.96*2.25/√200)
Confidence Interval = 20±(1.96*2.25/14.14)
Confidence Interval = 20±(1.96*0.159)
Confidence Interval = 20±0.312
Confidence Interval = (20-0.312, 20+0.312)
Confidence Interval = (19.688, 20.312)
Hence the interval for the mean rate of return on all real estate investments with 95% confidence is 19.688<x<20.312.
This means that the minimum rate of return on investment is 19.688% and the maximum rate of return on investment is 20.312%.(assuming 20% as the mean)
What is the range of the function y = x^2
Answer:
Option 1
Step-by-step explanation:
The square of a real number is always non-negative.
1. There are 60 players on a football team.
2/3
of the players are offensive players.
1/12
of the players are special teams players.
The remaining players are defensive players.
Each team member is either offensive, defensive, or special teams player. How many players are defensive player?
Answer:
3/12 players are defensive
Step-by-step explanation:
have to change demonitar to 12 so 3x4=12 so 2x4= 8
then 8+1=9 so 9/12
then 9-12=3 so 3/12 is the amount of defensive players
Which equation is y=-6x^2+3x+2
Answer: y = 39x +2
Step-by-step explanation: -6x^2 is equal to -6x-6 which is 36x + 3x is 39x, add the 2 and you get 39x +2.
Which of the following would represent the first step in simplifying the problem 7 + 5/6 - 2) = 2. 1216 - 2) - 2 07+30-2-2 07-516-1 07+ 5/4) - 2
Answer:its 7+5(4) divided by 2
Step-by-step explanation:
because of order of operations
you need to use PEMDAS
What is 61% percent written as a decimal? 100 points and Brainliest
Answer:
0.61
........
.......
Answer:
0.61 just did it!
Step-by-step explanation:
Find y when x equals 15 if y equals 6 when x equals 30
Name two segments that share an endpoint with JM
Answer:
b
Step-by-step explanation:
if an angle is obtuse, what type of angle is the supplement
all real numbers are irrational numbers?
Answer:
no.
Step-by-step explanation:
the group of all real numbers consists of both rational and irrational numbers.
Need help please.......
Answer:
right triangles
Which graph shows rotational symmetry?
Help with this question
Factor: m- 81
Answer:(x+9)(x−9)
Step-by-step explanation:
Which of the following relations is a function?
A.
{(8,3),(8,0),(-8,13),(-8,17)}
B.
{(6,11),(-8,7),(6,4),(9,5)}
C.
{(-12,1),(4,9),(-12,8),(-4,15)}
D.
{(5,9),(-7,3),(-5,11),(7,9)}
Answer:
D
Step-by-step explanation:
Because in D, there no x-value that are repeating in the list.
For example A, the value 8 and -8 are being repeated twice, which makes this relation not a fuction.
Answer:
d
Step-by-step explanation:
I WILL MARK YOU AS BRAINLIEST ANSWER
I need the full procedure of this, and it’s due in one hour. Do It With The Full Procedure And I Will Mark You As Brainliest answer.
Answer:
its b.
Step-by-step explanation:
sole the rational equation
This is adding and subtracting binomials please help (13 points)
Answer:
-5x - 1
Step-by-step explanation:
Step 1: Write expression
(-6x + 2) + (x - 3)
Step 2: Combine like terms
-5x - 1
How would you write 4/1000 in decimal form
Answer:
The correct answer is 0.004
Step-by-step explanation:
I got it correct
