Rewrite with only sin x and cos x.
cos 3x
cos x - 4 cos x sin2x
-sin3x + 2 sin x cos x
-sin2x + 2 sin x cos x
2 sin2x cos x - 2 sin x cos x
Answers
Final answer:
To rewrite expressions using only sin x and cos x, we can use trigonometric identities like [tex]cos 2x = 1 - 2sin^2 x[/tex] and sin 2x = 2sin x cos x. By applying these identities, we can simplify the given expressions.
Explanation:
To rewrite the given expressions using only sin x and cos x, we can use the following trigonometric identities:
[tex]cos 2x = 1 - 2sin^2 x[/tex]sin 2x = 2sin x cos x[tex]sin 3x = 3sin x - 4sin^3 x[/tex]Using these identities, we can rewrite the expressions as follows:
cos 3x = [tex]4cos^3 x - 3cos x[/tex]cos x - 4cos x sin^2 x = cos x - 4sin x cos x sin x = [tex]cos x - 4sin^3 x cos x[/tex]-sin 3x + 2sin x cos x = [tex]-(4sin^3 x) + 2sin x cos x[/tex] = [tex]-4sin^3 x + 2sin x cos x[/tex]-sin 2x + 2sin x cos x = -2sin x cos x + 2sin x cos x = 0[tex]2sin^2 x cos x - 2sin x cos x[/tex] = 2sin x cos x (sin x - 1)Related Questions
At a local University 54.3% of incoming first-year students have computers. If 3 students are selected at random, find the following probability. A) At least one has a computer
B) None have computers
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B is .457^3
solve: log 3=.5, then log 1/9=?
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log 1/9 = ?
log 1/9 = log 3^(-2) = -2 * log 3= ( because: log x^n = n log x )
- 2 * .5 = - 1
Answer: log 1/9 = - 1
Select all ratios equivalent to 5:15.
2:60, 20:9, 7:21, 1:3
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show that cos(3theta) = cos^3(theta)-3 cos(theta)sin^2(theta) ... use this to find an equation in rectangular coordinates for the curve r= 4 cos (3theta)......
ANY HELP ? ...?
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From there, it's distribute and simplify...
7 × 30 = 7 × ___ tens
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7 × 30 = 7 × 3 tens.
To solve 7 × 30 in terms of tens, we first observe that 30 can be written as 3 tens since 30 equals 3 × 10.
Therefore:
7 × 30 can be rewritten as 7 × (3 × 10), which simplifies to 7 × 3 tens.
So, 7 × 30 = 7 × 3 tens.
if f(2)=3 and f'(2)=5 find the equation of the tangent line and the normal line to the graph of y=f(x)
Answers
y - 3 = 5(x-2)
y = 5x - 10 + 3
y = 5x - 7
2) normal line: slope = - 1/ f '(2) = - 1/5, point (2,3)
y - 3 = [-1/5](x - 2)
y = - x/5 + 2/5 + 3
y = - x/5 + 17/5
The equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
What is tangent and normal to a curve?A tangent is a line touching the curve at one distinct point, and this distinct point is called the point of contact.
The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent.
Given is a function f(x) and f(2) = 3 and f'(2) = 5.
We can find the tangent to the curve at x = 2 by finding the value of the derivative of f(x) at x = 2. The slope of the tangent at x = 2 is -
m[T] = (dy/dx) [at x = 2] = f'(2) = 5
Now. the equation of tangent can be written as -
(y - y₁) = m [T] (x - x₁)
and
f(2) = 3
At x = 2, y =3 →
y - 3 = 5 (x - 2)
y - 3 = 5x - 10
y = 5x - 10 + 3
y = 5x - 7
This is the equation of the tangent.
In order to find the slope of Normal at x = 2, use the following formula -
m [T] x m [N] = -1
m [T] = 5
Then -
m [N] = - 1/5
The equation of the normal is given by -
(y - y₁) = m [N] (x - x₁)
(y - 3) = -1/5 (x - 2)
y - 3 = -x/2 + 2/5
y = -x/2 + 2/5 + 3
y = -1/2 x + 3.4
This is the equation of Normal.
Therefore, the equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
To solve more questions on Tangents and Normal, visit the link below-
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Which relationship between x and y in the equation shows a proportional relationship?
y=3x
y=5(x+3)
y+5=x+3
y=5x+3
Answers
they are in proportion of 1 to 3
The lines p and q intersect at point O. What is the value of x?
X =
Answers
Answer:
The value of x is 16 .
Step-by-step explanation:
Definition of vertically opposite angles
Two lines crosses angles opposite to each other are called vertically opposite angle .
Thus
(2x + 13)° = (3x-3)°
(Vertically opposite angles )
2x + 13 = 3x-3
2x - 3x = -3-13
-x = -16
x = 16
Therefore the value of x is 16 .
Solve the equation sin theta = 0.3 to the nearest tenth. Use the restrictions 90degrees < theta < 180degrees.
A)
θ=107.5
B)
θ=162.5
C)
θ=197.5
D)
θ=17.5
Answers
∅ = sin⁻¹(0.3)
∅ = 17.5°
To go into the second quadrant, we add 90°.
∅ = 17.5 + 90
= 107.5°
The answer is A.
Wxyz is a parallelogram. name an angle congruent to xyz
Answers
Answer: The answer is ∠XWZ.
Step-by-step explanation: Given that WXYZ is a parallelogram. We are to name an angle that is congruent to ∠XYZ.
Attached herewith, an image of parallelogram WXYZ.
We know that the opposite angles in a parallelogram are congruent to each other. So, in the parallelogram WXYZ, we must have
∠WXY ≅ ∠WZY and ∠XYZ ≅ ∠XWZ.
Therefore, angle congruent to ∠XYZ is ∠XWZ.
Thus, the answer is ∠XWZ.
Final answer:
Angle congruent to angle XYZ in parallelogram WXYZ would be angle W since opposite angles in a parallelogram are congruent.
Explanation:
If WXYZ is a parallelogram and you are asked to name an angle congruent to angle XYZ, you should look at the properties of a parallelogram. One key property is that opposite angles are congruent. Therefore, the angle congruent to angle XYZ would be angle W. If we consider the vertices in order around the parallelogram W, X, Y, Z, angle XYZ corresponds to angle WZY, so its opposite angle is angle WXZ (or simply angle W).
It's important to remember that in a parallelogram, consecutive angles are supplementary (their sum is 180 degrees). This supplementary property could help you in other problems related to angles in a parallelogram, but for this particular case—identifying a congruent angle—the opposite angles property directly gives us the answer.
Question 8
8 pts + 4 pts for the best answer Thanks!
Question is attached.
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If AB is parallel to CD and the slope of CD is -8, what is the slope of AB ?
Answers
Answer:
and only if they have the same slope. Any two vertical lines are parallel. Therefore, the slope of AB is -8 if AB is parallel to CD.
Step-by-step explanation:
Joe paid $14.00 for a board game this is 70% of the original price what was the original price
Answers
start off by finding 10% of $14. in order to find 10%, divide it by 70 which gives 2. you now need to make the 30% to add to the 70%, by timesing the 2 by 3to give 6. now all you need to do it add the 6 to 14 to make 20!
so your answer is $20
Answer:
The original price was $20.00
Step-by-step explanation:
Joe paid $14.00 for a board game.
This is the 70% of the original price.
Let the original price of a board game be x
70% of x = $14.00
0.70x = 14.00
x = [tex]\frac{14}{0.7}[/tex] = $20.00
The original price was $20.00
The length of a rectangle is 4/5 feet. The width is 5/8 feet. How much greater is the length of the rectangle than the width?
A.)7/40 feet
B.)1/5 feet
C.)3/20 feet
D.)1/3 feet
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1. Solve for Y 1/2y+4x=z
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The recipe calls for 1 egg, which makes 8 slices of pumpkin pie. how many eggs would be needed to make 56 slices of pumpkin pie ?
Answers
cross multiply
8x = 56
x = 56/8
x = 7 eggs are needed to make 56 slices
To find the number of eggs needed for 56 slices of pumpkin pie when the recipe calls for 1 egg for 8 slices, simply set up a proportion and solve. In this case, you would need 7 eggs for 56 slices of pie.
To determine how many eggs are needed to make 56 slices of pumpkin pie, we use a proportion. Given that 1 egg makes 8 slices of pie, we set up the proportion as follows:
1 egg / 8 slices = x eggs / 56 slicesSolving for x, which represents the number of eggs needed for 56 slices, we get that x = 7 eggs.
What does the equal sign with an arrow mean?
Answers
2/3 of a circle is what percent of a circle
Answers
360.2/3=240
if 360 240
100 ?
?.360=240.100
?=66,6
GRAPHING EXPONENTIAL FUNCTIONS
1. If (-1, y) lies on the graph of y = 3^x+1, then y =
a) 0
b) 1/3
c) 1
2. If (x, 1/100) lies on the graph of y = 10^x, then x =
a) 2
b) -1/2
c) -2
3. If (-1, y) lies on the graph of y = 2^2x, then y =
a) -4
b) 1/4
c) 1
4. What is the relationship between the graphs of y = 2^x and y = 2^-x?
a) reflections over the x-axis
b) reflections over the y-axis
c) reflections over y = x
5. If (3, y) lies on the graph of y = -(2x), then y =
a) 1/8
b) -6
c) -8
6. Which of the following equations is not exponential?
a) y = 1x
b) y = (1/2)x
c) y = -2x
7. If (-2, y) lies on the graph of y = 4^x, then y =
a) -16
b) 1/16
c) 16
8. If (-3, y) lies on the graph of y = 3^-x, then y =
a) -27
b) 1/27
c) 27
9. If (-3, y) lies on the graph of y = 3^x, then y =
a) 1/27
b) -1
c) -27
10. If (-3, y) lies on the graph of y = (1/2)^x, then y =
a) 8
b) 1/8
c) -8
Answers
2. If (x, 1/100) lies on the graph of y = 10^x, then 1/100 = 10^x
10^-2 = 10^x
x = -2
3. If (-1, y) lies on the graph of y = 2^2x, then y = 2^2(-1) = 2^(-2) = 1/4
4. The relationship between the graphs of y = 2^x and y = 2^-x is reflections over the y-axis.
5. If (3, y) lies on the graph of y = -(2x), then y = -2(3) = -6
6. All are not exponential
7. If (-2, y) lies on the graph of y = 4^x, then y = 4^(-2) = 1/4^2 = 1/16
8. If (-3, y) lies on the graph of y = 3^-x, then y = 3^-(-3) = 3^3 = 27
9. If (-3, y) lies on the graph of y = 3^x, then y = 3^(-3) = 1/3^3 = 1/27
10. If (-3, y) lies on the graph of y = (1/2)^x, then y = (1/2)^(-3) = 2^3 = 8
The detailed answer provides the solutions to a series of questions involving finding specific values for y given x in various exponential equations, as well as recognizing the relationship between graphs of exponential functions and identifying which equations are not exponential.
1. If (-1, y) lies on the graph of y = 3ˣ+1, then y equals the value of the function when x is -1. Therefore, y = 3⁻¹ + 1 which simplifies to y = 1/3 + 1 = 4/3, which is not one of the provided options.
2. If (x, 1/100) lies on the graph of y = 10ˣ, then we need to find the value of x such that 10ˣ equals 1/100. 10ˣ = 1/100 is equivalent to 10ˣ = 10⁻², so x = -2.
3. If (-1, y) lies on the graph of y = 2²ˣ, we substitute x with -1. Then y = 2²*⁻¹ = 2⁻² = 1/4.
4. The relationship between the graphs of y = 2ˣ and y = 2⁻ˣ is that they are reflections over the y-axis. When x is replaced by -x in the function, the resulting graph is a reflection over the y-axis.
5. If (3, y) lies on the graph of y = -(2ˣ), then y is the negative value of 2 raised to the power of 3, which is -8. So, y = -8.
6. Among the given equations, y = -2ˣ is not exponential because it lacks the variable as an exponent. So, y = -2ˣ is not exponential.
7. If (-2, y) lies on the graph of y = 4ˣ, then y = 4⁻² = 1/16.
8. If (-3, y) lies on the graph of y = 3⁻ˣ, then y = 3⁻⁽⁻³⁾ = 3³ = 27.
9. If (-3, y) lies on the graph of y = 3ˣ, then y = 3⁻³ = 1/27.
10. If (-3, y) lies on the graph of y = (1/2)ˣ, then y = (1/2)⁻³ = 2³ = 8.
denise bought 5.2 pounds of rice for $5.29. using the unit rate, how much would 2 pounds of rice cost?
Answers
times both sides by (5.2)(2)
(2)(5.29)=5.2x
10.58=5.2x
divide both sides by 5.2
2.034=x
answer is $2.03 for 2lb rice
What is the range of the function on the graph
Answers
Answer:
all real numbers less than or equal to 3
Step-by-step explanation:
The range of the function is set of all y value for which the function is defined
To find out the range we look at the maximum or minimum point on the graph
Maximum point on the graph that is vertex is (-1,3)
x=-1 and y=3
The graph of y is below 3 (vertex)
So the range of the function is set of all real numbers less than or equal to 3
If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the least education?
a. accountant
b. architect
c. pharmacist
d. surveyor
Answers
Answer:
D
Step-by-step explanation:
The horizontal axis of the graph is Salary.
Given there is a positive correlation between salary and education, means that as if education increase, salary increase OR if education decrease, salary decrease, and vice versa.
Out of the 4 choices, they wanted to know the one that requires LEAST education. So we will look at the bar that has LEAST salary.
Looking at the graph and bars, out of the 4 choices, Surveyor has the LEAST SALARY, so SURVEYOR would require LEAST EDUCATION. Answer choice D is right.
The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}.[/tex] Option (d) is correct.
Further Explanation:
Given:
The options are as follows,
(a). Accountant
(b). Architect
(c). Pharmacist
(d). Surveyor
Explanation:
Correlation is a relationship between the two events. The change in one will affect the in change of another one.
There are two type correlations.
A positive correlation mean that if one increases the second event will also increase and if one decreases the second event will also decreases.
A negative correlation mean that if one increases the second event will also decrease and if one decreases the second event will also increase.
There is a positive correlation between salary and education.
The least salary in the given option is of surveyor and has least education.
The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}[/tex]. Option (d) is correct.
Learn more:
Learn more about normal distribution https://brainly.com/question/12698949 Learn more about standard normal distribution https://brainly.com/question/13006989 Learn more about confidence interval of meanhttps://brainly.com/question/12986589
Answer details:
Grade: High School
Subject: Statistics
Chapter: Correlation
Keywords: correlation, salary, education, positive correlation, based, careers, least education, accountant, architect, pharmacist, surveyor, negative correlation, average salaries, personal trainer,
What is the end of the CD account time when the money can be withdrawn?
Maturity date
End date
Completion date
Withdrawal date
Answers
Correct Answer: maturity date
18 is 240% of what? basic percent equation ...?
Answers
what = 18 x (100/240);
what = 1800/240;
what = 7.5;
mai is saving money to buy a game so far she has saved 20$ which is four fifths of the total cost of the game how much does the game cost
Answers
In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.
A. 20 degrees
B. 30 degrees
C. 120 degrees
D. 180 degrees
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John invested $400 in a savings account. How much interest will he earn in 5 years if the imterest rate is 7%?
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answer: John will earn $140 of interest in 5 years
what is 475.53 minus 67.37
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What is the difference between 7 and -8?
Answers
Hope this helps. :)
7 + 8 (simplify brackets by switching it from subtraction to addition.)
15 (simplify)
How many points are shared by concentric circles?
a. 0
b. 1
c. 2
d. infinite points
Answers
Answer:
Option a. 0
Step-by-step explanation:
As we know if we draw two circles with same center but with the different radii, they neither touch each other nor intersect. This is true not only for two circles but for infinite number of the circles having the same center. They never have the common points to share. Set of points lying on each concentric circles are different.
Therefore Option a. 0 points is the correct answer.