Use a power-reducing identity to rewrite the following expression below in terms containing only firstpowers of cosine.cos4(x)tan?(x)
Answers
Given:
\(\cos ^4x\tan ^2x\)To rewrite: The expression below in terms containing only the first powers of cosine.
Explanation:
Using the identity,
\(\tan ^2x=\frac{\sin ^2x}{\cos ^2x}\)We can write,
\(\begin{gathered} \cos ^4x\tan ^2x=\cos ^4x\cdot\frac{\sin ^2x}{\cos ^2x} \\ =\cos ^2x\cdot\sin ^2x \end{gathered}\)Using the identity,
\(\sin ^2x=1-\cos ^2x\)So, we can write,
\(\begin{gathered} =\cos ^2x(1-\cos ^2x) \\ =\cos ^2x-\cos ^4x \\ =\cos ^2x-(\cos ^2x)^2 \end{gathered}\)Using the identity,
\(\cos ^2x=\frac{1+\cos2x}{2}\)Substituting we get,
\(\begin{gathered} =\frac{1+\cos2x}{2}-(\frac{1+\cos2x}{2})^2 \\ =\frac{1+\cos2x}{2}-(\frac{1+\cos ^22x+2\cos 2x}{4}) \\ =\frac{1+\cos2x}{2}-(\frac{1+\cos^22x+2\cos2x}{4}) \\ =\frac{1}{2}+\frac{\cos2x}{2}-\frac{1}{4}-\frac{\cos^22x}{4}-\frac{\cos 2x}{2} \\ =\frac{1}{4}-\frac{\cos^22x}{4} \\ =\frac{1}{4}-\frac{\frac{1+\cos4x}{2}}{4} \\ =\frac{1}{4}-\frac{1+\cos 4x}{8} \\ =\frac{1}{4}-\frac{1}{8}-\frac{\cos 4x}{8} \\ =\frac{1}{8}-\frac{\cos4x}{8} \\ =\frac{1}{8}(1-cos4x) \end{gathered}\)Final answer: The power reduced form in terms of only first powers of cosine is,
\(\frac{1}{8}(1-\cos 4x)\)
Related Questions
Two buses leave a station at the same time and travel in opposite directions. One bus travels 20 mi/h faster than the other. If the two buses are 576 miles apart after 4 hours, what is the rate of each bus?
Answers
EXERCISES 1. The mean of the number 5, 2, 3, x, 9 is 48. Find the value of and state the mode of the five numbers Given the following observations: 37.5, 255, 305, 41.5, 52.5, 28.25, and 30.5 calculate: The mean (11) Median and () mode The table below shows the number of people in the familles living in the houses of Phase 1, Gwagwalada Size of Family Frequency 2 11 Fine the mean of the distribution Find the median of the distribution Find the mode of the distribution Given the following frequency distribution 0-4 5-9 10-14 6 15-19 7 20-24 10 25-29 12 4 37 5 31 6 10 25 2 4.6 (() (b) (c) 4. X 30-34 35-39 2 40-44 Find the mean of the distribution directly (and using assumed mean) Find the median of the distribution Find the mode of the distribution 30
Answers
Answer:
66
Step-by-step explanation:
I don't know the explanation but the answer is correct.
Jo has a 10 GB monthly cell phone plan. Jo has used 8 GB in the first 10 days of the month. At that rate, how many GB will Jo use after a month of 30 days?
Answers
Answer:
Step-by-step explanation:
1st 10 days - 8 GB
2nd 10 days - 8 GB
3rd 10 days - 8 GB
________________
30 days - 24 GB
m^-2p^-1×2pn^2 ____________ (mnp^4)^0
Answers
You have the following expression:
\(\frac{m^{-2}p^{-1}\cdot2pn^2}{(mnp^4)^{0}}\)in order to simplify the previous expression, write each variable with negaive exponent as the inverse with positive exponent. Moreover, conisder that any expression powered to zero is equal to 1:
\(\frac{2pn^{2}}{m^{2}p\cdot(1)}=\frac{2n^{2}}{m^{2}}\)Hence, the simplified expression is
2n²/m²
anong uri ng wika mayroon ang pilipinas ?heterrogenous o homogenous?
Answers
Answer:
Sa tingin ko ang wika ng Pilipinas ay heterogeneous dahil magkakaiba ang ating pananalita base sa kung saan tayo nagmula o nakatira. may ilocano may bisaya may tagalog at marami pang iba.
Fill in the missing statements and reasons in the proof:
Answers
Answer:
2. definition of congruence
Step-by-step explanation:
sorry I just know that one
Which statement is correct when solving the expression 5y2 – 3y2?
A. Add the coefficients (5 + 3).
B. Add the exponents (2 + 2).
C. Subtract the coefficients (5 – 3).
D. Subtract the exponents (2 – 2).
Answers
Answer:
C. Subtract the coefficients (5 – 3)
Step-by-step explanation:
\(5y^2-3y^2=(5-3)y^2=2y^2\)
how to factorise 3x + 6
Answers
Answer:
it is 3(x+2)
Answer:
3(x+2)
Step-by-step explanation:
You first find the common factor.
3x+6
3(x+2) solution.
Use wage data (Data is posted on blackboard) to estimate the following model and answer the questions: Wage= Bo+ Bi educ+ B2 exper+B3 gender +B4 race+Bs gender*exper+E Gender=1 for male and gender=0 for female Race=1 for white and race=0 for non-white 1- Interpret all the coefficients. 2- Is there a significant wage difference between white and non-white? at a=0.05 3- Test for global usefulness of the model at a=0.05. 4- Test if the experience is a significant determinant of wage at a=0.10.
Answers
A unit increase in gender will result in decrement of -52.73 in wage provided holding all other parameter constant.
What is parameter?
A parameter is a piece of information that an equation passes on. In terms of statistics, it means something different. In contrast to statistics, which only provide information about a small portion of the population, this value provides information about the entire population.
A parameter is constant because it was determined by surveying everyone (or everything). The average age of the students in your class, for instance, might be of interest to you. Maybe after asking everyone, you discovered that the average age was 25. Given that you polled the entire class, that qualifies as a parameter. Let's say you were curious about the median age of your grade or year.
Learn more about parameter here
brainly.com/question/13794992
#SPJ4
find 7x +y when x=7 and y=1
Answers
Answer:
7x+y
7(7)+1
49+1
50
Step-by-step explanation:
please mark me as brainlest
Answer:
7x + y
x=7 y=1
7(7) + 1
49 + 1
= 50
find the equation of the line through point (4,-7) and parallel to y = -2/3x + 3/2.
Answers
Answer:
y = -2/3 x - 13/3
Step-by-step explanation:
y = -2/3 x + 3/2
y = mx + b
m = -2/3
The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.
m = -2/3
y = mx + b
y = -2/3 x + b
Substitute the given point for x and y and solve for b.
-7 = -2/3 (4) + b
-21/3 = -8/3 + b
b = -13/3
Answer: y = -2/3 x - 13/3
different equation dy÷dx+ytanx=secx
Answers
Answer:
First, we rearrange the equation to isolate the y-term on one side:
dy/dx + ytanx = secx
Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1
Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1
Integrating both sides with respect to x, we get: y |secx| = x + C
where C is the constant of integration. Solving for y, we have:
y = (x + C)/|secx|
Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined
On 1 April mazibane has R540, 00 in his credit card account. He buys a lounge suit for R8300, 00 on credit. There is no interest on the debit amount for the first month. Thereafter the interest is 16% per year calculated daily but compounded monthly. On 1 June Mazibane pays R5000 into the account.
How much must Mazibane pay into the account on 30 June to have no debt in the account
Answers
According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.
How to calculate the amount Mazubane must pay on 30 June?To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.
Initial Debt:
On 1 April, Mazibane had a credit card debt of R8300.Interest Calculation:
The interest on the debt is 16% per year, calculated daily but compounded monthly. From 1 April to 1 June, a period of two months, there is no interest charged on the debt.Previous Payment:
On 1 June, Mazibane paid R5000 into the account.To determine the remaining debt on 1 June, we subtract the payment from the initial debt:
Remaining debt on 1 June = R8300 - R5000 = R3300.From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.
To calculate the interest for one month, we use the formula:
Interest = Principal x (1 + (rate/100))^(time/12) - Principal,where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).
Interest for one month = R3300 x (1 + (16/100)/12)^(1/12) - R3300.To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:
Total debt on 30 June = R3300 + Interest for one month.To have no debt on 30 June, Mazibane must pay the total debt amount:
Mazibane must pay R3300 + Interest for one month on 30 June.Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.
Learn more about debt in: https://brainly.com/question/31792485
#SPJ1
How many tons is 22,000 pounds?
Answers
Answer:
1 ton = 2,000 pounds
Step-by-step explanation:
With that said, 22,000 pounds is 11 tons because 2,000 x 11 = 22,000.
So 22,000 pounds is 11 tons.
Hope it helps and pls mark me brainliest if it did! :)
Diện tích xung quanh của hình chóp tứ giác đều có cạnh bằng 6cm và độ dài trung đoạn bằng 10cm là:
A. 120 cm2 B. 240 cm2 C. 180 cm2 D. 60 cm2
Answers
Answer:
A
Step-by-step explanation:
(6.2).10=120cm²
Đáp án đó chúc bạn học tốt
Simplify 6 to the fifth power over 7 cubed all raised to the second power.
Answers
Answer:
513.954016
Step-by-step explanation:
If what you mean was (6^5/7^3)^2 than:
(6^5/7^3)^2 is equal around 513.954016
Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Answers
= 173.903t
Step-by-step Explanation:
The given equation is: f(t) = 227e^(b*t)
To convert it to the form f(t) = ab, we need to write it in the form of f(t) = a * e^(k*t), where a and k are constants.
Let's start by taking the natural logarithm (ln) of both sides:
ln(f(t)) = ln(227e^(b*t))
Using the properties of logarithms, we can simplify this to:
ln(f(t)) = ln(227) + ln(e^(b*t))
ln(f(t)) = ln(227) + b*t
Now, let's define a new constant, k = b, and rewrite the equation in terms of a and k:
ln(f(t)) = ln(a) + k*t
where a = 227 and k = -0.09
Taking the exponential of both sides, we get:
f(t) = e^(ln(a) + k*t)
f(t) = e^(ln(a)) * e^(k*t)
f(t) = a * e^(k*t)
Substituting the values of a and k, we get:
f(t) = 227 * e^(-0.09*t)
Therefore, the equation f(t) = ab is:
f(t) = 227e^(-0.09t) ≈ 173.903t (rounded to three decimal places)
Identify the constant in the following algebraic expression: 9 - z
Answers
Answer:
9
Step-by-step explanation:
a number by itself is a constant.
Which expression is equivalent to 6x - 5 - 2x + 1?
Answers
Answer: 4x-4 is the correct answer
Step-by-step explanation that is the correct answer
pls help anyone? thank you ;)
Answers
Answer:
36 units ⇒ Answer 1 is correct
Step-by-step explanation:
To find the perimeter of a triangle you have to simply add the 3 sides together.
They have given the lengths of three sides as follows.
9 , 12 , 15 units
Let us solve now.
Perimeter = 9 + 12 + 15
= 21 + 15
= 36 units
Hope this helps you :-)
Let me know if you have any other questions :-)
Answer:
○ \(\displaystyle 36\)
Explanation:
All you are doing is adding the edges up:
\(\displaystyle \boxed{36} = 15 + 12 + 9\)
I am joyous to assist you at any time.
12 water pumps can empty a water tank in 20 minutes. If 2
pumps are out of order, how long will the remaining pumps take
to make the tank empty?
Answers
Answer:
one pump alone would take 20 minutes * 12
=240
10 pumps can do in in 240 minutes / 10
your answer is 24 minutesplease brainliest
help plz give correct..
Answers
Answer:
(-4)¹² now it's solution 16,777,216.
11) What is the slope of the line below * X
Answers
to find the slope of a line select the two points given.
in this case the point to the left will be (-4,-1) and the one to the right will be (3,1)
use the formula of the slope to calculate
\(m=\frac{y_2-y_1}{x_2-x_1}\)replace the points into the formula
\(\begin{gathered} m=\frac{1-(-1)}{3-(-4)} \\ m=\frac{2}{7} \end{gathered}\)the slope of the line will be 2/7
Properties of Light Lab Report
Instructions: In the Properties of Light—Bending Light Lab you will explore how light rays interact as they pass from one material, or medium, to another. Record your observations in the lab report below. You will submit your completed report.
Name and Title:
Include your name, instructor's name, date, and name of lab.
Objective(s):
In your own words, what was the purpose of this lab?
Hypothesis:
In this section, please include the if/then statement you developed during your lab activity. This statement reflects your predicted outcome for the experiment.
If I project light rays through (choose one: air, water, glass), then they will refract, or bend, the most.
Procedure:
Please be sure to identify the test variable (independent variable) and the outcome variable (dependent variable) for this investigation. Remember, the test variable is what is changing in this investigation. The outcome variable is what you are measuring in this investigation.
Test variable (independent variable):
Outcome variable (dependent variable):
Select Intro to begin.
Once the simulation loads, you will drag the protractor onto the screen so that the 0 lines up with the dotted line in the center of the screen. Select the More Tools icon at the bottom of the lab interactive and be sure to select the Normal and Angles boxes. Do Not move the laser light.
You will test all three materials in the bottom, blue half of the screen: air, water, and glass. Remember, do not move the laser light.
Record your observations of how the light rays interact as they pass from air, on the top of the screen, through the three materials on the bottom of the screen
Data:
Record the data from each trial in the data chart below. Be sure to fill in the chart completely.
Material Interactions
List any observations you made as the light rays passed from the air on the top of the screen to the selected material on the bottom of the screen. Evidence
Using the protractor, measure the angle as the light passes from the top material to the bottom material on the screen. Also, note the index of refraction for each as indicated on the screen.
Trial One Air on top
Bottom angle:
Bottom index of refraction:
Air on bottom
Trial Two Air on top
Bottom angle:
Bottom index of refraction:
Water on bottom
Trial Three Air on top
Bottom angle:
Bottom index of refraction:
Glass on bottom
Conclusion:
Your conclusion will include a summary of the lab results and an interpretation of the results. Please write in complete sentences.
Did your data support your hypothesis? Use evidence to explain.
Which material refracted the light rays the most: air, water, or glass?
Which material refracted the light rays the least: air, water, or glass?
How does density affect refraction?
Diamonds are a very dense material. Predict what would happen to the light ray if you projected it from air through a diamond.
Explain where you observe reflection, refraction, and absorption of light in your everyday activities.
Answers
Answer:
Can You Give Me Some More Information
Step-by-step explanation:
Solve for x
4^2x = 4^-2x-1
Answers
The value of x is equal to -1/4.
What is an exponent?In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;
bⁿ
Where:
the variables b and n represent numerical values or an algebraic expression.
From the information provided, we can logically deduce the following algebraic expression:
Expression = 4^{2x} = 4^{-2x-1}
Next, we would apply exponent rules of power to the expression because the bases are equal:
2x = -2x - 1
4x = -1
x = -1/4.
Read more on exponent here: brainly.com/question/9524319
#SPJ1
answer fast and correct pls
Answers
Answer:
A
Step-by-step explanation:
What are the important variables in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 4 points. If the test has 25 questions, how
many multiple-choice questions are there?
OA. p for points, m for multiple choice
OB. s for short answer, t for test
OC. m for multiple choice, s for short answer
OD. t for test, q for questions
Answers
The important variables are the two types of test questions which can be represented as :
m for multiple choice, s for short answerVariables are used to represent unknown values which could be worked out in a mathematical expression or problem.
The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer
Therefore, the correct option is C. m for multiple choice, s for short answer
Learn more on word problems:https://brainly.com/question/25693822
#SPJ1
What is the length of the third side?
Answers
Answer:
√115
Step-by-step explanation:
14²= 9² + x²
x= √14²-9² = √115
Step-by-step explanation:
using Pythagores theorem
h²=p²+b²
14²=p²+9²
p²=196-81
p=√115
p=10.72
stay safe healthy and happy...The quadratic function f(x)= ax2 + 8x + c has a vertex at (1,9). What are the values of a and c?
Answers
we get that the x coordinate of the vertex is
\(\frac{-8}{2a}=1\rightarrow2a=-8\rightarrow a=-\frac{8}{2}=-4\)and if we replace 1 in the function we get 9. So
\(\begin{gathered} -4\cdot1+8\cdot1+c=9\rightarrow-4+8+c=9 \\ 4+c=9\rightarrow c=9-4=5 \end{gathered}\)so we get that a=-4 and c=5
write 768,676 in words
Answers
Answer:
seven hundred sixty-eight thousand six hundred seventy-six
hope this answer correct :)