Answers
Answer:
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)
Step-by-step explanation:
You want cos(x -π/3) written in terms of sine and cosine.
Angle differenceThe formula for the cosine of the difference between two angles is ...
cos(a -b) = cos(a)cos(b) +sin(a)sin(b)
ApplicationWe have a=x, b=π/3, so the desired function is ...
cos(x -π/3) = cos(x)cos(π/3) +sin(x)sin(π/3)
We know that ...
cos(π/3) = 1/2sin(π/3) = √3/2so the rewrite is ...
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)
Related Questions
Solve the differential equation dy/dx=(1+y²)e^x ?
Answers
This is a separable differential equation, which means we can separate the variables y and x on either side of the equation. To do this, we'll move all the terms involving y to one side and all the terms involving x to the other side.
dy/dx = (1+y²)e^x
We'll divide both sides by (1+y²)e^x:
dy/(1+y²)e^x = dx
Now we'll integrate both sides with respect to their respective variables. The integral of dy/(1+y²) with respect to y is the inverse tangent (tan^-1) function, so we'll use that on the left side:
∫ dy/(1+y²) = ∫dx + C
tan^-1(y) = x + C
On the right side, we'll integrate e^x with respect to x, which gives us e^x. So we have:
tan^-1(y) = e^x + C
We can solve for y by reversing the tan^-1 function:
y = tan(e^x + C)
Where C is an arbitrary constant of integration.
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Solve 2 < n +1| ≤ 7. Explain your reasoning and graph
the solution set.
Answers
Let n = the number
The solution set is {x | x > 10}. 2. 5 ≥ 7 + y.
What is the value of N?It's used to refer to the collection of all natural numbers. Positive whole numbers that are not zero make up the natural numbers. N = 1 , 2 , 3 , 4 . By multiplying the integers from 1 to n, the factorial of n is calculated and denoted by the symbol n!. n! = n (n - 1)! is the formula for n factorial. Example: What is9! if8, which is40,320, is?The sample size, or n, is the number of data points. described in Chapter 2 here. in a probability experiment using a binomial model, the total number of trials.Instead of the product n n, which is typically pronounced"n squared," the equivalent exponentiation n2 is used to represent a number's square.To learn more about exponentiation refer to:
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A student made two patterns to show multiplication of a decimal by powers of ten. the equations shown for both patterns are incorrect. pattern A
3.675. 10 =3.7650
3.675. 100= 3.67500
3.675.1,000= 3.675000
pattern B
3.675. 10=3.0675
3.675.0.01= 3.00675
3.675. 0.001= 3.000675
explain why the equations in each of the patterns are false. Include in your explanation the values that should appear on the right side of each equation in both patterns to make the equations true.
Answers
If a student made two patterns to show multiplication of a decimal by powers of ten. All the value are incorrect. The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
How to find the correct value?Pattern A
3.675×10 =3.7650 Incorrect
3.675×10 = 36.75 Correct
3.675× 100= 3.67500 Incorrect
3.675×100= 367.5 Correct
3.675×1,000= 3.675000 Incorrect
3.675×1,000 = 3,675 Correct
Pattern B
3.675×10=3.0675 Incorrect
3.675× 10= 36.75 Correct
3.675×0.01= 3.00675 Incorrect
3.675×0.01= 0.03675 Correct
3.675×0.001= 3.000675 Incorrect
3.675×0.001= 0.003675 Correct
The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
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If these two shapes are similar, what is the measure of the missing length j?
Answers
Step-by-step explanation:
since the 2 shapes are similar then their sides are proportional
9/18= j/90
then j equals 45
Insurance companies are interested in the average health costs each year for their dients, so that they can
determine the costs of health insurance. Match the vocabulary word with its corresponding example.
888
All of the insurance company's dients
The cost each year for health care
The average health care cost each year for all of the insurance company's dients
The average health care cost each year for the 400 dients that the insurance company
included in this study
The 400 dients that the insurance company included in this study
The list of the 400 annual health care costs for the dients that the insurance company
indude in the study
a. Parameter
b. Population
c. Sample
d. Statistic
e. Data
f. Variable
Answers
Therefore , the solution of the given problem of population is . Sample - The 400 clients that the insurance company included in this study
Define Population.In common parlance, a population is a distinct group of people who share a common citizenship, identity, or set of traits. A population is a sampling that is typical of a broader group of individuals (or even objects) that share one or more variables characteristics.
Here,
A party promises to reimburse another party in exchange for a fee in the case of a certain loss, damage, or injury as a way of financial loss protection. It is a method of risk management that is primarily employed to protect against the risk of a potential loss.
a. Parameter - The average health care cost each year for all of the insurance company's clients
b. Population - All of the insurance company's clients
c. Sample - The 400 clients that the insurance company included in this study
d. Statistic - The average health care costs each year for the 400 clients that the insurance company included in this study
e. Data - The list of the 400 annual health care costs for the clients that the insurance company includes in the study
f. Variable - The cost each year for health care
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Illustrate the effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream
Answers
The effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream is that there will be more production and demand in the market.
What is Market?This is referred to as a place where buyers and sellers can meet to facilitate the exchange or transaction of goods and services.
A decrease in the price of milk and input to ice cream means that production costs would fall, which will cause the suppliers to produce more thereby shifting the supply curve to the right with the demand for the goods being increased which is therefore the effect on the market.
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(3,-3) m= -2/3
Formula
Y-Y1= m(x-x1)
Answers
slope form -
y - y1 = m(x - x1)
y - (-3) = -2/3(x - 3)
y + 3 = -2/3x + 2
y = -2/3x - 1
Given:
f(x) = x² + x − 6
g(x) = x + 3
Find: (f/g)(x)
Answers
Answer:
x–2, x ≠ -3
Step-by-step explanation:
Solution in the diagram
Can someone solve 18?
Answers
The piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function. Piecewise functions are implemented in the Wolfram Language as PiecewiseAdditional piecewise functions include the Heaviside step function, rectangle function, and triangle function.Given is the absolute value function -
f(x) = 1/2 |x|
We can write it as a piecewise function as follows. The given function is as follows :
f(x) = 1/2 |x|
The absolute value function is given as -
|x| = - x {x < 0}
|x| = x {x ≥ 0}
So, we can write the piecewise function as -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
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Cones A and B both have volume 48pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B.
Answers
The possible radius and height for Cone B are 3 units and 16 units respectively
How to determine the radius and height of the cone
The formula for calculating the volume of a cone is expressed mathematically;
Volume = 1/3 πr²h
Given that;
π takes the value 3.1 4r is the radius of the coneh is the height of the coneFrom the information given, we have that;
Both cone A and B have volume of 48πCone A has 6 units and height of 4 unitsNow, let the height of cone B be 16 units
Substitute the value into the formula, we have;
48π = 1/ 3 × π × r² × 16
multiply the values, we have
48 = 16r²/3
cross multiply
16r² = 144
Divide both sides by 16
r² = 144/16
r² =9
Find the square root of both sides
r = 3units
Hence, the values are 3 units and 16 units
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The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have an equal monthly salary of P7200, P7600, P6900, P8200, P7800 and P7400 respectively. What is the mean monthly salary of all the employees of the company?
Answers
The average monthly wage for the entire workforce of the business is $7489.09.
What is Mean?
The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.
Given, The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have equal monthly salaries of $7200, $7600, $6900, $8200, $7800, and $7400 respectively.
First, calculate the total monthly salary
22*7200 + 32*7600 + 18*6900 + 16*8200 + 10*7800 + 12*7200 dollars.
Total monthly salary = $823,800
Then divide this sum by the total number of employees
22 + 32 + 18 + 16 + 10 + 12
Total number of employees = 110
the mean monthly salary of all the employees = [tex]\frac{Total salary}{total number of employee}[/tex]
the mean monthly salary of all the employees = 823800/ 110
the mean monthly salary of all the employees = 7489.0909
Therefore, the mean monthly salary of all the employees of the company is $7489.09.
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Express The Ratio 36 : 42 In it's Simplest Form ?
Answers
Answer:
6/7
Step-by-step explanation:
36/42 = 36:6/42:6 = 6/7
This tablet shows an example of
was first used by the
>
It
Answers
Answer: the answer is 1.cuneiform & 2.sumerians
Step-by-step explanation: searched it up
Teddy works part-time in the Sony Store. He has a base salary of $12.50/h plus a commission of 12% of the total sales he makes.
If Teddy works 10 hours and sells $1500 electronics, how much will he earn this week?
Answers
Answer: $305
Step-by-step explanation:
1) 12.50 multiplied by 10= 125
2) 12% of 1500 is 180
3) 125+180=305
A growing amusement park is able to sell 7 times as many tickets each year as it did the year before. If you list the number of tickets sold over time, what kind of sequence will you see?
tysm! :)
Answers
If you list the number of tickets sold over time, the kind of sequence which you would see include the following: B. geometric.
What is a geometric sequence?In Mathematics, a geometric sequence can be defined as a series of real and natural numbers that are calculated by multiplying the next number by the same number (common or constant ratio) each time.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Assuming the variable x represents the number of ticket sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression which models this situation is given by geometric sequence:
x, 7x, 49x, 343x, .....
Check:
7/1 = 49/7 = 343/49 = 7 (proof).
Therefore, this is a geometric sequence.
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Complete Question:
A growing amusement park is able to sell 7 times as many tickets each year as it did the year before. If you list the number of tickets sold over time, what kind of sequence will you see?
arithmetic
geometric
both
neither
Question
Enter a linear equation that models the situation.
A drugstore sells pens for $1.40 each and notebooks for $2 each. The owner would like to sell $40 of these
items each day. Use p for the number of pens and n for the number of notebooks.
A linear equation that models the situation is
= 40.
Answers
This equation represents the total daily revenue from the pens (1.4p) and notebooks (2n) and sets it equal to the target revenue of $40. The variables p and n represent the number of pens and notebooks sold, respectively. This equation can be used to determine the number of pens and notebooks that need to be sold in order to reach the target revenue of $40.
Answer:
1.40p+2n=40
Step-by-step explanation:
Perry borrows $150 from his brother to fix his car. His brother doesn't like lending Perry money and so charges him 7% interest per month. a. Write a rule in the "y=..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments.
Answers
Answer: Let's say,
y = the amount of money Perry will owe his brother after n months.
x = the principal (the initial amount borrowed) = 150
r = the interest rate per month = 7/100 = 0.07
n = number of months.
We know that Interest on a loan is calculated by multiplying the principal by the interest rate.
Therefore, the interest for n months is (0.07*x)*n
So to find the total amount Perry will owe his brother after n months, we need to add the interest to the principal amount.
y = x + interest
y = x + (r*x)n
y = x(1 + rn)
Therefore, the rule in the "y =..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments is:
y = 150(1 + 0.07*n)
It's worth noting that this formula can be used to calculate the amount he will owe after any number of months by changing the value of n, and It's assuming he doesn't make any payments, meaning if he makes any payments, the total amount he will owe will change.
Step-by-step explanation:
What are the more appropriate measures of center and spread for this data
set?
Answers
Except Option - A all satisfy the more appropriate measures of center and spread for the data that is median and IQR.
Given that,
We have to find what are the more appropriate measures of center and spread for data.
We know that,
Mean, median, and mode are the three central tendencies, and median is the more accurate indicator.
This is because
i) Extreme values affect the mean.
ii) If there are more outliers, the mean is in error.
iii) Means that are biassed to the right or left may not accurately reflect the nature of the data.
However, median is preferable to mean because it represents the center entry and is unaffected by extreme items or outliers.
Since extreme items will show higher standard deviation and some outliers may be misleading, IQR is a superior spread measurement tool. However, IQR provides an excellent idea.
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Maya went shopping for a new video game because of a sale. The store was offering a 40% discount. If the price on the tag was pp, which expression does NOT represent the price after the discount but before tax?
Answers
The expression that represents the price of the video game after the discount is
p - 0.4p
Where p is the original price of the video game.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Price of the video game = p
Discount = 40%
The price of the video game after the discount.
= p - (40% of p)
= p - (40/100)p
= p - 0.4p
Thus,
The expression is p - 0.4p.
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What is the probability of picking a month at random that starts with the letter “J”
Answers
Answer:
A 1 in 4 chance or a probability of 0.25
Step-by-step explanation:
There is only 3 months that start with J and 12 months in a year so simplify 3/12 you get 1/4 or 0.25
Refer to the diagram shown.
I need help with this please help me
Answers
Answer: Angle-Side-Angle Theorem
Step-by-step explanation:
The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.
Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.
What is the equation of the line that passes through the point (7, -4) and has an
undefined slope?
Answers
y = mx + b
y = -4
Shana wants to buy a music player. She has $100 cash.
1. Can she afford a $79 unit plus HST? Yes or No?
Provide an estimate or a calculation to support your answer:
Answers
Answer:
Yes
Step-by-step explanation:
A $79 unit plus HST will be 89.27
Consider all five-digit numbers that can be created from the digits 0-9 0 - 9 where the first and last digits must be odd and no digit can repeat. What is the probability of choosing a random number that starts with 7 7 from this group? Enter a fraction or round your answer to 4 4 decimal places, if necessary.
Answers
Of these numbers, there are 504 numbers that start with 7, because there are 504 choices for the middle 3 digits and 1 choice for the first digit. Therefore, the probability of choosing a random number that starts with 7 from this group is 504 / 10,080 = 0.05, or approximately 5%.
i’m not sure if the first one right but i need help
Answers
The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.
A quadratic equation is defined.Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.
here ,
[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]
factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,240 ft Determine the flag's width and length if the length is 460 ft greater than the width.
Answers
Answer:
the flag is 50 feet long and 160 feet wide
Answer: The width is 330 feet and the length is 790 feet.
Step-by-step explanation:
We will write a system of equations to help us solve. Let w be the width and l be the length.
2w + 2l = 2,240 ft
l = 460 ft + w
Now, we will solve for w, the width, by substituting one equation into the other.
2w + 2l = 2,240 ft, l = 460 ft + w
2w + 2(460 ft + w) = 2,240 ft
2w + 920 ft + 2w = 2,240 ft
4w + 920 ft = 2,240 ft
4w = 1,320 ft
w = 330 ft
The width is 330 feet.
Now, we will solve for l, the length.
l = 460 ft + w, w = 330 ft
l = 460 ft + 330 ft
l = 790 ft
The length is 790 feet.
An engine spins a wheel with radius 5 inches at 800 rpm. How fast is this wheel spinning in miles per hour?
Answers
The wheel is spinning at 23.80 miles per hour
How determine how fast the wheel spinning in miles per hour?The wheel speed in miles per hour can be calculated using the expression below:
Speed in miles per hour = Wheels RPM × 2 × π × r × (60 / 63360),
where r is the radius of wheel , 60 converts minute to hour and 63360
converts inches to miles
Speed in miles per hour = 800 × 2 × π × 5 × (60 / 63360)
Speed in miles per hour = 23.80 miles per hour
Thus, the wheel spins at 23.80 miles per hour
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B. Higher Order Thinking For keeping business records, every three months of a year is called a quarter. How many months are equal to three-quarters of a year? Explain how you found your answer.
Answers
Answer:
9 months
Step-by-step explanation:
1 quarter is 3 months
3 quarters is 3 times 1 quarter, so it is 3 times 3 months.
3 x 3 months = 9 months
Answer: 9 months
Find the volume of a cone with a base radius of 3in and a height of 11in. Use the value 3.14 for π, and do not do anu rounding. Be Sure to include the correct unit in your answer.
Answers
So the formula to find the volume of a cone is,
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
Given,
Base of the cone is 3 inchesHeight of the cone is given as 11 inchesTo Find : The Volume of the cone
Applying the values we get,
[tex]V = 3.14X(3)^{2} X \frac{11}{3}[/tex]
[tex]V = 28.26X\frac{11}{3}[/tex]
[tex]V = 103.62in^{3}[/tex]
Hence , the volume of the cone is 103.62in³
Jacob runs 2652 yards in 15 minutes. Michael runs 7920ft in .375 hours. who will win the race?
Answers
Answer:
I think Jacob wins the race