Sin (2x -9)= Cos (x +30) to solve for x
Answers
f(x) = sin(2x -9°) -cos(x +30°)
in the range 0° ≤ x ≤ 360°
Solutions are x ∈ {23°, 129°, 143°, 263°).
_____
You can make use of a couple of trig identities to rearrange this equation.
cos(x) = sin(x+90°)
sin(a) -sin(b) = 2*cos((a+b)/2)*sin((a-b)/2)
So
sin(2x -9°) -sin(x +120°) = 2*cos((3x +111°)/2)*sin((x -129°)/2) = 0
The cosine factor will be zero for
(3x +111°)/2 = n*180° +90°
3x -69° = n*360°
x = 23° +n*120° . . . . . . for any integer n
The sine factor will be zero for
(x -129°)/2 = n*180°
x = 129° +n*360° . . . . . for any integer n
Combined, these solutions give the ones listed above in the range 0..360°.
Related Questions
what is the measure of the angle?
Answers
Measure of the angle=55°+180°=235°
We can conclude that the measure of the angle in the picture is 235°
If using the method of completing the square to solve the quadratic equation x^2+13x-35=0x 2 +13x−35=0, which number would have to be added to "complete the square"?
Answers
Answer:
42.25 or 169/4 on delta math
Step-by-step explanation:
In the coordinate plane line p had slope 8 and y intercept (0,5). Line r is the result of dilating line p by a factor of 3 with (0,3) what is the slope and y intercept of line r?
Answers
The slope of line r is 24 and the y-intercept is (0, 3).
How to find the slope and y-intercept?
To find the slope and y-intercept of line r, which is the result of dilating line p by a factor of 3 with a center at (0,3), we can use the following steps:
The slope of the dilated line r is the product of the dilation factor and the slope of the original line p.
The y-intercept of the dilated line r is the point where the original line p intersects the line of dilation.
Given that line p has a slope of 8 and a y-intercept of (0,5), the slope of line r is:
8 * 3 = 24.
The y-intercept is (0, 3)
Therefore, the slope of line r is 24 and the y-intercept is (0, 3).
The sum in a half adder can be represented by what boolean expression (assuming a
Answers
If they are both 0, the sum is 0. If they are both 1, the sum is 0 and the carry is 1.
This is the XOR logic gate; either one of the two inputs, but not both. In boolean algebra, XOR can be represented as: ¬AB + A¬B
A rectangular room has an area of 315 square feet. the length is 6 feet more than the width. find the dimensions of the room.
Answers
Length - (x+6)ft.
x(x+6)=315
x²+6x-315=0
a=1, b=6, c=-315
D=b²-4ac=36+4*1*315=1296, √D=√1296=36
[tex] x = \frac{-b+/- \sqrt{D} }{2a} \\ \\ x= \frac{-6+/-36}{2} \\ \\ x=15, x=-21[/tex]
For the width we can use only positive number.
The width =15 ft.
The length =15+6=21 ft.
Check :
Area =15*21=315 ft²
The room's width is calculated to be 15 feet, and the length, which is 6 feet more than the width, comes to 21 feet. These dimensions satisfy the given area of 315 square feet for the rectangular room.
To find the dimensions of a rectangular room with a known area where one dimension is dependent on the other, we can use algebraic methods to determine the length and width. In this case, the area of the room is given as 315 square feet and it is known that the length is 6 feet more than the width. Let's denote the width of the room as 'w' feet. Therefore, the length will be 'w + 6' feet. The area of a rectangle is calculated by multiplying the length by the width, so we have the following equation:
w imes (w + 6) = 315
Expanding the left side of the equation gives us:
w²+ 6w = 315
To find the value of w, let's move all terms to one side to form a quadratic equation:
w²+6w - 315 = 0
Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. For this case, factoring is applicable. We look for two numbers that multiply to -315 and add up to 6. The numbers 21 and -15 satisfy this condition. Therefore, we can write the equation as:
(w + 21)(w - 15) = 0
The possible solutions for w are -21 or 15; since a width cannot be negative, we take the positive solution:
w = 15 feet
Having obtained the width, we can now find the length:
Length = w + 6 = 15 feet + 6 feet = 21 feet
Therefore, the dimensions of the room are 15 feet in width and 21 feet in length.
Why are jobs at food stands and restaurants good for college students?
Answers
Answer:
The reason a university student is looking for work is that he needs an extra salary income.
Step-by-step explanation:
It is a way to get a salary without overloading tasks.
In addition to that many times, they are given the time to study and work because there are very flexible schedules.
The university student gets used to the need to work for a fixed salary.
In addition, many university students need income to be able to pay the value of the semester or any project necessary for the university.
What is the first step to simplify the expression: [–23 – [5 · (2 – 4)]] ÷ 32
Answers
Short answer: 2 - 4
Why?
When you have an equation with parenthesis, you do those first. When you have parenthesis inside of parenthesis, you do that first.
Hope this helped you! ♥
Answer:
According to PEDMAS , We first simplify the PARENTHESES
[5 · (2 – 4)] = [5· -2] = -10
Step-by-step explanation:
Given expression [–23 – [5 · (2 – 4)]] ÷ 32
We have to find the first step to simplify the given expression.
We apply PEDMAS
P stands for PARENTHESES
E stands for EXPONENTS
D stands for DIVIDE
M stands for MULTIPLY
A stands for ADDITION
S stands for SUBTRACTION.
So, according to PEDMAS , We first simplify the PARENTHESES
Thus, [5 · (2 – 4)] = [5· -2] = -10
The perimeter of a rectangular garden is 43.8 feet. Its length is 12.4 feet. What is the width
Answers
43.8 =2(12.4 + w)
21.9=12.4 +w
21.9-12.4 = w
w=9.5 feet
First you know what the length is. You must find the measurement of both combined.
12.4 x 2 = 24.8 (Length)
Subtract this number from the perimeter. 43.8 - 24.8 = 19.
19 is your width multiplied by two. The total measurement of both, to find just the width divide by 2.
19 / 2 = 9.5 (WIDTH)
in a cylinder the radius and height was quadrupled. How much bigger would the new surface area be then the original surface area.
Answers
A = 2 * pi * r ^ 2 + 2 * pi * r * h
Where,
r: radio
h: height
The area when the dimensions are modified is:
A '= 2 * pi * (4r) ^ 2 + 2 * pi * (4r) * (4h)
Rewriting we have:
A '= 16 * 2 * pi * r ^ 2 + 16 * 2 * pi * r * h
A '= 16 (2 * pi * r ^ 2 + 2 * pi * r * h)
A '= 16A
Answer:
the new surface area would be 16 times bigger than the original surface area
if in a cylinder the radius and height was quadrupled
so
the scale factor is equal to 4
scale factor=4
and
new surface area=[scale factor]²*original surface area
new surface area=[4]²*original surface area
new surface area=16*surface area original
therefore
the new surface area will be 16 times the original surface area.
alternative method
we know that
surface area of cylinder=2*[area of the base]+perimeter of the base*height
area of the base=pi*r²
perimeter of the base=2*pi*r
original surface area=2*[pi*r²]+[2*pi*r]*h-----> 2*pi*r*[r+h]
if the radius and height was quadrupled
so
new surface area=2*pi*(4*r)*[4r+4h]-----> 2*pi*(4*r)*4*[r+h]
new surface area=16*[2*pi*r*(r+h)]----> 16*[original surface area]
the answer is
the new surface area will be 16 times the original surface area.
Two angles whose measures add up to 90º are called?
Answers
If Kareem’s living room has an area of 225 square feet, how much will he spend to carpet his living room?
Answers
Answer: $ 568.99
Because 18.99+22 x 225/9 = 568.99
Answer: 568.99
Step-by-step explanation: your mom
saidhari bought a toaster oven for $60. this price was 1/4 off the list price. What was the list price
Answers
Final answer:
The list price of the toaster oven was $80.
Explanation:
To find the list price, we need to determine the price of the toaster oven before the discount. Let's call the list price 'x'. The discount is 1/4 off the list price, so the discounted price is 3/4 of the list price. We can set up the equation 3/4 * x = $60 to find the value of 'x'. To solve for x, we can multiply both sides of the equation by 4/3: (3/4 * 4/3) * x = $60 * 4/3. Simplifying the equation gives us x = $80.
The table below shows the number of hours some college athletes in two states spend on indoor sports each week:
State A 7 9 5 4 25 21 6 6 8
State B 14 12 10 13 15 14 11 15 16
Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)
Part B: Are the box plots symmetric? Justify your answer. (4 points)
Answers
State B: 14 12 10 13 15 14 11 15 16
When arranged in order,
State A: 4 5 6 6 7 8 9 21 25
State B: 10 11 12 13 14 14 15 15 16
Part A:
For state A, Q1 = minimum number = 4, Q2 is the lower quartile = 6, Q3 is the middle number = 7, Q4 is the upper quartile = (9 + 21)/2 = 15, Q5 = maximum number = 25
Interquatile range = upper quatile - lower quatile = 15 - 6 = 9
For state B, Q1 = minimum number = 10, Q2 is the lower quartile = 11.5, Q3 is the middle number = 14, Q4 is the upper quartile = 15, Q5 = maximum number = 16
Interquatile range = upper quatile - lower quatile = 15 - 11.5 = 3.5
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Answers
To prove this one way, you can show the multiplication of the quotient and divisor. If the division was correct, it would end up as the value of the dividend:
84 * 15 = 1260
1260 = 1260
To prove this another way, you can show 84 being added 15 times and seeing if it totals 1260:
84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 + 84 = 1260
1260 = 1260
Answer:
1260/15=84
Step-by-step explanation:
1200/15=80 and 60/15=4
80 + 4 = 84.
Another way is 15 + 15 + 15 and keep counting 84 times and you would get 84
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A class is trying to eliminate t from the parametric equations x=t^2+3 and y=4t. Beth says that she can write t=sqrt(x-3) to eliminate the parameter. Why is this wrong?
She should have added 3 to x, not subtracted.
She should always solve for t as a function of y.
She should have taken both the positive and negative square root.
She should first substitute y for t before solving.
Answers
Because when a number is squared, even if it is negative it can become positive,
so taking square should include + and - to the answer.
Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
We have to find the error which is done by Beth to eliminate the parameter. So, we will take the first equation and do all the steps to find the error and get the desired result.
Given that, x=t²+3 and y=4t
Try find the expression of "t" in terms of "x". We will use equation (1) and we have
x-3=t²
t=√(x-3)
Thus, Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.
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An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was interested in investigating the proportion of the new cars that experienced a mechanical problem within the first 5,000 miles driven. (a)
A list of the names and addresses of all customers who bought the new cars is available. Describe a sampling plan that could be used to obtain a simple random sample of 1,000 customers from the list.
Each customer from a simple random sample of 1,000 customers who bought one of the new cars was asked whether they experienced any mechanical problems within the first 5,000 miles driven. Forty customers from the sample reported a problem. Of the 40 customers who reported a problem, 13 customers, or 32.5%, reported a problem specifically with the power door locks. (b)
Explain why 0.325 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven. (c)
Based on the results of the sample, give a point estimate of the number of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven.
Answers
1) Define the sample population: who are the customers you want to contact?
The costumers who bought a new car on a certain year.
2) Define the size of population: how many customers are you going to contact?
Of the 30000 customers who bought a car, you want to contact 1000 customers.
3) Define the contact options: how are you going to contact the customers?
You have a list of names and addresses, therefore you can send a questionnaire via mail.
4) Form a sampling frame: what is the time or contact frame to get in touch with your customers?
You will send the questionnaires and you will wait two months for the answer.
5) Define the analysis method: is yours a qualitative or quantitative research?
In your case, you want a quantitative research and therefore a probabilistic sampling.
B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.
C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
P = 13 / 1000
= 0.013
Therefore,
N = 0.013 × 30000
= 390
Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
Analyzing the situation of the automobile industry it will be important that:
A)build a list that attracts buyers to cars, looking for an interested audience, through emails, nearby residents.
B) 0.013
C)390
If it is necessary to analyze how to attract a corresponding public so that a car sale can take place, a list will be created that takes into account:
A) 1) Define the sample population: The costumers who bought a new car on a certain year.
2) Define the size of population: Of the 30000 customers who bought a car, you want to contact 1000 customers.
3) Define the contact options: You have a list of names and addresses, therefore you can send a questionnaire via mail.
4) Form a sampling frame: You will send the questionnaires and you will wait two months for the answer.
5) Define the analysis method: In your case, you want a quantitative research and therefore a probabilistic sampling.
B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.
C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
[tex]P= \frac{13}{1000} = 0.013[/tex]
[tex]N=0.013*30000=390[/tex]
Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
Simplify the expression.
(–1 + 6i) + (–4 + 2i)
Answers
= -1 + 6i - 4 + 2i
= -5 + 8i
Hope it helped!
according to the U.S. census bureau, the population of Hawaii in 2010 was 1,360,301 and it was growing at an annual rate of 1.2%. Predict the population in Hawaii in 2032
Answers
The ratio of the areas of two similar polygons is 400:25. what is the ratio of their corresponding sides
Answers
A1 / A2 = 400/25 = k ^ 2
Therefore, the relationship of the sides is given by:
L1 / L2 = k
Clearing k we have:
k = root (400/25)
Rewriting we have:
L1 / L2 = k = 20/5
Answer:
The ratio of their corresponding sides is:
20: 5
Answer: 16:1
simplify 400:25 by dividing 400 by 25, which is 16.
simplify
3 (2x+4y-2z)+7 (x+y-4z)
Answers
A and B share the cost in a ratio of 3:2. A pays £125 how much does b pay?
Answers
3 + 2 = 5
125 divided by 5 = 25
25 x 3:2 = 2
25 x 2 = 50
To solve this problem, we can set up proportion, which is two equivalent ratios. In this case, we are using the ratio of A to B to figure out the amount that B pays using our value for A. We are allowing x to represent the unknown value for the B payment. This is modeled below:
3/2 = £125/x
To simplify, we can perform cross-multiplication. This means multiplying the numerator of one fraction by the denominator of the other and setting it equal to the product of the other numerator and denominator. This is modeled below:
(125)(2) = (3)(x)
Next, we can simplify the equation by performing the multiplication on both sides of the equation.
250 = 3x
Finally, we should divide both sides by 3 to get our unknown variable x alone on the right side of the equation.
x = 83.33
Therefore, B costs £83.33.
Hope this helps!
How to find the length of a rectangle when given the height?
Answers
The formula for area is:
Area = length • width
If you were given the width and area of the rectangle you would be able to find the length by doing inverse operations. In this case, the opposite of multipication is division
Example: 56 = l • 8
56 / 8 = 7
56 = 7 • 8
The length is 7.
I hope this helps!
The length of a rectangle can be found by dividing the area of the rectangle by its height if the area is known. Without the area, additional information is necessary to calculate the length.
To find the length of a rectangle when given the height, we typically need additional information such as the area or the aspect ratio of the rectangle. However, without that information, directly calculating the length is not possible. Let's explore a scenario where we have the area of the rectangle. In such a case, if we are given the area (A) of the rectangle and the height (h), we can use the formula for the area of a rectangle which is A = length times height. Solving for the length (l), we rearrange the formula to get l = A/h. For instance, if the area of the rectangle is 150 square centimetres and the height is 10 centimetres, the length would be 150 cm2 / 10 cm = 15 cm. It's also important to consider proportions when scaling shapes.
A bag contains 2 blue, 4 green, and 3 white chips. What is the probability of drawing a white chip then another white chip without replacement?
A.) 7/9
B.) 8/81
C.) 2/3
D.) 1/12
Answers
total white chips = 3
probability of picking white first = 3/9 = 1/3
after taking one chip there would be 9-1 = 8 chips left
and 3-1 2 white chips left
probability of picking 2nd white chip = 2/8 = 1/4
probability of picking both = 1/3 x 1/4 = 1/12
answer is D
complete the general solution to y=cos^-1(1) for K a whole number
Answers
Answer:
If the equation is exactly the one you posted then the unique answer is:
[tex]y = 0[/tex]
or what is the same:
[tex]y=0K[/tex]
Explanation:
If your equation is exactly the one you posted then it has only one solution: y = 0
Because the range of [tex]y=\cos^{-1}(x)[/tex] is the interval [tex][0, \pi][/tex]
The meaning of [tex]\cos^{-1}(1)[/tex] is to find the angle whose cosine is 1.
In the range of the function arccosine the only angle whose cosine is 1 is the angle 0.
But if your equation was the following one:
[tex]\cos(y)=1[/tex]
Then in that case we would have infinite solutions since it will be the set:
[tex]y=\cos^{-1}(1)+2K\pi[/tex] where K is an integer, since the period of cosine is [tex]2\pi[/tex]
So, in such a case the solution set would be:
[tex]y=0+2K\pi=2K\pi[/tex]
But for the equation you posted, the unique solution is: y = 0 or what is the same y = 0K
Graph f(x)=- square root -x
Answers
[tex]x=0\to f(0)=-\sqrt0=0\to(0;\ 0)\\\\x=-0.25\to f(-0.25)=-\sqrt{-(-0.25)}=-\sqrt{0.25}=-0.5\to(-0.25;-0.5)\\\\x=-1\to f(-1)=-\sqrt{-(-1)}=-\sqrt1=-1\to(-1;-1)\\\\x=-4\to f(-4)=-\sqrt{-(-4)}=-\sqrt4=-2\to(-4;-2)[/tex]
The graph of function f (x) = - √- x is shown in image.
We have to given that,
Graph the function,
f (x) = - √- x
Here, Function is defined as,
f (x) = - √- x
At x = 0;
f (x) = - √-0
f (x) = 0
Plot the graph of function f (x) = - √- x.
Hence, The graph of function f (x) = - √- x is shown in image.
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m 2 = 40°, m 4 = 150°, m 3 =
Answers
First you have to find angle 1
angle 1 and angle 4 are supplementary meaning they add to 180
angle 1 + angle 4 = 180
angle 1 + 150 = 180
angle 1 = 30
The angles in a triangle always add up to 180
angle 1 + angle 2 + angle 3 = 180
30 + 40 + angle 3 = 180
70 + angle 3 = 180
angle 3 = 110
The answer is 110°
Hope this helps!
The answer is 110° Hope this helps!
Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+11x+21=0
Answers
Then we see were the graph cuts the x-axis, and these values of x are the real solutions of the given equation:
The real solutions of the given equation are:x = -1, 3, and 7
Answer:
c: x=-1,3,7
Step-by-step explanation:
Barbara is making bracelets to sell on her Etsy site. It costs her $0.79 per bead and she needs 22 beads per bracelet. She sells her bracelets for $28 each. What is the percent markup per bracelet?
Answers
Training course a takes 9 weeks and 4 days to complete.training course b takes 54 days to complete.how much longer does training course a take than training coure b to complete
Answers
[tex]7 \times 9 + 4 = 67 \\ 67 - 54 = 13[/tex]
Training course A takes 13 more days than training course B.
Training course A takes 13 days longer than training course B to complete.
Explanation:To find how much longer training course A takes than training course B to complete, we need to compare the durations of the two given courses with given values.
Training course A takes 9 weeks and 4 days to complete, which is found to be :
9 x 7 + 4 = 67 days in total.
Training course B takes 54 days to complete.
To find the difference, we subtract the duration of course B from the duration of course A:
67 - 54 = 13 days.
Therefore, training course A takes 13 days longer than training course B to complete.
Ernie is making a cylinder-shaped container to store his pens. The container has a base on one end and an opening on the other end. He is going to spray paint the outside of the container. The container has a diameter of 3 inches and a height of 18 inches.
Answers
We have then:
A = pi * r ^ 2 + 2 * pi * r * h
Where,
r: cylinder radius
h: cylinder height
Substituting values:
A = 3.14 * (3/2) ^ 2 + 2 * 3.14 * (3/2) * 18
A = 176.625 in ^ 2
Answer:
The amount of paint needed is:
A = 176.625 in ^ 2