Answer:
89.6°
Step-by-step explanation:
180-90.4=89.6°
Answer: 89.6
Step-by-step explanation:
Supplementary means angles adding up to 180
180-90.4 = x
x=89.6 this is your supplemental angle
Find the equation that has given solutions: x=-5 and x =2
The equation that has given solutions x = -5 and x = 2 is [tex]x^2 + 3x - 10 = 0.[/tex]
If the given solutions of an equation are x = -5 and x = 2, then the equation can be written as a product of two linear factors, (x + 5) and (x - 2), because when either of these factors is equal to zero, the corresponding solution is obtained.
So, the equation is:
(x + 5)(x - 2) = 0
Expanding the product, we get:
[tex]x^2 + 3x - 10 = 0[/tex]
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Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x) = 2300 + 5x + 0.01x2 + 0.0002x? (a) Find the marginal cost function 5 + 0.02x + 0.0006r2 (b) Find C'(100) C'(100) = 11 What does this predict? The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans. (c) Find the difference between C'(100) and the actual cost of manufacturing the 101st pair of jeans (Round your answer to two decimal places.) $ 3100
The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans.
The marginal cost function of C(x) = 2300 + 5x + 0.01x2 + 0.0002x is $3100
Process of finding marginal cost:
(a) To find the marginal cost function, we need to take the derivative of the cost function C(x) with respect to x. This gives us:
C'(x) = 5 + 0.02x + 0.0006x^2
So the marginal cost function is:
MC(x) = 5 + 0.02x + 0.0006x^2
(b) To find C'(100), we simply plug in x = 100 into the marginal cost function we just found:
C'(100) = 5 + 0.02(100) + 0.0006(100)^2 = 11
This predicts the exact cost of manufacturing the 101st pair of jeans.
The approximate cost of the 101st pair of jeans can be found by plugging in x = 101 into the original cost function C(x):
C(101) = 2300 + 5(101) + 0.01(101)^2 + 0.0002(101) ≈ $3120.02
The approximate cost of the 101st pair of jeans.
The exact cost of the 100th pair of jeans can be found by plugging in x = 100 into the original cost function C(x):
C(100) = 2300 + 5(100) + 0.01(100)^2 + 0.0002(100) = $3100
Hence the marginal cost is $3100
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In a poll of students at the football championship, 90% of the students say that football is better than basketball.
Explain why it is not a valid conclusion to say that football is more popular than basketball at school.
Suggest a better method of determining which sport is more popular.
Answer:
Part (a): Because the survey was held at basketball championship.
Part (b): The survey among students should held at school or in any common place.
Step-by-step explanation:
Find the value of each variable. For theâ circle, the dot represents the center.
A four sided polygon is inside a circle such that each vertex of the polygon is a point on the circle. The top and bottom sides of the polygon slowly rise from left to right. The left and right sides of the polygon quickly fall from left to right. The angle measures of the polygon are as follows, clockwise from the top left: "c" degrees, 123 degrees, 92 degrees, and "d" degrees. The arc bounded by the left side of the polygon is labeled 94 degrees. The arc bounded by the right side of the polygon is labeled "b" degrees. The arc bounded by the bottom side of the polygon is labeled "a" degrees.
123 degrees
92 degrees
94 degrees
c degrees
d degrees
b degrees
a degrees
The values of the variables are:
c = 86 degrees
d = 168 degrees
a = 57 degrees
b = 94 degrees
Since the polygon is inscribed in a circle, the opposite angles of the polygon are supplementary. Thus, we have:
The top and bottom angles of the polygon are supplementary to angle "d":
c + 92 + 123 = 180 + d
The left and right angles of the polygon are supplementary to angle "c":
c + 94 = 180, so c = 86
The angle "a" is supplementary to angle "d":
a + 123 = 180 + d
The angle "b" is supplementary to angle "c":
b + 86 = 180
Substituting the values of "c" and solving the system of equations, we get:
d = 168
a = 57
b = 94
Therefore, the values of the variables are:
c = 86 degrees
d = 168 degrees
a = 57 degrees
b = 94 degrees
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O A fifth grade
class is split into groups
of
students. The teacher brought in candy
bars for a fraction celebration. When it
was time for
the celebration,
the teacher'
gave each
group
6
candi bars. How much
does each student get. Al representation
Answer:
IT depends on how many kids there are per group.
Step-by-step explanation:
Describe the transformations f(x)= square root 4x
The transformation of f(x) = √(4x) from the parent function g(x) = √(x) includes a horizontal stretch by a factor of 1/4, with no horizontal or vertical shifts.
The function f(x) = √(4x) is a transformation of the parent function, g(x) = √(x). The transformations include a horizontal stretch, a horizontal shift, and a vertical shift. Let's break down each transformation step-by-step:
1. Horizontal Stretch: The factor 4 inside the square root function multiplies the input (x) by 4. This results in a horizontal stretch by a factor of 1/4, meaning the graph is compressed horizontally towards the y-axis.
2. Horizontal Shift: There is no additional value added or subtracted from the input (x), so there is no horizontal shift in this function. The graph remains in its position along the x-axis.
3. Vertical Shift: Similarly, there is no additional value added or subtracted from the output (the entire function), so there is no vertical shift in this function. The graph remains in its position along the y-axis.
This results in the graph of f(x) being compressed towards the y-axis compared to the graph of g(x).
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Solve systems of Equation by substitution method
3(x-2) + y = 7
4x - 3(y-1) = 16
The values of the variables are x = 4 and y = 1
How to solve the equationWe have the equations as;
3(x-2) + y = 7
4x - 3(y-1) = 16
Using the substitution method
Make 'y' the subject of formula from equation (1), we have;
y = 7 - 3(x-2)
Now, substitute the expression as y in equation (2), we get;
4x - 3(7 - 3(x-2) - 1) = 16
expand the bracket, we have;
4x - 3(7 - 3x + 6 - 1) = 16
collect the like terms
4x - 3(12 - 3x) = 16
4x - 36 + 9x = 16
collect the like terms
13x = 52
x = 4
Substitute the value
y = 7 - 3(4 -2 )
y = 7 -3(2)
y = 1
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Write an expression for the nth term of the sequence. (Your formula should work for n=1,2,...) 4 5 6 7 5 6 7 8 Need Help? Watch
The nth term of the sequence 4 5 6 7 5 6 7 8 is given by a_n = 3 + (n-1)/2 for odd n and a_n = 4 + (n-2)/2 for even n.
How to find the nth term of a given sequence?To find the nth term of the given sequence, we need to observe the pattern in the sequence. We can see that the sequence consists of two parts:
the first part is a consecutive sequence of integers starting from 4, and the second part is a consecutive sequence of integers starting from 5, where the second part starts right after the first part ends.
So, we can express the nth term of the sequence as follows:
If n is odd, then the nth term is given by:
a_n = 3 + (n-1)/2
If n is even, then the nth term is given by:
a_n = 4 + (n-2)/2
Using this formula, we can find any term of the given sequence by plugging in the corresponding value of n. For example:
When n=1, the first term is 4: a_1 = 4.
When n=6, the sixth term is 6: a_6 = 6.
When n=7, the seventh term is 7: a_7 = 7.
When n=8, the eighth term is 8: a_8 = 8.
Note that this formula works only for n = 1, 2, 3, 4, 5, 6, 7, 8, ... , since the sequence has only 8 terms.
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A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0. 90. The population proportion of kernels that will pop for Brand S is 0. 85. Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0. 92 Brand S 200 0. 89 The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0. 3. Is the consumer group’s claim correct? Yes. The mean is 0. 92−0. 89=0. 3. Yes. The mean is 0. 92 minus 0. 89 equals 0. 3. A No. The mean is 0. 92+0. 892=0. 905. No. The mean is the fraction 0. 92 plus 0. 89 over 2 equals 0. 905. B No. The mean is 0. 92−0. 892=0. 15. No. The mean is the fraction 0. 92 minus 0. 89 over 2 equals 0. 15. C No. The mean is 0. 90+0. 852=0. 875. No. The mean is the fraction 0. 90 plus 0. 85 over 2 equals 0. 875. D No. The mean is 0. 90−0. 85=0. 5
The mean of all possible differences in sample proportions (Brand R minus Brand S) is given by:
mean = pR - pS,
where pR is the population proportion of kernels that will pop for Brand R, and pS is the population proportion of kernels that will pop for Brand S.
Substituting the given values, we get:
mean = 0.90 - 0.85 = 0.05
However, the consumer group claims that the mean of all possible differences in sample proportions is 0.3. This claim is not supported by the calculations above.
Therefore, the correct answer is:
C) No. The mean is 0.90+0.85/2=0.875. No. The mean is the fraction 0.90 plus 0.85 over 2 equals 0.875.
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A designer is planning a trai
l mix box that is
shaped l
ike a rectangular prism. The front of
the box must have the width and height shown.
The volume of the box must be 162 cubic
inches. What must be the depth, d, of the box?
HELP
The depth of trail mix box that is shaped like a rectangular prism must be 2.4 inches.
How can we estimate the depth of the box?We are going to use the formula for determining volume to work out the depth of the rectangular prism.
The volume of a rectangular prism is given by the formula:
V = l × w × h
where:
V = the volume
l = the length
w = the width
h = the height.
Given:
w = 7.5 inches
h = 9 inches
V = 162 cubic inches
Now, we are to find the value of d, the depth of the box, which corresponds to the length of the rectangular prism.
Substituting the values into the formula for volume:
162 = d × 7.5 × 9
Simplifying the right-hand side:
162 = 67.5d
Dividing both sides by 67.5, we get:
d = 162 ÷ 67.5
d = 2.4 inches
Therefore, the depth of the box shaped as rectangular prism = 2.4 inches.
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If I lose 20 cents an hour, and I make 10. 50 an hour. How much money do I lose every 10 dollars?
This is the simplest way I could figure out how to put it, sorry
You lose 515 dollars every time you lose 10 dollars.
Now that we know it takes 50 hours to lose 10 dollars, we can calculate how much money you lose every 10 dollars by
the hourly rate of 10.50 dollars by 50 hours and subtracting that amount from 10 dollars:
Money lost = (10.50 dollars/hour) x 50 hours - 10 dollars
Money lost = 525 dollars - 10 dollars
Money lost = 515 dollars
Therefore, you lose 515 dollars every time you lose 10 dollars.
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John owns 10 shirts and needs to select 5 to wear to school next week. How many ways can he choose the shirts? (hint: combinations)
50 ways
B 252 ways
500 ways
D 792 ways
There are 252 different combinations of shirts, the correct option is B.
In how many ways he can choose the shirts?Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:
[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]
There are 252 different combinations, so the correct option is B.
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Neave is designing a prize wheel for her school. 200 students will each spin the wheel once. Neave wants the expected number of winners to be 60.
If the wheel is split into 40 equally sized sections, how many sections should be marked “win”
Neave should mark 12 sections as "win" on the prize wheel to achieve the expected number of winners of 60 out of 200 students.
To determine how many sections should be marked "win" on Neave's prize wheel, we need to consider the expected number of winners and the total number of sections on the wheel.
Neave wants the expected number of winners to be 60 out of 200 students. This means that the probability of winning should be 60/200 = 0.3 or 30%.
If the wheel is split into 40 equally sized sections, we can assume that each section has an equal probability of being selected by a student. Therefore, to have a 30% chance of winning, we need to mark a proportionate number of sections as "win".
To calculate the number of sections to mark as "win", we multiply the total number of sections by the desired probability of winning:
40 sections * 0.3 = 12 sections.
It's important to note that the concept of expected value assumes an idealized scenario with perfect randomness. In reality, the actual number of winners may vary due to random chance and individual spin outcomes.
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Rosemary chooses to attend the University of Houston to earn her degree. Rosemary has $2,500 in her savings and a $1,000 savings bond from her grandparents to use for college. What is the estimated contribution needed from other sources to pay for Rosemary's first year? Display keyboard shortcuts for Rich Content Editor
The estimated contribution for Rosemary's first-year college fee is $6,500 including all her savings and available funds.
Savings of Rosemary = $2,500
Savings from bond = $1000
To calculate the contribution needed for Rosemary from other sources, to pay her college fee, we need to add all the available funds and subtract the money for her college fee.
Let us imagine that the total cost of Rosemary's college = $10,000
Total available funds = $2,500 + $1,000
Total available funds = $3500
The remaining amount needed = $10,000 - $3,500 = $6,500
Therefore, we can conclude that Rosemary would need an estimated contribution of $6,500.
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A student has a rectangular bedroom. If listed as ordered pairs, the corners of the bedroom are (21, 18), (21, −7), (−12, 18), and (−12, −7). What is the perimeter in feet?
A: 116
B: 58
C: 33
D: 25
The perimeter of the bedroom is 116ft
What is perimeter of rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel.
The perimeter of a rectangle is expressed as;
P = 2(l+w)
where l is the length and w is the width of the rectangle.
length = √ 21-21)²+ 18-(-7)²
= √25²
l = 25 ft
width = √ 21-(-12)²+18-18)²
= √ 33²
= 33
Perimeter = 2(33+25)
= 2 × 58
= 116ft
therefore the perimeter of the bedroom is 116ft.
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The assembly consists of two 10mm diameter rods a-b and c-d, a 20 mm diameter rod e-f and a rigid bar h; point g is located at mid-distance between points e and f. all rods are made of copper with e = 101 gpa. if the magnitude of one force p is 10 kn, determine reactions at points a, c, and f.
Reactions at points A, C, and F are as follows: RA = -RC, RAy = RCy, and RF = 10 kN.
To determine reactions at points A, C, and F for the assembly consisting of two 10mm diameter rods (A-B and C-D), a 20mm diameter rod (E-F), and a rigid bar (H), with point G located midway between points E and F, and a force of 10 kN applied:
First, calculate the cross-sectional areas of the rods:
A1 = π(10mm)² / 4 = 78.54 mm² (for rods A-B and C-D)
A2 = π(20mm)² / 4 = 314.16 mm² (for rod E-F)
Next, calculate the effective modulus of elasticity for each rod:
E1 = E2 = 101 GPa
Now, use equilibrium equations to determine reactions at points A, C, and F:
ΣFx = 0: RAx + RCx = 0
ΣFy = 0: RAy + RCy + RF = -10 kN
ΣMG = 0: (RAy)(L/2) - (RCy)(L/2) = 0
Solving the equilibrium equations, we get:
RAx = -RCx
RAy = RCy
RF = 10 kN
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Segments OT and OV are?
True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.
We have,
The factors which are be used to member a request are the segmentation variables. Common variables include demographic, geographic, psychographics and behavioral considerations.
Quantifiable population characteristics, similar as age, gender, income, education, family situation.
The primary ideal of segmentation is to identify guests with analogous attributes, and to find which parts of guests that are seductive from a profit perspective.
Understanding the request segmentation allows marketers to produce a more effective and effective marketing blend.
Hence, True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.
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complete question:
The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely ot be.[See p.104]Group of answer choicesTrueFalse
1)calculate the mean and standard deviation of the sampling distribution of
for srss of size 15.
2)interpret the standard deviation from part (1).
3)find the probability that the sample mean weight is greater than 3.55 kilograms.
It should be noted that to calculate the mean and standard deviation of the sampling distribution, you need to know the population mean (μ) and standard deviation (σ) and the sample size (n) of the distribution.
How to explain the meanThe mean (μx) of the sampling distribution of the sample mean (x) is equal to the population mean (μ):
μx = μ
The standard deviation (σx) of the sampling distribution of the sample mean (x is equal to the population standard deviation (σ) divided by the square root of the sample size (n):
σx = σ / √n
Therefore, in order to calculate the mean and standard deviation of the sampling distribution, you just need to plug in the values of μ, σ, and n into these formulas.
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How does one calculate mean and standard deviation of the sampling distribution.
How to interpret the standard deviation from part (1).
19. The functions f and g are defined by f(x) = 2x/x-2 and g(x) = x + 4 respectively. Find
gf.
Answer:
gf(x) = g(f(x)) = (x+4)(2x/x-2) = 2x^2 + 8x - 8
Which of the lines below match the function given? y = x + 5 A graph with 4 lines, labeled A, B , C, and D. Line A contains the points 0 comma 0, and 2 comma 2. Line B contains the points 0 comma 5, and 2 comma 7. Line C contains the points 0 comma 0, and 2 comma 4. Line D contains the points 0 comma 2, and 1 comma 5.
Therefore , the solution of the given problem of function comes out to be Line B to the function y = x+5.
Describe function.On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
The function is represented as
=> y = x + 5, which has a y-intercept of 5, a slope of 1, and a slope of 1.
By comparing the slope and y-intercept of each line to those of the function, we may determine which line best fits it.
Line A does not fit the function because it has a slope of 1 and a y-intercept of 0.
The function y = x + 5 is satisfied by line B, which has a slope of 1 and a y-intercept of 5.
Line C does not fit the function because it has a slope of 2 and a y-intercept of 0.
Line D does not fit the function because it has a slope of 3 and a y-intercept of 2.
Line B therefore corresponds to the function y = x+5.
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Use the function f(t) = -16t^2 + 60t + 16 to answer parts A, B, and C.
(Look at the image!)
1) Note that t is either 4 or -0.25 by virtue of the quadratic function.
2) the vertex and line of summer try are t = 1.875. See the attached graph.
How did we arrive at the above conclusion?
First, identify the values of a, b, and c in the equation...
a = -16
b = 60
c = 16
substitute these values into the quadratic formula
t = (-b ± √(b² - 4ac)) / 2a
t = (-60 ± √(60² - 4(-16)(16))) / 2(-16)
t = (-60 ± √(3600 + 1024)) / (-32)
t = (-60 ± √(4624)) / (-32)
t = (-60 ± 68) / (-32)
So, t can be:
t = (-60 + 68) / (-32) = -1/4
or
t = (-60 - 68) / (-32) = 4
2) To find the line of symmetry, we used t = -b/2a
-60/2(-16)
t = 1.875
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Find the volume of the cone in cubic feet. Use 3. 14 for π and round your answer to the nearest tenth.
(1 m ≈ 3. 2808 ft)
135,648 ft3
3,843. 8 ft3
4,790,189. 2 ft3
444,925. 4 ft3
The volume of the cone in cubic feet is approximately 0.0 cubic feet
We need to convert the given dimensions from inches to feet before calculating the volume in cubic feet.
The height of the cone is 6 inches, which is equivalent to 6/12 = 0.5 feet (since there are 12 inches in 1 foot).
The radius of the cone is 4.5 inches, which is equivalent to 4.5/12 = 0.375 feet.
Using the formula for the volume of a cone, which is:
V = (1/3) * π * r^2 * h
Substituting the given values, we get:
V = (1/3) * 3.14 * (0.375 feet)^2 * 0.5 feet
V ≈ 0.0221 cubic feet
Rounding this to the nearest tenth gives:
V ≈ 0.0 cubic feet
Therefore, the volume of the cone in cubic feet is approximately 0.0 cubic feet. None of the given options match this result.
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7. Melissa wants to check the accuracy of the finance charge on her promissory note. She has a $6,000, four-year loan at an APR of 10%. A. What is the monthly payment? b. What is the total amount of the monthly payments? c. What is the finance charge?
A. Melissa's monthly payment is approximately $146.89.
B. The total amount of the monthly payments over the four-year period is approximately $7,052.72.
C. The finance charge on the loan is approximately $1,052.72.
What is simple interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.
To calculate the monthly payment, we can use the formula:
Monthly payment = [P x r x (1 + r)ⁿ] / [(1 + r)ⁿ⁻¹]
where P is the principal (the amount of the loan), r is the monthly interest rate, and n is the number of monthly payments.
A. To find the monthly payment, we first need to calculate the values of r and n.
Since the APR is 10%, the monthly interest rate is 10% / 12 = 0.00833 (rounded to 5 decimal places).
The number of monthly payments over four years is 4 x 12 = 48.
Using these values, we can calculate the monthly payment:
Monthly payment = [6000 x 0.00833 x (1 + 0.00833)⁴⁸] / [(1 + 0.00833)⁴⁸⁻¹]
Monthly payment ≈ $146.89
So Melissa's monthly payment is approximately $146.89.
B. To find the total amount of the monthly payments, we can multiply the monthly payment by the number of payments:
Total amount of monthly payments = Monthly payment x Number of payments
Total amount of monthly payments = $146.89 x 48
Total amount of monthly payments ≈ $7,052.72
So the total amount of the monthly payments over the four-year period is approximately $7,052.72.
C. To find the finance charge, we can subtract the original principal from the total amount of the monthly payments:
Finance charge = Total amount of monthly payments - Principal
Finance charge = $7,052.72 - $6,000
Finance charge ≈ $1,052.72
So the finance charge on the loan is approximately $1,052.72.
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#1 - The value of y varies directly with x. When y = 75, x = 4. What is the value of y when x = 2? **For your response, enter the numerical value ONLY. NO Letters & NO Spaces. ** *
The answer is 37.5.
What is the value of y when x = 2 if y varies directly with x and when y = 75, x = 4?The problem provides the information that "the value of y varies directly with x", which means that there is a constant of proportionality between y and x, denoted by k. This can be written as an equation: y = kx. To find the value of k, we can use the information given in the problem. When y = 75 and x = 4, we have 75 = k(4), which means k = 75/4. Now, we can use this value of k to find the value of y when x = 2: y = (75/4)(2) = 37.5.
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Find the absolute maximum and minimum of the function f(x,y)=y√x−y2−x+3y on the domain 0≤x≤9, 0≤y≤8
The absolute maximum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8 is 2√2, which occurs at the point (2,2).
The absolute minimum of the function is -8, which occurs at the point (0,2).
To find the absolute maximum and minimum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8, we need to evaluate the function at the critical points and at the boundary of the domain.
The critical points of the function are the points where the partial derivatives with respect to x and y are both zero. Solving these equations, we get:∂f/∂x = -1 + y/(√(x-y^2)) = 0∂f/∂y = √(x-y^2) - 1 + 3 = 0Solving these equations, we get two critical points: (0,2) and (2,2). Evaluating the function at these points, we get:f(0,2) = -8f(2,2) = 2√2Next, we need to evaluate the function at the boundary of the domain. This includes the points (0,y), (9,y), (x,0), and (x,8).
Evaluating the function at these points, we get:f(0,y) = -x+3yf(9,y) = y√(9-y^2)-6f(x,0) = -xf(x,8) = 8√(x-64/9)-x+24Taking the maximum and minimum values of the function at the critical points and on the boundary of the domain, we see that the absolute maximum of the function is 2√2, which occurs at the point (2,2), and the absolute minimum of the function is -8, which occurs at the point (0,2).
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How would the equation for the blade of the wind turbine change if the point starts at the π2
position?
If the point starts at the π/2 position, the equation for the blade of the wind turbine will be sin(θ + π/2) = sin(θ - π/2)cos(β) + cos(θ - π/2)sin(β).
The equation for the blade of the wind turbine is given by the expression sin(θ) = sin(θ - β)cos(α) + cos(θ - β)sin(α), where θ represents the angle of the blade, β represents the angle between the wind direction and the blade, and α represents the pitch angle of the blade.
If the point starts at the π/2 position, we need to substitute θ + π/2 for θ in the equation. This gives us sin(θ + π/2) = sin(θ - β + π/2)cos(α) + cos(θ - β + π/2)sin(α).
Using trigonometric identities, we can simplify this expression to sin(θ + π/2) = cos(θ - β)cos(α) - sin(θ - β)sin(α).
Finally, substituting β for (π/2 - β) in the above equation, we get sin(θ + π/2) = sin(θ - π/2)cos(β) + cos(θ - π/2)sin(β). This is the required equation for the blade of the wind turbine if the point starts at the π/2 position.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
Here we try the method of trial and error to find out if the equations have a common answer as zero
Step-by-step explanation:
Now,
(a) x²-4=0
(b) x²=-4
(c) 3x²+12=0
(d) 4x²=16
(e) 2(x-2)2=0
Here if we check the first equation i.e x²-4=0
Equating - 2²-4=4-4
=0
2²-4= 4-4
=0
So option (a) is true
Now x²=-4
Substituting, - 2²=4 & 2²=4
So here we get 4≠-4
Therefore, (b) is not true
Now 3x²+12=0
3(-2)²+12= 3(4)+12
=12+12= 24
3(2)²+12= 12+12
= 24
4x²=16
Substituting, 4(-2)²= 4(4)= 16
4(2)²= 4(4)= 16
So option (d) is also true
Now, 2(x-2)2=0
Substituting, 2(-2-2)2= 2(-4)2
4(-4)= - 16
2(2-2)2= 2(0)2
=4(0)=0
Here when we put x=-2, we get - 16
when we put x=2, we get 0
So the following equation is true only for x=2 and not x=-2
I hope this helps ;)
Eratosthenes was born 276 BC. Abraham Lincoln died in 1865. How many years apart were these two events. Answer choices: 276 1865 1589 -1589
The number of years apart between Eratosthenes was born in 276 BC (Before Christ) Abraham Lincoln died in 1865 is 2140 years.
Eratosthenes was born in 276 BC
Abraham Lincoln died in 1865 AD
BC = Before Christ
AD = anno dominie
The difference between the born date of Eratosthenes and the death date of Abraham Lincoln is to be calculated by
Year difference = BC year + AD year - 1
Year difference = 276 + 1865 - 1
Year difference = 2140
hence the difference between the born date of Eratosthenes and the death date of Abraham Lincoln is 2140
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Use variation of parameters to find the particular solution to y''+y' - 12y = - 340 sin(t) Y(t) =
The particular solution Yp(t) is found by following these steps and combining it with the complementary solution Yc(t) to get the general solution Y(t) = Yc(t) + Yp(t).
To find the particular solution to [tex]y'' + y' - 12y = -340sin(t)[/tex] using variation of parameters, follow these steps:
1. Find the complementary solution Yc(t) for the homogeneous equation [tex]y'' + y' - 12y = 0[/tex]. The characteristic equation is[tex]r^2 + r - 12 = 0[/tex], which has roots r1 = -4 and r2 = 3. Thus, [tex]Yc(t) = C1e^(-4t) + C2e^(3t)[/tex].
2. Assume the particular solution Yp(t) is in the form [tex]Yp(t) = u1(t)e^(-4t) + u2(t)e^(3t)[/tex]. Calculate the Wronskian [tex]W(Y1, Y2) using Y1 = e^(-4t) and Y2 = e^(3t).[/tex] 3. Find u1'(t) and u2'(t) using the given nonhomogeneous equation: -340sin(t) = -Y1(t)u1'(t) + Y2(t)u2'(t).
4. Integrate u1'(t) and u2'(t) to find u1(t) and u2(t).
5. Plug u1(t) and u2(t) back into the particular solution [tex]Yp(t) = u1(t)e^(-4t) + u2(t)e^(3t[/tex]).
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The dot plot shows the number of pencils each boy has at his desk in class.
+++ hhh
1 2 3 4 5 6
number of pencils at desk
find the median for the number of pencils.
The median for the number of pencils can be found by locating the middle value on the dot plot, which appears to be 3 pencils.
What is the middle value of the number of pencils on the dot plot?The dot plot displays the number of pencils each boy has at his desk in class. By locating the middle value of the data on the dot plot, the median number of pencils can be determined to be 3.
This indicates that half of the boys have 3 pencils or fewer, while the other half have 4 pencils or more.
The dot plot provides a visual representation of the distribution of the data and allows for easy identification of the median value.
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