The partial derivatives of the function f(t, a) = cos(2mTt - a) with respect to each variable are as follows:
∂f/∂t = -2mT sin(2mTt - a)
∂f/∂a = sin(2mTt - a)
To compute these partial derivatives, we use the chain rule of differentiation. The chain rule states that if we have a function g(h(x)), then the derivative of g with respect to x is given by g'(h(x)) multiplied by h'(x). In our case, the function g is the cosine function and the argument h is 2mTt - a.
To find the partial derivative with respect to t, we consider t as the independent variable and treat a as a constant. We differentiate the function with respect to t while keeping a constant, and we multiply the result by the derivative of the inner function, which is 2mT.
∂f/∂t = -sin(2mTt - a) * (2mT) = -2mT sin(2mTt - a)
Similarly, to find the partial derivative with respect to a, we differentiate the function with respect to a while keeping t constant. The derivative of the inner function, 2mTt - a, with respect to a is -1.
∂f/∂a = -sin(2mTt - a) * (-1) = sin(2mTt - a)
So, the partial derivative of f(t, a) with respect to t is -2mT sin(2mTt - a), and the partial derivative with respect to a is sin(2mTt - a).
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Precious treated 3 of her friends and herself to ice cream sundaes. The bill for the sundaes $16 . Each sundae cost the same amount. How much was each sundae
50 POINTS!!!!!!!!
ANSWER PLEASE
Answer:
3
15
Step-by-step explanation:
15 is the number that forms the ratio 3/7 of 35
follow the column up until the row 3
Answer:
3 and 15
Step-by-step explanation:
I hope this helps (✿◡‿◡)
True or False: The dependent variable should be graphed on the x-axis. plzzzzzzzzzzzzzzzzzzzzzz help asap first to answer gets brainliest
Answer:
true
Step-by-step explanation:
which of the following equations produces a direct variation?
I. f(x) = xyz
II. f(x) = x3
III. f(x) = 3x
a. III only b. I only c. I and II only d. II only
The following equations produces a direct variation : III.) f(x) = 3x. Hence, option a) III. only is the correct answer.
If f(x) varies directly with x, then it can be represented by the equation f(x) = kx, where k is a constant of proportionality. Therefore, to determine if an equation represents a direct variation, you need to determine if it can be written in this form of kx.
Now, let's examine each of them: I. f(x) = xyz: This equation is not in the form of kx. It has three variables: x, y, and z. Since we don't know how each variable relates to one another, we can't determine if it represents a direct variation.
II. f(x) = x³: This equation is not in the form of kx either. It has a variable x, but it's cubed. This means that f(x) does not vary directly with x.
III. f(x) = 3x: This equation can be written in the form of kx. If k = 3, then the equation becomes f(x) = 3x. This shows that f(x) varies directly with x.
Therefore, the correct answer is III only.
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What is the minimum number of pieces of information you think you would need in order to prove that a given quadrilateral is a square? When you answer this question, post your answer along with theorems, postulates, or definitions that support your answer. Come to a conclusion as a group about what the minimum number is, as well as if there is more than one way to prove a quadrilateral is a square using that minimum number of pieces of information.
Answer:
At least 4 numbers of information is needed
The four are highlighted below in the explanation section
Step-by-step explanation:
1. Given that the shape has four right angles and that all its sides are congruent then it's a quadrilateral
2. If two sides are consecutively congruent it is a quadrilateral shape
3. If a rhombus contains a right angle, then it’s a square shaped rhombus
4. If a quadrilateral is both a rectangle and a rhombus, then it’s a square
What is the image point of (5, 1) after a translation right 5 units and down 2 units?
a point (-20,48) is on the terminal side of angle \theta. find the exact value of sin\theta.
please! Thank you.
Answer:
The exact value of sinθ for the given point (-20, 48) is 12/13.
Step-by-step explanation:
To find the exact value of sinθ, we need to determine the ratio of the y-coordinate (-20) to the distance from the origin to the point (-20, 48).
Using the Pythagorean theorem, we can calculate the distance from the origin to the point (-20, 48). The distance is the square root of the sum of the squares of the x and y coordinates:
Distance = √((-20)^2 + 48^2)
Distance = √(400 + 2304)
Distance = √2704
Distance = 52
Now that we have the distance, we can calculate the sine of θ. Since the point (-20, 48) is in the second quadrant, the y-coordinate is positive. Therefore, sinθ = y-coordinate / distance:
sinθ = 48 / 52
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
sinθ = 12 / 13
Therefore, the exact value of sinθ for the given point (-20, 48) is 12/13.
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Which equation best represents the following: In a class of 46 students, there are 10 more girls than boys?
Let boys =b
and girls =g
First,
46-10 = 36
36 /2 =18
therefore, 18g and 18b but there are 10 more girls than boys
so for g,
= 18 +10
= 28g
so .. the equation is:
28g + 18b = 46
Calculation: According to Fedex’s 2017 annual report, the operating revenue in 2017 was $60,319 million while its operating expenses were $55,282 million. Calculate the operating ratio of Fedex in 2017 (show your work).
The operating ratio of FedEx in 2017 was approximately 91.64%.
To calculate the operating ratio of FedEx in 2017, we need to divide the operating expenses by the operating revenue and then multiply the result by 100 to express it as a percentage.
Operating Ratio = (Operating Expenses / Operating Revenue) * 100
Given:
Operating Revenue = $60,319 million
Operating Expenses = $55,282 million
Calculating the operating ratio:
Operating Ratio = (55,282 / 60,319) * 100
Operating Ratio ≈ 91.64%
Therefore, the operating ratio of FedEx in 2017 was approximately 91.64%.
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Question 3: (5+2+5 Marks) Let S = 1) Show that Sis linearly independent. -{[H 3 H] ii) Deduce that S is a basis for M22. iii) Express A as a linear combination of the vectors in S and find (A)s, where A = 24 -15)
We are given a set of vectors S and we need to determine whether S is linearly independent. The vectors in S are given as {[1, 2], [3, 4], [1, 5]}. We also need to deduce if S forms a basis for the vector space M22. Additionally, we are asked to express the matrix A as a linear combination of the vectors in S and find the coordinates of A with respect to the basis S.
To show that the set S is linearly independent, we need to check if there exist any scalars (c₁, c₂, c₃) such that c₁[1, 2] + c₂[3, 4] + c₃[1, 5] = [0, 0]. Setting up the system of equations, we have:
c₁ + 3c₂ + c₃ = 0
2c₁ + 4c₂ + 5c₃ = 0
By solving this system of equations, we can find the values of c₁, c₂, and c₃. If the only solution is c₁ = c₂ = c₃ = 0, then the set S is linearly independent.
If S is linearly independent and contains three vectors in the vector space M22 (2x2 matrices), then it forms a basis for M22. This is because a basis for a vector space must be linearly independent and span the entire space.
To express the matrix A as a linear combination of the vectors in S, we set up the equation A = c₁[1, 2] + c₂[3, 4] + c₃[1, 5] and solve for the coefficients c₁, c₂, and c₃. Once we have the coefficients, (A)s represents the coordinates of A with respect to the basis S.
In conclusion, we determine the linear independence of S by solving the system of equations. If S is linearly independent, it forms a basis for M22. We can express matrix A as a linear combination of the vectors in S and find the coordinates of A with respect to the basis S by solving the corresponding system of equations.
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In the country of Mordor, Y=A∗
∗∗
L
. In the first year, Y=18 and K=4 and L=9 In the second year, Y=26 and K=4 and L=16 What percent of this growth came from higher productivity? Careful: don't calculate the percent that came from inputs, you have to do an extra step once you've done that. If you think the answer was 31%, write 31 , not 31%. If you think the answer is zero, write 0 , not 0.
Approximately 114.29% of the growth came from higher productivity.
To determine the percent of growth that came from higher productivity, we need to compare the change in output (Y) with the change in inputs (K and L). Here's how we can calculate it:
In the first year:
Initial output (Y₁) = 18
Initial inputs (K₁, L₁) = (4, 9)
In the second year:
Final output (Y₂) = 26
Final inputs (K₂, L₂) = (4, 16)
Change in output = Y₂ - Y₁ = 26 - 18 = 8
Change in inputs = (K₂ + L₂) - (K₁ + L₁) = (4 + 16) - (4 + 9) = 7
Now, let's calculate the percent of growth that came from higher productivity:
Percent of growth from higher productivity = (Change in output / Change in inputs) * 100
= (8 / 7) * 100 ≈ 114.29
Therefore, approximately 114.29% of the growth came from higher productivity.
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In The Country Of Mordor, Y = AVK* VL . In the first year, Y=18 and K=4 and L=9 In the second year, Y=26 and K=4 and L=16 What percent of this growth came from higher productivity? Careful: don't calculate the percent that came from inputs, you have to do an extra step once you've done that. If you think the answer was 31%, write 31 , not 31%. If you think the answer is zero, write 0 , not 0.
A rectangle has a fun property. The value of its perimeter is equal to the value of its area. The rectangle has a length of 2x feet and a width of 3 feet. 1. Write the equation perimeter equals to the area. 2. Solve for 'x' 3. Write both the value of the perimeter and the value of the area.
Answer:
1) [tex]6\cdot x = 4\cdot x+6[/tex], 2) The value of [tex]x[/tex] is 3, 3) The perimeter and the area of the rectangule are 18 feet and 18 square feet, respectively.
Step-by-step explanation:
Let be a rectangle with a length of [tex]2\cdot x[/tex] feet and a width of 3 feet. The area ([tex]A[/tex]), measured in square feet, and perimeter ([tex]p[/tex]), measured in feet, formulas are, respectively:
[tex]A = (2\cdot x)\cdot (3)[/tex]
[tex]A = 6\cdot x[/tex] (Eq. 1)
[tex]p = 4\cdot x + 6[/tex] (Eq. 2)
1) Now, we assume that [tex]p = A[/tex], then we reduce the system of linear equation into a sole linear equation:
[tex]6\cdot x = 4\cdot x+6[/tex] (Eq. 3)
2) We proceed to solve for [tex]x[/tex]:
[tex]2\cdot x = 6[/tex]
[tex]x = 3[/tex]
The value of [tex]x[/tex] is 3.
3) Lastly, we obtain the values of the perimeter and area:
[tex]A = 6\cdot (3)[/tex]
[tex]A = 18\,ft^{2}[/tex]
[tex]p = 4\cdot (3)+6[/tex]
[tex]p = 18\,ft[/tex]
The perimeter and the area of the rectangule are 18 feet and 18 square feet, respectively.
Find the next two numbers in the pattern.
7, -28,112, -448,
Fill in the blank with 2 numbers
Answer:
1792, -7168
Step-by-step explanation:
If you can find the constant number multiplied in the pattern, you know that it multuplies by -4. -448 times -4 will be a positive number, which the answer is 1792 if you use the calculator, then you use 1792 and multiplie that by -4 to get -7168.
That's the answer, 1792, then -7168.
proving triangle similarity
could someone explain this to me? kinda confused
Based on the AA Similarity Theorem, triangles PQR and TSR are proven to be similar to each other because they have two pairs of corresponding angles that are congruent to each other.
What is the AA Similarity Theorem?The AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are in proportion to each other.
With the information given, the proof that shows that the two triangles are similar as as follows:
Statements Reasons
1. ∠QPR ≅ ∠STR 1. Given
2. QR ⊥ PT 2. Given
3. ∠QRP ≅ ∠SRT 3. def. of perpendicular
4. ΔPQR ~ ΔTSR 4. AA Similarity Theorem
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What is a y-coordinate
Answer:
A y coordinate is the vertical (upwards) of a graph there is the x and y coordinate x is is horizontal (left to right)
Step-by-step explanation:
help me with this please
Convert 2 + 3/8 to an improper fraction:
2 + 3/8 = 16/8 + 3/8 = (16 + 3)/8 = 19/8
Then
5 / (2 + 3/8) = 5 / (19/8) = 5 • (8/19) = 40/19
If you want to convert this to a mixed fraction, then
40/19 = (38 + 2)/19 = 38/19 + 2/19 = 2 + 2/19
is this a linear or a non linear
Answer:
No idea
Step-by-step explanation:
If their was an image, or a chart, then we could tell, but there is none.
If P'(-1,-3) is obtained by a 180ºccw rotation about the origin what are the coordinates of P?
The temperature of a city was 28⁰C on Tuesday. The temperature rose by 1.5⁰C on everyday upto Friday and fell by 2.5⁰C on Saturday. What was the temperature of the city on Saturday
Answer: 30 degrees
Step-by-step explanation:
1.5 x 3 (days until friday from tuesday) = 4.5
28 + 4.5 = 32.5
32.5 - 2.5 = 30 degrees
Answer:
30 degree C check it once.......
What is the formula V=1/3[tex]\pi r^{2}[/tex] for?
Answer: cylinder
Step-by-step explanation:
Find the volume of the part of the ball rho ≤ 7 that lies between the cones ϕ = π/6 and ϕ = π/4.
the volume of the part of the ball `ρ ≤ 7` that lies between the cones `ϕ = π/6` and `ϕ = π/4` is approximately `481.87` cubic units.
Let's say that we have the equation of the sphere as `ρ² + ϕ² + θ² = r²`.
Using cylindrical coordinates, the volume of a ball with radius `r` would be:
`V = ∫∫∫ρ sin ϕ dρ dϕ dθ`
We're also given that `ρ ≤ 7` and the two cones that the ball lies between:
`π/6 ≤ ϕ ≤ π/4`
Using these constraints, the limits of integration for `ρ`, `ϕ`, and `θ` are as follows:
`0 ≤ ρ ≤ 7``π/6 ≤ ϕ ≤ π/4``0 ≤ θ ≤ 2π`
Therefore, we have:
`V = ∫∫∫ρ sin ϕ dρ dϕ dθ``V = ∫₀^(2π) ∫_(π/6)^((π/4)) ∫₀^7 (ρ sin ϕ)ρ dρ dϕ dθ`
Evaluating this integral gives us the volume of the part of the ball:
`V = π/12 (7^4 - 1)`
Therefore, the volume of the part of the ball `ρ ≤ 7` that lies between the cones `ϕ = π/6` and `ϕ = π/4` is approximately `481.87` cubic units.
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A cable 90.6 meters long is cut into two pieces so that one piece is 37.2 meters longer than the other. Find the length of each piece of cable.
Answer:
53.4
Step-by-step explanation:
It said cut that means subtraction also in different length. So you subtract 90.6-37.2=53.4
Answer:
26.7 meters and 63.9 meters
Step-by-step explanation:
37.2 + 2x = 90.6
-37.2 -37.2
2x = 53.4
53.4 ÷ 2 = 26.7 meters
26.7 + 37.2 = 63.9 meters
63.9 + 26.7 = 90.6 meters
Hope that helps.
the rectangular garden shown has a width of 50 feet and a length of 45 feet and is surrounded by a paved path with a uniform width of x feet. if the combined area of the garden and the paved path is 2646 square feet, what is the value of x ?
Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.
The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,
we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.
Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet
Paved path:
If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.
Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50
The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet
= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675
We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646
= 64x² + 760x + 675 - 264664x² + 760x - 1971
= 0(8x - 27) (8x + 73) = 0
The value of x cannot be negative,
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What is the relationship between angle 3 and angle 7?
Group of answer choices
Supplementary
Complementary
Congruent
Adjacent
Answer:
Congruent
Step-by-step explanation:
∠3 and ∠7 are Complementary Angles. This means that they are congruent angles.
Answer:
congruent
Step-by-step explanation:
Whatever measure you get for 3 is the same for measure 7
4.5 times 6-12 divided by 3
Answer:5
Step-by-step explanation:
23 is the answer for this question
a runner ran tow laps around a 400m track. she completed the first lap in 50 seconds and then decreased her speed by 5% for the second lap. find:
A) her total time for the two laps
B) her average speed for the two laps
Please helppp!
Answer:
Step-by-step explanation:
Her average speed for the first lap is 8m per second. Her speed for the second lap is about 7.6m per second. So her total time for the two laps is 1 minute and 42 seconds.
Which segment is not skew to segment EK?
Answer:
segment CI
Step-by-step explanation:
its the correct answer on the test
Problem 7-12 How many work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 99 percent if a pilot study yielded these times (minutes): 5.2, 55, 6.3, 5.3, 5.5, and 5.1? The standard deviation is 431 minutes per cycle. (Use the "mean time" value to 2 decimal places and other values to 3 decimal places for intermediate calculations. Round up your final answer to the next whole number.) 4.34 points Skipped References
The number of work cycles that should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 99 percent is 14.
We can use the following formula to calculate the sample size:
n = z^2 * σ^2 / E^2
where:
n is the sample sizez is the z-score for the desired confidence level (z = 2.576 for a confidence level of 99%)σ is the standard deviation (σ = 0.431 minutes per cycle)E is the margin of error (E = 0.02 * mean = 0.01 minutes per cycle)Plugging in these values, we get: n = 2.576^2 * 0.431^2 / 0.01^2 = 14.04
We round up the answer to the next whole number, so we need to time 14 work cycles.
The z-score is a number that tells us how far away from the mean we need to be in order to be confident that our estimate is accurate within a certain margin of error.
In this case, we want to be 99% confident that our estimate is accurate within 2% of the mean. The z-score for a confidence level of 99% is 2.576.
The standard deviation is a measure of how spread out the data is. In this case, the standard deviation is 0.431 minutes per cycle.
The margin of error is the amount of error we are willing to tolerate in our estimate. In this case, we want our estimate to be accurate within 2% of the mean, so our margin of error is 0.02 minutes per cycle.
The sample size is the number of work cycles that we need to time in order to be confident that our estimate is accurate within a certain margin of error.
The formula above tells us that the sample size is inversely proportional to the square of the margin of error. This means that if we want to reduce the margin of error, we need to increase the sample size.
In this case, we want to reduce the margin of error to 2%, which means we need to increase the sample size to 14.
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Which expression is equivalent to (b + 0.22b - 0.23b)
A. (B - 0.01)
B. (1 - 0.01b)
C. (-.55b)
D. (.99b)
The circle below is centered at the point (-2, 1) and has a radius of length 3. What is its equation? (Image) A. (x - 2)2 + (y + 1)2 = 3 B. (x + 1)2 + (y - 2)2 = 9 C. (x - 1)2 + (y + 2)2 = 3 D. (x + 2)2 + (y - 1)2 = 9
Answer:
(x + 2)² + (y - 1)² = 9
Step-by-step explanation:
(x - h)² + (y - k)² = r²
(x - (-2))² + (y - 1)² = 9
(x + 2)² + (y - 1)² = 9
