Evaluate c∫sinxdx+cosydy where C is the top half of x2+y2=4 from (2,0) to (−2,0) joined to the line from from (−2,0) to (−4,6). Let's split the contour C into two parts; one over the circular arc C1, and another over the straight line segment C2. The line integral over C is the sum of the line integrals over C1 and C2. We need the parametric equations for C1. Let's select bounds for t as t=0 to t=π. Given those bounds, we have: x(t)= and y(t)= Build the parameterized version of the line integral computed along C1 and evaluate it: c1∫sinxdx+cosydy= Which of the following is a perfectly good set of parametric equations for C2? x=−2−ty=3t for 0≤t≤1x=−2−ty=3t for 0≤t≤2x=−2+ty=3−t for 0≤t≤2x=t−2y=−3t for −1≤t≤0 Find the value of the line integral along the straight line segment C2, and give the result here: c2∫sinxdx+cosydy= The value of the complete integral is: c∫sinxdx+cosydy= ___
Answers
The value of the complete line integral is -cos(4) - sin(6) + cos(2).
The value of the line integral along C1 can be evaluated by substituting the parameterized equations into the integrand and integrating with respect to t. The parametric equations for C1 are x(t) = 2cos(t) and y(t) = 2sin(t), where t ranges from 0 to π. Therefore, the line integral along C1 is:
c1∫sinxdx + cosydy = c1∫sin(2cos(t))(-2sin(t)) + cos(2sin(t))(2cos(t)) dt
Simplifying this expression and integrating, we get:
c1∫sinxdx + cosydy = c1∫[-4sin^2(t)cos(t) + 2cos^2(t)sin(t)] dt
= c1[-(4/3)cos^3(t) + (2/3)sin^3(t)] from 0 to π
= c1[-(4/3)cos^3(π) + (2/3)sin^3(π)] - c1[-(4/3)cos^3(0) + (2/3)sin^3(0)]
= c1[-(4/3)cos^3(π)] - c1[-(4/3)cos^3(0)]
= c1[(4/3) - (4/3)]
= 0.
Now, for C2, the correct set of parametric equations is x = -2 - t and y = 3t, where t ranges from 0 to 2. Using these parametric equations, the line integral along C2 can be computed as follows:
c2∫sinxdx + cosydy = c2∫[sin(-2 - t)(-1) + cos(3t)(3)] dt
= c2∫[-sin(2 + t) - 3sin(3t)] dt
= [-cos(2 + t) - sin(3t)] from 0 to 2
= [-cos(4) - sin(6)] - [-cos(2) - sin(0)]
= -cos(4) - sin(6) + cos(2) + 0
= -cos(4) - sin(6) + cos(2).
Finally, the value of the complete line integral is the sum of the line integrals along C1 and C2:
c∫sinxdx + cosydy = c1∫sinxdx + cosydy + c2∫sinxdx + cosydy
= 0 + (-cos(4) - sin(6) + cos(2))
= -cos(4) - sin(6) + cos(2).
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Related Questions
Sam screen prints custom t-shirts. He spends $320 each month for the paints he needs to make the shirts. He has found he can purchase quality plain shirts for $9.00 each. He screen prints the shirts and sells them at a local thrift shop for $24.00 each. The thrift shop charges him $100 per month to rent. How many shirts does Sam have to sell each month in order to break even?
Answers
Given parameters:
Cost of paint per month = $320
Cost of quality plain shirts = $9 each
Selling price = $24
Rent per month = $100
Unknown:
Number of shirts Sam has to sell to break even = ?
Solution :
Let the number of shirt sold each month = y
To break even the cost price per shirt must be equal to the selling price;
i.e;
Cost price = selling price at break even point;
Cost price = Cost of paint + Cost of quality plain shirt + Cost of rent
= 320 + 9y + 100
= 420 + 9y
Selling price = 24y
To break even;
420 + 9y = 24y
420 = j24y - 9y
420 = 15y
y = \(\frac{420}{15}\) = 28
To break even, Sam must sell 28 shirts in a month.
ezra is redrawing the blueprint shown of a stage he is planning to build for his band. by what percentage should he multiply the dimensions of the stage so that the dimensions of the image are 12 the size of the original blueprint? what will be the perimeter of the updated blueprint?
Answers
The perimeter of the updated blueprint will be 24 times the sum of the original length and width.
If Ezra wants to multiply the dimensions of the stage by a certain percentage to make the image 12 times larger than the original, he needs to find out what percentage that is.
To do this, he can divide the desired size of the new stage by the original size of the stage, and then multiply by 100 to get the percentage increase. So, if the original blueprint dimensions are x by y, and he wants to make the image 12 times larger, the new dimensions will be 12x by 12y.
To find the percentage increase, he can use the following formula:
Percentage increase = [(new size - original size) / original size] x 100
In this case, the new size is 12 times the original size, so the formula becomes:
Percentage increase = [(12x * 12y - x * y) / (x * y)] x 100
Simplifying this expression gives:
Percentage increase = [(144xy - x * y) / (x * y)] x 100 = 14300%
Therefore, Ezra needs to multiply the dimensions of the stage by 14300% to make the image 12 times larger than the original blueprint.
To find the perimeter of the updated blueprint, he can use the formula for the perimeter of a rectangle, which is: Perimeter = 2(length + width)
In this case, the length and width have been multiplied by 12, so the new perimeter becomes:
Perimeter = 2(12x + 12y) = 24(x + y)
Therefore, the perimeter of the updated blueprint will be 24 times the sum of the original length and width.
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what is f(-3) given that f(x)=-x+2
Answers
Answer:
f(-3) = 5
Step-by-step explanation:
f(-3) → x = -3
f(x) = -x+2
f(-3) = -(-3)+2
f(-3) = 3+2
f(-3) = 5
samanth drew this pictogram
Answers
Answer:
la verdad noce no me acuerdo
Answer:
4
Step-by-step explanation:
There are 6 grey diamonds in the row labelled "cat".
Each diamond means two hours.
6 × 2 = 12
Samanth's table shows that cats sleep 12 hours.
Tony is going to use a circle that means 3 hours.
12 ÷ 3 = 4
Tony needs 4 circles to show 12 hours.
4 × 3 = 12
Tony will use 4 circles.
could someone please answer the questions in the photo
Answers
Answer:
10. A dice has 6 sides each from 1-6, rolling each time can give 6 different possible results, hence the chances of rolling a 2, 3, and 5 will be 1/6 respectively.
To roll a 2, 3, and 5 in order, which are independent events,
the required probability will be
= 1/6 x 1/6 x 1/6
= 1/216
11. Using Pythagoras theorem,
8² + B² = 15²
B =√161
=12.689
13. Area of trapezoid= (upper base+ lower base)(height)/2
= (16+23)(3)/2
= 58.5 m²
Answer:
Answers:
Question #10:
Rolling a die three times gives 6 · 6 · 6 possibilities this makes 216 possibilities in total. Rolling the die in the order 2, 3, 5 is only one so the answer is: \(\frac{1}{16}\).
Question #11:
Since the triangle is a right triangle we can use the pythagorean theorem:
\(B^{2}\) + \(8^{2}\) = \(15^{2}\)
Working backwards we get that B is equal to 225 minus 64 which gets the square root of 161 or \(\sqrt{161}\).
Question #12:
First we can start with finding the area of the rectangle in the trapezoid:
3 · 16 = 48
Next the two right triangles. 21 - 16 = 5 That is the length of the additional two triangles. Dividing 5 by two gets the base of one of them, but if we don't divide it by two we will be able to solve for both at the same time:
3 · 5 = 15
\(\frac{15}{2}\) = 7.5
7.5 + 48 = 55.5
Which polynomial represents the sum below?
7x9.5x*-**8
5x 0.9x**
A. 5x10.7x8 + 5x5.9x+16
B. 5x10 + 7x8 + 5x5 + 8x+ 16
C. 12x18+1474+8x+ 16
D. 12/16 + 4X4+ 7x+ 16
Answers
a 17 feet ladder is placed against a building. the bottom of the ladder is sliding away from the building at a rate of 5 feet per second. find the rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building.
Answers
The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second
The length of the ladder = 17
Consider the length of the base as x and the height is h
The rate at which the ladder is sliding = 5 feet per second
dx/dt = 5
Apply the Pythagorean theorem
x^2 + h^2 = 17^2
h^2 = 289 - x^2
h = \(\sqrt{289-x^2}\)
The rate of change of height with respect to x is
dh/dx = - x / (289 - x^2)^(1/2)
dh/dt = dh/dx × dx/dt
Substitute the values in the equation
= - 15 / (289 - 15^2)^(1/2) × 5
= -15/8 × 5
= -75/8 feet per second
Therefore, the rate of change of height when x = 15 is -75/8 feet per second
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If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.
Answers
The required ratio of is (a + c) : c 11:8.
How to find ratio ?Given that a:b=1:4 and b:c=3:2.
We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.
To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have \(a=\frac14 b$\). From the second ratio, we have \(c=\frac{2}{3}b$\). Substituting these values into the expression (a+c):c, we get:
\($$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$\)
Simplifying the expression inside the parentheses, we get:
\($\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$\)
Therefore, the ratio \($(a+c):c$\) is:
\($(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$\)
Hence, the required ratio is 11:8$.
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For the following 8 problems, find a normal vector and a tangent vector at the point indicated. Write an equation for the tangent line and an equation for the normal line.
1. x ^ 2 + xy + y ^ 2 = 3 (-1,-1).
2(y - x) ^ 2 = 2x; (2, 4)
3(x ^ 2 + y ^ 2) ^ 2 = 9(x ^ 2 - y ^ 2); (sqrt(2), 1) .
4x ^ 3 + y ^ 3 = 9 / (1, 2) .
5. x * y ^ 2 - 2x ^ 2 + y + 5x = 6; (4, 2)
x ^ 5 + y ^ 5 = 2x ^ 3 (1, 1).
72x ^ 3 - x ^ 2 * y ^ 2 = 3x - y - 7; (1, - 2)
8x ^ 3 + y ^ 2 + 2x = 6 (-1,3).
Answers
For the equation x^2 + xy + y^2 = 3, at the point (-1, -1), the normal vector can be found by taking the gradient of the equation. The gradient is given by ∇f = (df/dx, df/dy), where f is the given equation.
In this case, the normal vector is (∇f(-1, -1)) = (2(-1) + (-1), (-1) + 2(-1)) = (-3, -3). The tangent vector can be found by taking the derivative of one variable with respect to the other, giving (dy/dx) = -1/3. Therefore, the equation for the tangent line is y - (-1) = (-1/3)(x - (-1)), which simplifies to y = (-1/3)x - 2/3. The equation for the normal line can be obtained by using the point-slope form with the normal vector (-3, -3), resulting in y - (-1) = -3(x - (-1)), which simplifies to y = -3x + 2.
For the equation (y - x)^2 = 2x, at the point (2, 4), the normal vector can be found by taking the gradient of the equation. The gradient is (∇f(2, 4)) = (df/dx, df/dy) = (2(4) - 2, 2(2 - 4)) = (6, -4). The tangent vector can be found by taking the derivative of one variable with respect to the other, giving (dy/dx) = 2 - 1/(2(y - x)). Substituting the point (2, 4) into the equation, we get (dy/dx)(2, 4) = 2 - 1/(2(4 - 2)) = 2 - 1/4 = 1.75. Therefore, the equation for the tangent line is y - 4 = 1.75(x - 2), which simplifies to y = 1.75x - 1.5. The equation for the normal line can be obtained by using the point-slope form with the normal vector (6, -4), resulting in y - 4 = -4(x - 2), which simplifies to y = -4x + 12.
For the equation (x^2 + y^2)^2 = 9(x^2 - y^2), at the point (sqrt(2), 1), the normal vector can be found by taking the gradient of the equation. The gradient is (∇f(sqrt(2), 1)) = (df/dx, df/dy) = (2(sqrt(2))^2(2) - 9(2sqrt(2)), 2(1)^2(2) - 9(-2)) = (4 - 36sqrt(2), 4 + 18) = (-36sqrt(2), 22). The tangent vector can be found by taking the derivative of one variable with respect to the other, giving (dy/dx) = -((x^2 + y^2) / (4x^3 - 9y^2)). Substituting the point (sqrt(2), 1) into the equation, we get (dy/dx)(sqrt(2), 1) = -((sqrt(2)^2 + 1^2) / (4(sqrt(2))^3 - 9(1)^2))
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9. Determine whether the following graph is a function or a relation.
Answers
Answer: Relation
Step-by-step explanation: it is a relation because if you take any number on the x axis and look at its points there are two points on multiple parts
hey you can you help and if your don’t know then don’t answer pls thx
Answers
The cοrrect statement is the segment GC is transversal tο segments KG and QC.
What is a transversal line?A line that crοsses twο οr mοre lines in the same plane at different lοcatiοns is said tο be transversal. Accοrding tο the fundamental prοpοrtiοnality theοrem (alsο knοwn as Thales' theοrem), if three οr mοre parallel lines crοss acrοss twο transversals, they prοpοrtiοnally cut οff the transversals.
We have given the statements are:
A). KG QC.
B) KG and QC intersect at a right angle.
C) KQ || GC.
D) GC is transversal tο KG and QC.
Therefοre, here in the figure, segment GC intersects segments KG and QC in the same plane at different lοcatiοns.
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based on the data in the table, what is the probability that a randomly selected persons favorite restaurant is a deli?
Answer choices
8/25
2/5
1/10
9/50
Answers
The probability that a randomly selected persons favorite restaurant is a deli is 9/50
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
Total = 100
Deli = 18
So, the probability is
P = Deli/Total
Substitute the known values in the above equation, so, we have the following representation
P = 18/100
Simplify
P = 9/50
Hence, the probability is (d) 9/50
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NEED HELP ASAP PLZZZZ
Marcus has a part-time job at the water park. He makes between $73.99 and $79.25 a day. Which is a reasonable amount of money that Marcus makes for working 5 days a week for 9 weeks?
A.
$3,613
B.
$3,421
C.
$351
D.
$3,278
Answers
Answer
b
highest he should make is 3599.55 and lowest is 3332.55 so a doesnt fit and b does
Lines m and n are parallel. They are intersected by transversals, p and q.
what is the value of x?
A)52
B)73
C)86
D)107
Answers
Since x is corresponding angle of 52
A ball is thrown upward with an initial velocity of 32ft/sec from a tower 48 feet above ground. Assume that the only force affecting the ball during travel is from gravity, which produces downward acceleration of 32ft/sec2, then (i) The maximum height reached by the ball is:- (ii) The ball hits the ground at time t:=
Answers
The maximum height reached by the ball is 64 feet and the ball hits the ground after 2 seconds.
Given, Initial velocity, u = 32 ft/sec
Height of the tower, h = 48 feet
Acceleration due to gravity, a = 32 ft/sec²
(i) Maximum height reached by the ball, h = (u²)/(2a) + h
Substituting the given values, h = (32²)/(2 x 32) + 48 = 16 + 48 = 64 feet
Therefore, the maximum height reached by the ball is 64 feet.
(ii) For time, t, s = ut + ½ at²
Here, the ball is moving upwards, so the value of acceleration due to gravity will be negative.
s = ut + ½ at² = 0 (since the ball starts and ends at ground level)
0 = 32t - ½ x 32 x t²
0 = t(32 - 16t)
t = 0 (at the start) and t = 2 sec. (at the end)
Therefore, the ball hits the ground after 2 seconds.
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How many significant figures should be included in the answer to the following calculation? (3.4876)/(4.11+1.2
Answers
The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.
To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.
First, let's analyze the number of significant figures in the given values:
- 3.4876 has five significant figures.
- 4.11 has three significant figures.
- 1.2 has two significant figures.
To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:
4.11 + 1.2 = 5.31
Now, we divide 3.4876 by 5.31:
3.4876 / 5.31 = 0.6567037...
Now, let's determine the number of significant figures in the result.
Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.
In this case, the value with the fewest significant figures is 5.31, which has three significant figures.
Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.
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Help me solve this, please
2/3s+5/6s=21
Answers
Answer: Are there any answer choices to pick from? Step-by-step explanation:
Answer:
After solving it i think the answer is 14 sorry if wrong
PLEASEE SOMEONE ANSWER ILL DO ANYTHING ANYTHING PLEAASEEE HELP ME this is myh 6th time posting this ;[
Answers
Answer: the third one
Step-by-step explanation:
y = 3x + 9; if x = 6
Answers
3(6)+9=18+9=27
x/2−5=−12
I need to know how to get the answer to what X is
Answers
Answer:
-14
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x/2-5=-12
1/2x+-5=-12
1/2x-5=-12
Step 2: Add 5 to both sides.
1/2x-5+5=-12+5
1/2x=-7
Step 3: Multiply both sides by 2.
2*(1/2x)=(2)*(-7)
x=-14
Answer:
-14
Step-by-step explanation:
x/2 = -12 + 5 << add both sides by 5
x/2 = -7 << Combine -12 + 5
x = -14 << Multiply both sides by 2
This revolves around the idea of inverse operations
To get x by itself we needed to bring the other numbers to the other side of the equation.
Inverse operations is bring the numbers to the other side by doing the opposite operation it shows.
ex: if the number is +5 on one side, it will be -5 on the other
Hope this helps!
If you don't understand, please feel free to comment and let me know!
Have a great day!
A Pyramid is placed inside a prism as shown in the pyramid has the same base area B as a prison but half the height H of the prism which expression gives the volume of the pyramid
Answers
Answer:
D) V= 1/6 bh
Step-by-step explanation:
The expression that provides the volume of the pyramid is as follows;
As mentioned in the question
It is given that the pyramid put inside a prism
Also the pyramid contains the similar base area but the height is half of the prism
so the base area of the pyramid is b
And, the Height of the pyramid = h ÷ 2
Now as we know that
The volume of the pyramid is
V = 1 ÷3 × base ares × height
= 1 ÷ 3 × b × h ÷ 2
V = 1 ÷ 6 bh
So, the volume is 1 ÷6 bh cube unit.
Answer:
V = 1/6 BH
Step-by-step explanation:
the volume of a pyramid is 1/3 BH , since the pyramid is only half the height of the prism you'll have to multiply 1/3 x 2 = 1/6
Which of the following functions grows the fastest as x grows without bound?
a)f(x) = x10
b)g(x) = ln(x10)
c)h(x) = 10x
d)They all grow at the same rate
Answers
The Option c) h(x) = 10^x grows the fastest as x grows without bound.
To determine which function grows the fastest as x grows without bound, we need to compare the rates of growth of the functions. We can do this by looking at the limits of the ratios of the functions as x approaches infinity.
For option a) f(x) = x^10, we can take the limit of f(x+1)/f(x) as x approaches infinity:
lim (x→∞) [f(x+1)/f(x)] = lim (x→∞) [(x+1)^10/x^10] = lim (x→∞) [(x+1)/x]^10
= lim (x→∞) [1+1/x]^10 = 1^10 = 1
For option b) g(x) = ln(x^10), we can take the limit of g(x+1)/g(x) as x approaches infinity:
lim (x→∞) [g(x+1)/g(x)] = lim (x→∞) [ln((x+1)^10)/ln(x^10)] = lim (x→∞) [10ln(x+1)/10ln(x)]
= lim (x→∞) [ln(x+1)/ln(x)] = ln(1) = 0
For option c) h(x) = 10^x, we can take the limit of h(x+1)/h(x) as x approaches infinity:
lim (x→∞) [h(x+1)/h(x)] = lim (x→∞) [(10^(x+1))/10^x] = lim (x→∞) [10] = 10
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Find the slope of the line which is perpendicular to a line having a slope of 5/7
Answers
Answer:
-7/5
Step-by-step explanation:
5/7
= -7/5
a rectangular screen has a width of 2x 8. the length is 4x 1. what is the area of the entire screen?
Answers
The area of the entire screen is \(8x^2 + 34x + 8\) square units.
To find the area of the entire screen, you need to multiply its width by its length.
Width = 2x + 8
Length = 4x + 1
Area = Width × Length
Area = (2x + 8) × (4x + 1)
Now, we'll use the distributive property to multiply these expressions:
Area = 2x * 4x + 2x * 1 + 8 * 4x + 8 * 1
Area = 8x^2 + 2x + 32x + 8
Now, we'll combine the like terms:
\(Area = 8x^2 + 34x + 8\)
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20 applicants from a pool of 90 applications will be hired. How many ways are there to select the applicants who will be hired?
Answers
The ways are the \(C_{20} ^{90}\) which are we there to select the applicants who will be hired with the help of combination.
According to the statement
we have to find that the number of ways are there to select the applicants who will be hired.
So, For this purpose, we know that the
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Here we use the combination.
And from the given information:
20 applicants from a pool of 90 applications will be hired.
And according to this the combination becomes:
\(C_{20} ^{90}\)
then solve it
\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)
\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)
Then after solve it
\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)
Now open another factorial
\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)
Now solve this then
\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).
So, The ways are the \(C_{20} ^{90}\) which are we there to select the applicants who will be hired with the help of combination.
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Sammy’s dad drove their car 150 miles in three hours. At this rate, how far would he drive in nine hours?
Answers
Answer:
distance in 3 hours = 150 miles
distance in 1 hour = 150/3 = 50 miles
distance in 9 hours = 50 × 9 = 450 miles
Answer:
Sammy's dad traveled 450 miles in 9 hours.
Step-by-step explanation:
mph = \(\frac{Miles}{Hours}\)
Miles = 150
Hours = 3
Plug into the formula of distance/time
\(\frac{150}{3} = 50mph\)
Sammy's dad is driving at 50mph
In three hours you can use this formula: \(50mph=\frac{miles}{9}\)
Multiply both sides by 9: \(50mph * 9 =\frac{miles}{9} *9\)
Solve:
\(50mph * 9 =miles\)
\(450 =miles\)
Sammy's dad traveled 450 miles in 9 hours.
Hope this helped! :)
between 1849 and 1852, the population of __________ more than doubled.
Answers
Answer:
Step-by-step explanation:
Between 1849 and 1852, the population of California more than doubled due to the California Gold Rush.
Between 1849 and 1852, the population of California more than doubled. California saw a population boom in the mid-1800s due to the California Gold Rush, which began in 1848. Thousands of people flocked to California in search of gold, which led to a population boom in the state.What was the California Gold Rush?The California Gold Rush was a period of mass migration to California between 1848 and 1855 in search of gold. The gold discovery at Sutter's Mill in January 1848 sparked a gold rush that drew thousands of people from all over the world to California. People from all walks of life, including farmers, merchants, and even criminals, traveled to California in hopes of striking it rich. The Gold Rush led to the growth of California's economy and population, and it played a significant role in shaping the state's history.
Find the minimum value of the parabola y=x^2+5/2.
Someone please help fast
Answers
The minimal value of the given parabola is y = 5/2, which occurs at x = 0.
To discover the minimum value of the given parabola & that's why we need to determine the vertex of the parabola.
The vertex of a parabola in the form of y = ax^2 + bx + c is given by means of (-b/2a, f(-b/2a)).
in the given parabola, a = 1, b = 0, and c = 5/2. consequently, the x-coordinate of the vertex is -b/2a = 0/(2*1) = 0.
To discover the y-coordinate of the vertex & we substitute x = 0 within the given equation:
y = 0^2 + 5/2 = 5/2
Therefore, the minimal value of the given parabola is y = 5/2.
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The figure below is reflected over y-axis and then rotated 180° counterclockwise.
What are the coordinates of the image of point Y after these transformations?
Answers
Answer:
The coordinates of point y after the transformation is (-6,5)
Step-by-step explanation:
Firstly , we need to get the coordinates of the point y before the transformation
The coordinates are
(-6,-5)
By reflecting over the y-axis, we have the following change;
(x,y) becomes (-x,y)
So we have;
(6,-5)
Then we are to rotate at an angle of 180 degrees counterclockwise
The operation here will be;
(x,y) to (-x,-y)
So we have;
(6,-5) to (-6,5)
what are the mean and standard deviation of the sampling distribution of the sample mean for samples of size 4 ?
Answers
On solving the provided question, we can say that standard deviation 15.4 is the mean of the sample means' sampling distribution.
What is standard deviation?Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.
If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size:
u = 15.4;
⊕ = 5.6
now
μ = 5.6\(\sqrt{5}\) =
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