evaluate the line integral, where c is the given curve. c xyz2 ds, c is the line segment from (−3, 6, 0) to (−1, 7, 4)
The line segment from (−3, 6, 0) to (−1, 7, 4) can be parameterized as:
r(t) = (-3, 6, 0) + t(2, 1, 4)
where 0 <= t <= 1.
Using this parameterization, we can write the integrand as:
xyz^2 = (t(-3 + 2t))(6 + t)(4t^2 + 1)^2
Now, we need to find the length of the tangent vector r'(t):
|r'(t)| = sqrt(2^2 + 1^2 + 4^2) = sqrt(21)
Therefore, the line integral is:
∫_c xyz^2 ds = ∫_0^1 (t(-3 + 2t))(6 + t)(4t^2 + 1)^2 * sqrt(21) dt
This integral can be computed using standard techniques of integration. The result is:
∫_c xyz^2 ds = 4919/15
Learn more about line segment here:
https://brainly.com/question/30072605
#SPJ11
Question 3
10 pts
In the transformed quadratic functiong (X) = (x – 8)2 + 5, two
transformations occurred: horizontal translation to the right by 8 units
and
O Vertical translation up by 5 units
O Vertical Translation down by 5 units
Vertical stretch by a factory of 5
O Reflection over the X – axis
10t
Answer:
Vertical translation up by 5 unitsExplanation:
From vertex form of quadratic function g(x)=a(x-h)²+k the h and k are coordinates of vertex transformed from point (0,0) which is the vertex of parental function f(x)=ax²
It means the h determines how many units we moved parental graph horizontaly (to the left if h<0, to the right if h>0) and the k determines how many units we moved parental graph verticaly (down if h<0, up if h>0)
g(x) = (x - 8)² + 5 ⇒ h = 8, k = 5
So if h and k are >0 it means the parental graph was moved to the right and up.
calculate the double integral. 4x 1 + xy da, r = [0, 4] × [0, 1] r
The value of Double integral will be \(\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\)
A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.
The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.
We know that by the property of integral \($\int u \mathrm{udv}=u v-v \int d u$\)
\($$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$\)
We have to evaluate the given double integral
\($$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$\)
\($$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$\)
For more questions on Double integral
https://brainly.com/question/14563964
#SPJ4
PLEASE HELP NOW 20 POINTS!
Use the formula to find the volume of the prism.
A. 12 1/2 cubic units
B. 6 1/4 cubic units
C. 7 cubic units
D. 4 1/2 cubic units
Answer:
The Answer is A. 12 1/2
Step-by-step explanation:
2 x 2 1/2 = 5
5 x 2 1/2 = 12.5
(っ◔◡◔)っ ♥ Hope It Helps ♥
Rotate triangle P 90° clockwise about the point (2, -1).
Please screenshot this and send me the answers cuz I really need help :(
Answer: (2,0), (2,1), and (6,1)
Step-by-step explanation: I just used the desmos graphing calculator to find the answer to your problem. I don't know any formulas to solve it so I just rotated the points by hand. I also made sure they were still equidistant from the point (2,-1) because if their distances from other points changed during the rotation, then the triangle would not be equal to the first triangle and the image would've been distorted.
I hope this helps! Have a nice day.
is this true or false? please help
Answer:
true jufhjjzjsjjajajw
(20 Points) I just want to be done with this so, some fast help would be much appreciated.
Answer:
I think it would be C
I'm not completely sure though!
I’ll mark you a branilyst if you answer this question
Answer:
The answer is 8 cm, i would show work but im in school
find the slope
5x -3y = 18
Answer:
m=5/3
Step-by-step explanation:
a baseball diamond is a square with side 90 ft. at what rate is the player's distance from home base increasing when he is half way from first to second base?
The rate is his distance from second base decreasing when he is halfway to first base is -45ft
The rate is his distance from third base increasing at the same moment is 26ft
Let's call the batter's distance from second base "x" and his distance from third base "y". We want to find dx/dt (the rate at which x is changing) and dy/dt (the rate at which y is changing) when the batter is halfway to first base.
Since the baseball diamond is a square, we know that the distance from second base to first base is also 90 ft. Therefore, when the batter is halfway to first base, his distance from second base is:
x = 90 ft - 45 ft = 45 ft
Now we can find dx/dt by taking the derivative of x with respect to time:
dx/dt = -26 ft/s
The negative sign indicates that x is decreasing, as we expected.
Next, we need to find the rate at which the batter's distance from third base is increasing when he is halfway to first base. We know that the distance from third base to first base is also 90 ft, so the distance from the halfway point to third base is:
y = 90 ft - 45 ft - 90 ft = -45 ft
Well, in this case, it means that the batter is actually behind third base when he is halfway to first base. So, we need to flip the sign of y to make it positive:
y = -(-45 ft) = 45 ft
Now we can find dy/dt by taking the derivative of y with respect to time:
dy/dt = 26 ft/s
The positive sign indicates that y is increasing, as we expected.
To know more about distance here
https://brainly.com/question/4199102
#SPJ4
Complete Question:
A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 26 ft/s.
At what rate is his distance from second base decreasing when he is halfway to first base?
At what rate is his distance from third base increasing at the same moment?
The bases on a baseball daimond are 90 feet apart on a standard baseball field what is the distance in feet for the cacther to throw a homerun to reach second plate
The catcher needs to throw the ball approximately 190.5 feet to reach second base from home plate.
Let's call the distance between the catcher and second plate "x" and the distance between the home plate and second plate "y". Using the Pythagorean theorem, we get:
distance² = x² + y²
We know that the distance between each base is 90 feet, so the distance between the home plate and second plate is
=> 90 + 90 = 180 feet.
Therefore, we can substitute "y" with 180 feet:
distance² = x² + 180²
We want to solve for "distance", so we need to isolate it on one side of the equation. We can do this by taking the square root of both sides:
distance = √(x² + 180²)
So, if the catcher is standing at home plate, the distance he needs to throw to reach second base is the square root of x² + 180², where "x" is the distance between the catcher and second plate.
The exact value of "x" would depend on where the catcher is standing on the field, but we can assume it's around 60 feet:
Which means that x = 60, then the distance is calculated as
distance = √(60² + 180²) = √(36000) = 190.5 feet
To know more about distance here
https://brainly.com/question/4199102
#SPJ4
Pleaseee helpp answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!!!!
Answer:
720
Step-by-step explanation:
interior angles of a hexagon is 720
Helppppppppppp:)))))))))
Hi there!
We are given the set of ordered pairs below:
\( \large \boxed{(3, - 1),(2, - 2),(0,2),(2,1)}\)
1. What is the domain?
Domain is a set of all x-values in one set of ordered pairs. So what are the x-values that I am talking about? In ordered pairs, we define x and y which both have relation to each others which we can write as (x,y). That's right, the domain is set of all x-values from ordered pairs.Therefore, we gather only x-values from (x,y). Hence, the domain is {3,2,0,2}. Whoops! Something is not right. As we learn in Set Theory that we don't write the same or repetitive in a set. Hence, the actual domain is {0,2,3}
2. What is the range?
Because domain is set of all x-values. Then what do you think the range is? That's right! The range is set of all y-values. If you got this right before looking up the underlined words then a handclap for you! So how do we find range? Simple, we just do like finding the domain in the Q1, except we gather the y-values in (x,y) instead and make sure that we don't write same number!Therefore, gather y-values from the ordered pairs. Hence, the range is {-2,-1,1,2}
3. Is the relation a function?
All functions are relations but not all relations are functions. Function is a set of ordered pairs where domain is not repetitive or in a set, there cannot be more than one same value. Consider the following relation: (1,1),(1,2) - Oh, looks like in a set of ordered pairs, there are two same domains which make it only a relation, and not a function. On the other hand, (1,1),(2,2) - Looking good! No same or repetitive domain, making it indeed a function.Consider the domain from Q1 and see if there are two same values of x in a set. Looks like the relation is not a function since there are same x-values which are 2 in a set, making it only a relation. Hence, the relation is not a function.
These are all 3 answers along with an explanation. Let me know if you have any doubts regarding Relations and Functions.
From the Q1's answer, there are two bold texts, please choose the second bold text to answer (the one with underline) and not the first one (the one with same 2's).
Good luck on your assignment, have a nice day!
Which graph shows a dilation? On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0).
A graph that shows a dilation include the following: A. On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0).
What is a dilation?In Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would be stretched or shrunk depending on the scale factor that is applied.
Read more on dilation and scale factor here: brainly.com/question/4421026
#SPJ1
Factor Each expression. If it cannot be factored write "Prime"
Question 1. 4x-16
Question 2. 18k+42
Answer:
1. is -64 bye hope this help
Please help me solve this problem!! (Algebra 1)
m≥5m-4
Answer:
Step-by-step explanation:
M is less than or equal to 1
What is 7 (x+3) -7 = y simplified
Answer:
7 (x+3) -7 = y
7x+21-7=y
7x+14=y
Solve x2 - 16x + 60 = -12 by completing the steps. First, subtract 60 from each side of the equation. Next, add 8 ⇒ 64 to each side of the equation to complete the square. Now, write x² - 16x + 64 = -8 as ✔ (x - 8)² = -8 Take the square root of both sides to get the solutions
Answer:
Step-by-step explanation:
Given x^2 - 16x + 60 = -12
Using the completing the square method to find x;
subtract 60 from both sides
x2 - 16x + 60-60 = -12-60
x2 - 16x = -72
Add square of the half of the coefficient of x to both sides
x2 - 16x + (1/2(-16))² = -72 + (1/2(-16))²
x^2 - 16x +64 = -72+64
(x-8)² = -8
Take the square root of both sides
√(x-8)² = √-8
x - 8 = ±√8i
x = ±√8i+8
x = ±2√2i+8
The solution of the given equation is: \(x = 8+\sqrt{-8}\) and \(\\x = 8-\sqrt{-8}\).
Given that:
Equation: \(x^2 - 16x + 60 = -12\)
Simplify the above equation as:
x² - 16x + 60 = -12
x² - 16x = -12 - 60
x² - 16x = -72
Add 64 to each side of the equation to complete the square.
x² - 16x + 64 = -72 + 64
x² - 16x + 64 = -8
Write x² - 16x + 64 as (x - 8)² since it is a perfect square trinomial.
(x - 8)² = -8
Take the square root of both sides to get the solutions.
\(x - 8 = \±\sqrt{-8}\\x = 8\±\sqrt{-8}\\x = 8+\sqrt{-8}\\x = 8-\sqrt{-8}\)
where i is the imaginary unit.
Hence, the value of x are: \(x = 8+\sqrt{-8}\) and \(\\x = 8-\sqrt{-8}\).
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ6
Find the area of a triangle with a base
of 10m and a height of 12m.
Area: 12(bxh)
Answer:
60
Step-by-step explanation:
1/2(b×h)
1/2(10×12)
1×5×12
60
I need help guys. I don't understand this. I tried to work this out but what i got didn't have an option for it. Can you leave all the notes. Anybody????????????
Answer:
7.5 i belive
Step-by-step explanation:
area= lenghthx width thats the formula 3mm converted is 3 cm 3cmx2.5=7.5
Kevin borrowed some money from his friend in order to help buy a new video game system. Kevin agreed to pay back his friend $5 per week and originally borrowed $90. Make a table of values and then write an equation for L, in terms of t, representing the amount Kevin owes his friend after t weeks.
1. The table of values showing the amount Kevin owes his friend after t weeks is as follows:
Table of Values:Week Amount Owed
0 $90
1 $85
2 $80
3 $75
4 $70
...
18 $0 ($5 - $5)
2. The equation representing the amount (L) Kelvin owes his friend after t weeks is L = 90 - 5t.
What is an equation?An equation is a mathematical statement showing that two mathematical expressions using the equation symbol (=) are equal or equivalent.
Equations establish the numerical relationship existing between two or more mathematical expressions, numbers, values, or variables.
Week Amount Owed
0 $90
1 $85 ($90 - $5)
2 $80 ($85 - $5)
3 $75 ($80 - $5)
4 $70 ($75 - $5)
The total amount borrowed = $90
The amount of repayment = $5
The repayment period = weekly
Equation:Let the balance after t weeks of payment = L
L = 90 - 5t
In eighteen weeks, Kevin will complete the repayment of the loan.
Check:
If t = 18
L = 90 - 5t
L = 90 - 5(18)
L = 90 - 90
L = 0
Learn more about equations at https://brainly.com/question/2972832
#SPJ1
Solve the augmented matrix by elementary row operations. 9. (4 points) Let A and B be 3 by 3 matrices with det (A) = 3 and det (b) = 5. Find the value of det (AB).
The value of determinant of the matrix det (AB) is 15.
Given matrices A and B are 3 by 3 matrices with
det (A) = 3 and
det (b) = 5.
We need to find the value of det (AB).
Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.
By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].
Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.

The determinant of AB can be calculated as det(AB) = det(A) × det(B)
= 3 × 5
= 15.
Conclusion: The value of det (AB) is 15.
To know more about determinant visit
https://brainly.com/question/11841826
#SPJ11
We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)
=> det(AB) = 3 × 5
=> det(AB) = 15.
Hence, the value of det(AB) is 15.
The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:
det(AB) = det(A)det(B).
Given that: det(A) = 3
det(B) = 5
Now, let C = AB be the matrix product. Then,
det(C) = det(AB).
To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.
Given matrices A and B are: Matrix A and B:
[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]
= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].
We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.
det(A) = 3.
Therefore, det(AB) = det(A)det(B)
= 3 × 5
= 15.
Conclusion: Therefore, the value of det(AB) is 15.
To know more about determinant visit
https://brainly.com/question/11843479
#SPJ11
hey guys i really need help pls dont waste the points i actually want help to understand how to solve equations like:
x + 2y = 4
or
y= -3/4x - 1
To get both the X value and the Y value? I would really appreciate it loves <3
Answer:
your question is unclear
Step-by-step explanation:
x+2y=4
-x -x
2y=4-x
divide by 2 to get y by it's self
y=2-(1/2x)
x+2y=4
-2y -2y
x=4-2y
i don't know if u want me to help u with the second one but i did it the first one
Chọn bốn ví dụ sau Ví dụ nào không phải là phân số
A.3/-5 B.1,7/3 C.0/2 D.-13/-4
Answer:
a
Step-by-step explanation:
vì số âm không nằm ở dưới
given that P = (4,1) and Q=(-4,4) find the component form and magnitude of the vector QP.
The magnitude of the vector QP is √73.
To find the component form of the vector QP, we need to subtract the coordinates of point P from the coordinates of point Q. The component form of a vector is represented as (x, y), where x and y are the differences in the x-coordinates and y-coordinates, respectively.
Given that P = (4, 1) and Q = (-4, 4), we can calculate the component form of the vector QP as follows:
x-component of QP = x-coordinate of Q - x-coordinate of P
= (-4) - 4
= -8
y-component of QP = y-coordinate of Q - y-coordinate of P
= 4 - 1
= 3
Therefore, the component form of the vector QP is (-8, 3).
To find the magnitude of the vector QP, we can use the formula:
Magnitude of a vector = √(\(x^2 + y^2\))
Substituting the x-component and y-component of QP into the formula, we get:
Magnitude of QP = √((\(-8)^2 + 3^2\))
= √(64 + 9)
= √73
Therefore, the magnitude of the vector QP is √73.
In summary, the component form of the vector QP is (-8, 3), and its magnitude is √73. The component form gives us the direction and the magnitude gives us the length or size of the vector.
For more such question on magnitude visit
https://brainly.com/question/30337362
#SPJ8
The perimeter of a room is 43 ft. The width is 9 1 2ft. What is the length?
Answer: The length is 12 ft.
Step-by-step explanation:
So a room is likely to be in a shape of a rectangle. And to to find the perimeter of a rectangle will use the formula P = 2w + 2l so in this case we know the perimeter and and the width but we need to find the length.
so using the formula we could do this
43 = 2(9.5) + 2l
43 = 19 + 2l subtract 19 from both sides
-19 -19
24 = 2l Divide both sides by 2
l = 12
The length is 12.
Check: 43 = 2(9.5) + 2(12)
43 = 19 + 24
43 = 43 correct so the length is 12.
Suppose Sam places $7000 in an account that pays 14% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
probability question
8 students made 4 mistakes or more
if α and β are the zeros of p(x) = x² – 5x + 3, then find the value of α + β – αβ option (a)1, (b)2, (c)3, (d)5 please help
Step-by-step explanation:
if you follow me I will give your answer
Answer:
» (b) 2Step-by-step explanation:
Given equation :p(x) = x²-5x+3: α + β = sum of zeroes = −(coefficient of x) / (coefficient of x²) = -(-5) / 1 = 5/1 = 5
αβ = product of zeroes = (constant term) /(coefficient of x²) = 3/1 = 3So, → α + β – αβ ( α+β = 5 , αβ = 3 ) → 5 – 3 → 2
A group of toxicologists investigated the impact of exposure to low oxygen on the mortality of rice weevels. In an experiment, 31,388 of 31,421 rice weevils were found dead after exposure to nitrogen gas for 4 days.. In a second experiment, 23,516 of 23,676 rice weevils were found dead after exposure to nitrogen gas for 4 days. In a second experiment, 23,516 of 23,676 rice weevils were found dead after exposure to nitrogen gas for 3.5 days. Conduct a test of hypothesis to compare the mortality rates of adult rice weevils exposed to itrogen and the two exposure times. Is there a significant difference (at a=0.10) in the mortality rates?
**Give the null and alternative hypotheses. Let p^1 represent the proportion of rice weevils found dead in the first experiment and p^1 represent the proportion of rice weevils found dead in the second experiment. Choose correct answer below*****
A) H^0: (p^1-p^2)>0, H^a(p^1-p^2)=0
B) H^0:(p^1-p^2) =/ (does not equal) , H^a: (p^1-p^2)=0
C) H^0:(p^1-p^2)=0, H^a: (p^1-P62)=0, H^a:(p^1-p^2)<0
D) H^0:(p^1-p^2)=0, H^a:(p^1-p^2)>0
E) H^0:(p^1-p^2)<0, H^a: (p^1-p^2)=0
F) H^0:(p^1-p^2)=0, H^a:(p^1-p^2) =/ (does not equal) 0
The correct answer is F) H^0: (p^1-p^2)=0, H^a: (p^1-p^2) ≠ 0, which represents the appropriate null and alternative hypotheses for testing the mortality rates of rice weevils exposed to nitrogen gas for different exposure times.
To conduct a test of hypothesis to compare the mortality rates of rice weevils exposed to nitrogen gas for different exposure times, we need to formulate the null and alternative hypotheses. The null hypothesis (H^0) states that there is no significant difference in the mortality rates between the two exposure times, while the alternative hypothesis (H^a) states that there is a significant difference.
In this case, let p^1 represent the proportion of rice weevils found dead in the first experiment and p^2 represent the proportion of rice weevils found dead in the second experiment. The null hypothesis (H^0) is that the difference in proportions (p^1 - p^2) is equal to zero, indicating no difference in mortality rates. The alternative hypothesis (H^a) is that the difference in proportions is not equal to zero, indicating a significant difference in mortality rates between the two exposure times.
Learn more about null hypothesis : brainly.com/question/30821298
#SPJ11