Find a point on the ellipsoid x2+y2+4z2=36x2+y2+4z2=36 where the tangent plane is perpendicular to the line with parametric equations
Answer:
A point on the ellipsoid is (-4,2,2) or (4,-2,-2)
Step-by-step explanation:
Given equation of ellipsoid f(x,y,z) :[tex]x^2+y^2+4z^2=36[/tex]
Parametric equations:
x=-4t-1
y=2t+1
z=8t+3
Finding the gradient of function
[tex]\nabla f(x,y,z)=<\frac{\partial{f}}{\partial{x}},\frac{\partial{f}}{\partial{y}},\frac{\partial{f}}{\partial{z}}>\\\nabla f(x,y,z)=<2x,-2y,8x>[/tex]
So, The directions vectors=(-4,2,8)
Now the line is perpendicular to plane when direction vector is parallel to the normal vector of line
[tex]\nablaf(x,y,z)=(2x,2y,8z)=\lambda(-4,2,8)[/tex]
So, [tex]2x=-4\lambda[/tex]
[tex]\Rightarrow x=-2\lambda[/tex]
[tex]2y=2\lambda\\\Rightarrow y=\lambda\\8z=8\lambda\\\Rightarrow z=\lambda[/tex]
Substitute the value of x , y and z in the ellipsoid equation
[tex](2\lambda)^2+(\lambda)^2+4(\lambda)^2=36\\9(\lambda)^2=36\\\lambda^2=4\\\lambda=\pm 2[/tex]
With [tex]\lambda = 2[/tex]
x=-2(2)=-4
y=2
z=2
With[tex]\lambda =- 2[/tex]
x=-2(-2)=4
y=-2
z=-2
Hence a point on the ellipsoid is (-4,2,2) or (4,-2,-2)
Elena’s bedroom door is 1.2 m wide. How wide should the door be on the scale drawing? Explain how you know.
Answer:
0.016cm
Step-by-step explanation:
I would convert 2cm in terms of meters
2cm/1 = 1m/100cm
since there are cm on top and bottom it cancels out
2•1 /1m• 100 = 2m/100 = .02 m
now you solve using proportions
x/.8 = .02/1
x= (.8)(.02) cross multiples)
x= 0.016
Greatest common factor of 81
Answer:
81
Step-by-step explanation:
I just looked it up :)
Answer:
27
Step-by-step explanation:
Kayla measures a distance of 50 inches. She needs to find the equivalent number of meters. Which conversion factors should she use? Check all that apply.
(A) StartFraction 2.54 centimeters Over 1 inch EndFraction
(B) StartFraction 1 inch Over 2.54 centimeters EndFraction
(C) StartFraction 1 meter Over 100 centimeters EndFraction
(D) StartFraction 100 centimeters Over 1 meter EndFraction
Answer: A and C
Step-by-step explanation: :)
Answer:
A and C [: (edg 2021)
Step-by-step explanation:
I got it correct on my assignment!
10. A minute hand will clearly turn a total of 360° in an hour. How many minutes will it take for the minute hand
turn 155? Round to the nearest minute. Show the calculations that lead to your final answer
Answer:
5 min
Step-by-step explanation:
If the minute hand takes an hour to go 360°, going 155° would take 26 minutes.
The first step is to find the number of degrees the minute hand goes in a minute:
= Degrees in an hour / Minutes in an hour
= 360 / 60
= 6° per minute
In order to go 155°, the minute hand would go for:
= Degrees / Degrees per minute
= 155 / 6
= 25.83
= 26 minutes
In conclusion, it would take 26 minutes for the minute hand to turn 155°.
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What is the answer tho
Answer:
to?
Step-by-step explanation:
Are the 2 triangles congruent?
Answer:
ya they r
Step-by-step explanation:
HELP WITH NUMBER 6 ASAP PLEASE!!!!!!!
Federico read the nutritional information on a package of gummi bears.
The points on the following coordinate plane show how many gummi bears there are in 2, 3, and 5 servings.
Answer:
80
gummi bears
Step-by-step explanation:
Why is the percent increase from 45 to 75 not equal to the percent decrease from 75 to 45? Select three options
Answer:
the answer is 2,3,and 5
Step-by-step explanation:
Answer:
2, 3, and 5
Step-by-step explanation:
Rachel is recording the temperature at her school every morning this week. On Monday, the temperature was 5°C. Part A: On Wednesday, Rachel calculated that the temperature was 13 degrees colder than Monday. What temperature did Rachel record on Wednesday? Part B: On Friday, Rachel calculated that the temperature was 4 degrees warmer than Wednesday. What temperature did Rachel record on Friday?
Answer:
Part A: -8
Part B: -4
Step-by-step explanation:
[tex]5-13=-8[/tex]
[tex]-8+4=-4[/tex]
Turn - Find the value of e
(4w - 6)
+
Find the value of each variable
HEELPPP ASAPP PLS
You deposit $4000 each year into an account earning 5% interest compounded annually. How much.
will you have in the account in 20 years?
Answer:
138,877.01
Step-by-step explanation:
Answer:
I think $5133.43
Step-by-step explanation:
How many 2/3 go into 4
Answer:
2/3,4/3.
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
the answer is 6, this is because 4/(2/3) turns into 12/2
Is ABC= A DEF? If so, name the congruence postulate that applies.
Answer:
Congruent ASA
Step-by-step explanation:
We are given 2 angles and 1 side length. In order, first there is the angle, then side length, then another angle. The ASA postulate says that the triangle will be congruent.
How do you do this question?
Answer:
B
Step-by-step explanation:
This is a ratio of polynomials. As n approaches infinity, an approaches 4n / n⁸ = 4 / n⁷, which is a convergent p-series.
Using Limit Comparison Test:
an = (2 + 4n) / (1 + n²)⁴
bn = 4 / n⁷
lim(n→∞) an / bn = 1
The limit is greater than 0, and bn converges, so an also converges.
Use the graph below to answer the following question:
What is the average rate of change from x = −4 to x = 1?
A.-3
B.-1
C.0
D.1
Answer:
The answer is B.-1
Step-by-step:
When you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. f(x) = x2 and f(x + h) = (x + h)2 Therefore, the slope of the secant line between any two points on this function is 2x + h.p explanation:
Find the area, in square units, of ABC plotted below.
A(0,7)
B(7,-2)
D(2, -3)
C(-3,-4)
The area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.
What is the distance between two points ( p,q) and (x,y)?The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The coordinates of the points A, B, C, and D in the given figure are:
A(0, 7)B( 7,-2)C(-3, -4)D(2, -3)Finding the length of the line segments AD and CB, which will be the distance between A and D, and C and B respectively.
Thus, we get:
Length of line segment AD = |AD| = distance between A and D = [tex]\sqrt{(0-7)^2 + (7-(-2))^2} = \sqrt{7^2 + 9^2} = \sqrt{130} \: \rm units.[/tex]
Similarly, we get:
|CB| = [tex]\sqrt{(-3-7)^2 + (-4-(-2))^2} = \sqrt{10^2 + 6^2} = \sqrt{136} \: \rm units.[/tex]
If we take CB as the base of ABC triangle, then as AD is perpendicular on CB, and touches the peak of the triangle ABC from its base, so AD is height of the triangle.
Thus, as we know know that:
Height's measurement of ABC = |AD|= [tex]\sqrt{130} \: \rm units[/tex]Base length of ABC = |BC| = [tex]\sqrt{136} \: \rm units[/tex]Thus, the area of the triangle ABC is:
[tex]A = \dfrac{base \times height}{2} = \dfrac{\sqrt{130} \times \sqrt{136}}{2} \approx 66.5 \: \rm unit^2[/tex]
Thus, the area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.
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the area of a square is 73.96 m^2 .calculate the length of its side.
Answer:
8.6m
Step-by-step explanation:
mark me as the brainliest
Answer:
8.6 m
Step-by-step explanation:
Given the area, squareroot the area of the square and you will find the length of it's side.
Can anybody help me please I need help
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
7n - 8n - 323
????????????
Answer:
−n−323
Step-by-step explanation:
What is the scale factor of ABC to DEF?
A. 1/2
B. 2
C. 10
D. 10/7
Express 3/4 in seconds. 30" 45" 50"
Answer:
45
Step-by-step explanation:
Find the distance from G(-3, -1) to the line whose equation is y = 4
The distance from G(-3, -1) to the line whose equation is y = 4 is; d = 5
How to find the Distance of a Line?
We are given the coordinate of point G as G(-3, -1).
We want to find the distance between that coordinate and the line y = 4.
Comparing the line with the equation Ax + By + C = 0 gives;
B = 1 and C = -4
Now, Equation for distance between line and coordinate axes points is;
d = |Ax + By + C|/√(A² + B²)
Thus;
d = |0(-3) + 1(-1) - 4|/√(0² + 1²)
d = |-5|
Since absolute value, then d = 5.
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Rate of change is a ______ that describes how much one quantity ______ in respect to another
Answer:
A rate of change is a RATE that describes how one quantity CHANGES in relation to another quantity.capital and underlined is your answer
if there are 7 fish and 3 drown how many are left?
Answer:
7
Step-by-step explanation:
there are 7 left because fish can't drown
My four-year-old son loves playing out in the garden. His favourite activity is digging up and inspecting creepy crawlies, especially snails. If he is patient enough, after the initial shock of being uprooted, they will emerge cautiously from the safety of their shells and start to glide over his little hands leaving viscid trails of mucus. Eventually, when he tires of them, he will discard them, somewhat callously, in the compost heap or on the woodpile behind the shed. Late last September, after a particularly busy session in which he had unearthed and disposed of five or six large specimens, he came to me as I was sawing up wood for the fire and asked ‘Daddy, how many snails is [sic] there in the garden?’ A deceptively simple question for which I had no good answer. It could have been 100 or it could have been 1000. To be quite honest, he would not have comprehended the difference. Nevertheless, his question piqued an interest in me. How could we figure this out together? We decided to conduct an experiment. The next weekend, on Saturday morning, we went out to collect snails. After ten minutes, we had a total of 23 of the gastropods. I took a sharpie from my back pocket and proceeded to place a subtle cross on the back of each one. Once they were all marked up, we tipped up the bucket and released the snails back into the garden. A week later we went back out for another round. This time, our ten-minute scavenge brought us just 18 snails. When we inspected them closely we found that three of them had the cross on their shells, while the other 15 were unblemished. This was all the information we needed to make the calculation. What is the total amount of snails
Answer:
There are 38 snails.
Step-by-step explanation:
help me with thisss simplify : 6³/6⁶
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b is (4,-10) and c is (10,-4) what is the length of b and c ?
Answer:
6rad2
Step-by-step explanation:
Answer:
8.845 units
Step-by-step explanation:
First start by plotting the points on a graph. Doing so will give you two points that you can connect and then turn into a triangle. Find the length and height of the triangle by counting how many units long each is. The length should be 6 units, while the height should also be 6 units. You can then use the pythagorean theorum to find the length of b to c:
A^2 + B^2 = C^2
6^2 + 6^2 = C^2
36 + 36 = C^2
72 = C^2
C = 8.845 units