let be the tangent plane to the graph of (,)=26−132−262 at the point (4,2,−286). let (,)=26−2−2. find the point on the graph of where the tangent plane is parallel to .
Answers
The point on the graph where the tangent plane is parallel is (52, 52, -5382).
What is the tangent plane?
The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.
Here, we have
Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².
We have to find the point on the graph where the tangent plane is parallel.
Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).
φ(x,y,z) = 13x² + 26y² + z - 26
Δφ = 26xi + 52yj + k
Δφ(4, 2, –286) = 104i + 104j + k
Then,
P: 104(x-4) + 104(y-2)+1(z+286) = 0
104x + 104y + z = 338...(1)
Now, Let
ψ(x,y,z) = x² + y² + z - 26
Δψ = 2xi + 2yj + k
Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).
Δψ (x₀,y₀,z₀) = (2x₀,2y₀,1)
= 2x₀/104 = 2y₀/104 = 1/1
x₀ = 52 = y₀
Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382
Hence, the point on the graph where the tangent plane is parallel is (52, 52, -5382).
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Related Questions
find the value of x ( 94 , 45, & x)
Answers
Explanation
We are given a triangle
and then asked to determine the value of x
To do so, we know that the total angles in a triangle are 180 degrees
Thus
\(\begin{gathered} x+94+45=180 \\ \\ x+139=180 \\ x=180-139 \\ x=41^0 \\ \end{gathered}\)The value of x is 41 degrees
What is the sum of the measures of the exterior angles of the polygon shown below? If necessary, round to the nearest tenth.
Answers
The sum of the exterior angle of the pentagon is 360 degrees.
How to find the angles in a polygon?The polygon above is a pentagon. A pentagon is a polygon with 5 sides.
If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. The sum of the exterior angles of a polygon is 360°.
Therefore, the sum of the measure of the exterior angles of the pentagon as shown is 360 degrees.
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You are going to an amusement park over Spring Break.
The cost of admission to enter the park is $30 and the
rides are an additional $6 each. If your parents give
you $100 to spend at the amusement park, what is the
maximum number of rides you can go on?
Please show work
Please hurry in 10 minutes
Answers
Answer:
you can go on a maximum of 11 rides
Step-by-step explanation:
you first have to subtract 30 from 100 since that is the admissons fee.
So now you are left with 70 dollars.
You divide 70 by 6 since you need 6 dollars to go on each ride.
and 70 divided by 6 is 11.6666666667 but round it to 11 since that the whole number you're left with.
hope this helped :)
Find the gain percent in the following:
Cost Price Rs 280,
(a) Selling Price
Rs 290
Answers
Answer:
3.57
Step-by-step explanation:
P=SP -CP
=290-280=10
P%=\(\frac{P*100}{CP}\)
=\(\frac{10*100}{280}\)
=\(\frac{1000}{280}\)
=3.57
Which properties belong to all isosceles triangles? Check all that apply.
The base angles are congruent.
All three angles are congruent.
The two sides opposite the base angles are congruent.
All three sides are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.
Answers
=====================================================
Explanation:
Let's go through the answer choices to see which are true and which are false.
A) True. The base angles are the same measure, and they are opposite the congruent sides. Any isosceles triangle has exactly two congruent sides.B) False. This is describing an equilateral triangle (where all three angles are 60 degrees each).C) True. See choice A.D) False. This is describing an equilateral triangle where all sides are the same length. E) True. You can use the SAS (side angle side) congruence theorem to prove that the angle bisector is also the perpendicular bisector. Furthermore, this segment is also a median. This only applies to the vertex angle.Answer:
The base angles are congruent.
The two sides opposite the base angles are congruent.
The bisector of the vertex angle is the perpendicular bisector of the base.
Step-by-step explanation:
Answer the following questions using 125 words or more:
Write about the similarity of the original comic to the enlargement. How similar are they and how can you tell? What would cause differences in the two pictures? If you drew another comic using a grid, is there anything you would do differently?
What would happen if you reduced the comic's size rather than enlarged it? Would the process be the same? What would you do differently?
Link to video 2min https://media-release.glynlyon.com/g_mat08_ccss_2016/4/media/html5/anm_scale_drawing_comic_project/media/video.mp4
Answers
Answer:
given in a triangle rst and another triangle ratOn a coordinate plane, triangle R S T has points (0, 0), (negative 2, 3), (negative 3, 1). Triangle R prime S prime T prime has points (2, ...
9 votes
Find the distance between (1, 5) and (5, 2) using the Pythagorean Theorem. Type a number for your answer.
Answers
Answer:
Distance = \(\sqrt{(1-5)^{2} + (5-2)^{2} }\) units
= \(\sqrt{(-4)^{2} + (3)^{2} }\) units
=\(\sqrt{25}\) units
= 5 units
simplify expression
Answers
Because first you do the exponent which is 16 than you multiply 16 times -2 which is -32 plus 1 which gives -31
The scale of a map is 1cm : 70km. What is the actual distance between two towns that are 3cm apart on the map
Answers
Answer:
210 km
Step-by-step explanation:
1cm : 70km
3 x 70 = 210
3cm : 210km
Hopefully this helps you :)
pls mark brainlest ;)
Round each mixed number to the nearest whole number. Then, estimate the difference.
27 3/8 - 1 1/10
Answers
Step-by-step explanation:
please mark me as brainlest
Plz answer fast it is due tmrw
Answers
Answer:
your answer is correct
Step-by-step explanation:
What is a function? Explain briefly
Answers
Answer:
in mathamatics...an algebraic function that can be defined as a root od a polynomial equation
Step-by-step explanation:
Answer:
A function is the difference between the input and the output in a given table. Here is an example:
Input | Output
2 | 4
4 | 6
6 | 8
The function is add 2. Best of Luck!
Which number line shows the solution to the inequality
4x-3>-7?
Answers
it is answer c/ x>-1
Step-by-step explanation:
4x-3>-7
add 3 to both sides
4x-3+3>-7+3
4x>-4
divide both sides by 4
4x/4 > -4/4
A sweater is on sale for $34.15 . If the markdown on the sweater is 45% off , what was the original cost for the sweater ? pls help me .
Answers
The complete cost of purchasing an asset is known as the original cost.The whole costs associated with purchasing and using an asset are taken into account when calculating its initial cost.
Find original cost ?Subtract the asset's cost from its salvage value (what you anticipate it to be worth at the end of its useful life) to determine depreciation using the straight-line technique.The amount that can be depreciated, or the depreciable basis, is the outcome.Subtract this sum from the asset's useful life, which is measured in years. Revenue less costs equals profit.Markup is calculated as follows: markup = 100 * (revenue - cost) / cost.And finally, use revenue = cost + cost * markup / 100 if you need to know the selling price. The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.The markup percentage, which is computed as (12 - 8) / 8, is 50% for an item that costs the business $8 to produce but is priced at $12.Original cost = $ 34.15 - $ 0.45/ 100
= 0.33%
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what is 4/5s divided by 2/3s .
Answers
Consider the equation 3x2−2x+5=0. What are the values of a, b, and c?
Answers
Answer:
So a = -2, b = 3 or 2, and c = 5.
Step-by-step explanation:
An equation like this is usually setup as: ax + by + c = 0
So assuming that with 3 x 2 one of the is y you can rearrange:
-2x + 3 x 2 + 5 = 0
So a = -2, b = 3 ( or 2 depending on which one is y), and c = 5.
big bucks bart purchased an extravagant, ornate antique baroque bookshelf with plenty of room. in how many ways can bart arrange 11 books on the shelf: using all the books in a row?
Answers
Solve for x. PLZ HELP ASAP!!!
Answers
X is a vertical angle to the angle marked as 100 degrees.
Vertical angles are the same so x = 100 degrees
Answer: 100 degrees
Pls help
Simplify the expression: -1.23x + 1.54x + 1.2 + 1.2 + 3.4p
Answers
Answer:
0.31x + 2.4 + 3.4p
Step-by-step explanation:
combine like terms
You combine like terms
Select 222 strategies that we can use to subtract 563-192563−192563, minus, 192. Choose 2 answers: Choose 2 answers: (Choice A) A Add 100+90+2100+90+2100, plus, 90, plus, 2. (Choice B) B Evaluate (563-200)+8(563−200)+8left parenthesis, 563, minus, 200, right parenthesis, plus, 8. (Choice C) C Subtract 571-200571−200571, minus, 200.
Answers
The value of x is:
.
9.
18.
None of these choices are correct.
Answers
Hello!
In the given figure we can see that it is a right angled triangle .
Where,
Base is 9
We have to find the value of x i.e Hypotenuse
Here we are given base and we need to find the Hypotenuse.
Also we have been given the value of theta = 45°
Using trigonometric ratio :
cos \(\theta = \dfrac{ B}{H} \)
As per the question we have hypotenuse = x
Plugging the required values,
\( \cos 45 \degree = \dfrac{9}{x} \)
\( \dfrac{1}{ \sqrt{2} } = \dfrac{9}{x} \: \: \: \: \bigg(\because \cos 45\degree = \dfrac{1}{\sqrt2} \bigg)\)
further solving by cross multiplication
\(x = 9 \sqrt{2} \)
Hence, The value of x is 9√2
Answer : Option 1
Hope it helps! :)
please I need help with both problems .( also show work plz)
Answers
Answer:
4. x = 50
5. x = 5
Step-by-step explanation:
For question 4:
Multiply both sides: x + 35 = -15Move the constant to the right: x = -15 - 35Calculate: x = -50For question 5:
Move the constant to the right: -3x = -17 + 2Calculate the sum: -3x = -15Divide both sides: x = 5Answer:
4) x= -50
5) x= 5
Step-by-step explanation:
Number 5
Simplifying
-3x + -2 = -17
Reorder the terms:
-2 + -3x = -17
Solving
-2 + -3x = -17
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2' to each side of the equation.
-2 + 2 + -3x = -17 + 2
Combine like terms: -2 + 2 = 0
0 + -3x = -17 + 2
-3x = -17 + 2
Combine like terms: -17 + 2 = -15
-3x = -15
Divide each side by '-3'.
x = 5
Simplifying
x = 5
Number 4
x/5+7 = -3 // + 3
x/5+3+7 = 0
1/5*x+10 = 0 // - 10
1/5*x = -10 // : 1/5
x = -10/1/5
x = -50
x = -50
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $9,000, annual interest: 9%, interest periods: 12, number of years: 20
After 20 years, the investment compounded periodically will be worth:
(Round to two decimal places as needed.)
more than the investment compounded annually.
Answers
After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.
How to find the investment value ?First, find the value of the investment when it is compounded periodically, 12 times a year.
The formula is:
= Amount invested x ( 1 + rate ) ^ number of periods
= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰
= $ 53, 678. 16
If compounded annually, the value would be :
= 9, 000 x ( 1 + 9 % ) ²⁰
= $ 50, 439. 69
The difference is :
= 53, 678. 16 - 50, 439. 69
= $ 3, 238. 47
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an amusement park ride consists of a large vertical wheel of radius r that rotates
Answers
The best description of the passenger's linear and angular velocity while passing point A is option d) Linear Velocity Constant, Angular Velocity Constant.
When the passenger is at point A, which is the highest point of the ride, the seat exerts a normal force with a magnitude of 0.8F, where F represents the person's weight. This normal force provides the necessary centripetal force to keep the person moving in a circular path. At this point, the passenger's linear velocity remains constant, as there is no change in speed.
Since the passenger releases a small rock without hitting anything, there are no external torques acting on the system. Therefore, according to the law of conservation of angular momentum, the passenger's angular velocity remains constant as well. The angular velocity is determined by the rotational motion of the wheel and does not change as the passenger passes point A.
Therefore, the passenger's linear velocity is constant, and their angular velocity is also constant while passing point A, resulting in the most accurate description being d) Linear Velocity Constant, Angular Velocity Constant.
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figure 6-23 refer to figure 6-23. how much tax revenue does this tax produce for the government? group of answer choices $480 $600 $800 $1120
Answers
The tax revenue produced for the government in Figure 6-23 is $800.
What is the amount of tax revenue generated in Figure 6-23?To determine the tax revenue produced, we need to analyze Figures 6-23 and identify the corresponding value.
In Figure 6-23, the tax revenue is represented by the area of the rectangle formed by the tax rate and the quantity subject to the tax. By calculating the area of the rectangle, we can find the amount of tax revenue generated.
In this case, the rectangle has a height of $8 and a base of 100 units. Multiplying these values, we obtain a tax revenue of $800.
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what is the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c}$ has a domain of all real numbers?
Answers
The smallest integer value of c that ensures the function f(x) has a domain of all real numbers is c = 5.
For the function f(x) to have a domain of all real numbers, the denominator x^2 + 4x + c cannot be equal to zero. If the denominator equals zero, the function would have undefined values.
To find the smallest integer value of c that satisfies this condition, we need to find the values of c that make the quadratic x^2 + 4x + c = 0 have no real solutions.
For a quadratic equation ax^2 + bx + c = 0 to have no real solutions, the discriminant (b^2 - 4ac) must be negative.
In this case, we have a = 1, b = 4, and c is the variable we are trying to determine.
The discriminant is:
b^2 - 4ac = 4^2 - 4(1)(c) = 16 - 4c
To have no real solutions, the discriminant must be negative:
16 - 4c < 0
Solving this inequality, we find:
4c > 16
c > 4
Since c must be an integer, the smallest integer value of c that satisfies this condition is 5.
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write the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1)
Answers
Answer:
y = - 5/2x + 24
Step-by-step explanation:
2x - 5y = - 12. (10, -1)
- 5y = - 2x - 12
y = -2/-5x -12/-5
y = 2/5x + 12/5
Slope: 2/5 (slope of the perpendicular line: - 5/2)
y - - 1) = - 5/2(x - 10)
y + 1 = - 5/2x + 25
y = - 5/2x + 24
performs an experiment. Harper randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Harper performs the experiment 38 times.
The results are shown below:
An apple chew was selected 22 times.
A cherry chew was
selected 6 times.
A lime chew was selected 10 times.
Based on these results, express the probability that the next chew Harper removes
from the bag will be lime chew as a percent to the nearest whole number.
Answers
The probability that the next chew Harper removes from the bag will be a lime chew is 26%.
We know that there are a total of 38 chews in the bag, and that 10 of them are lime chews. This means that the probability of randomly selecting a lime chew is 10/38 = 0.2631578947. To the nearest whole number, this is 26%.
It is important to note that this is just a probability. It is possible that the next chew Harper removes from the bag will not be a lime chew. However, based on the results of the experiment, the probability is 26% that it will be.
Here are some additional details about the probability of randomly selecting a lime chew from the bag:
The probability of randomly selecting a lime chew is not guaranteed to be 26%. If Harper performs the experiment more times, the probability may change.
The probability of randomly selecting a lime chew is also affected by the number of lime chews in the bag. If Harper removes more lime chews from the bag, the probability of randomly selecting a lime chew will decrease.
The probability of randomly selecting a lime chew is also affected by the way that Harper removes the chews from the bag. If Harper does not return the chews to the bag after each selection, the probability of randomly selecting a lime chew will increase.
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Which equation could be used to find the length of the hypotenuse?
А
С
5 cm
С
B
8 cm
Answers
Answer:
The first option (5^2 + 8^2 = c^2).
Step-by-step explanation:
According to the Pythagorean Theorem, a^2 + b^2 = c^2.
If a is 5 cm, and b is 8 cm, you would have the following equation...
5^2 + 8^2 = c^2.
That matches with the first option.
Hope this helps!
The class president lost the lunch receipt. She knows that 21 students ate lunch and the total cost was $117.27. Each student ordered either a $4.99 sandwich meal or a $5.95 pizza meal. The sandwich meal included one sandwich, one'small order of fries, and one medium drink. The pizza meal included two slices of pizza and one medium drink How many of each meal were ordered?
Answers
According to the given conditions, there were 8 sandwich meals and 13 pizza meals ordered.
What are equations?Solving equations involves finding the values of the variables that make the equation true. This is often done by manipulating the equation using algebraic operations and rules until the variable being solved for is isolated on one side of the equation.
According to the given information:Let's represent the number of sandwich meals ordered by 'x' and the number of pizza meals ordered by 'y'.
From the problem statement, we know that:
x + y = 21 (since there were 21 students who ate lunch)
4.99x + 5.95y = 117.27 (since the total cost of all the meals was $117.27)
We can use the first equation to solve for one variable in terms of the other. Solving for 'x', we get:
x = 21 - y
Substituting this into the second equation, we get:
4.99(21-y) + 5.95y = 117.27
104.79 - 4.99y + 5.95y = 117.27
0.96y = 12.48
y = 13
So, 13 pizza meals were ordered. Substituting this back into the first equation, we get:
x + 13 = 21
x = 8
8 sandwich meals were ordered.
Therefore, according to the given conditions there were 8 sandwich meals and 13 pizza meals ordered.
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