find the equation of the tangent plane to z = x2 5y3 at (1, 1, 6).
Answers
The equation of the tangent plane to z = x2 5y3 at (1, 1, 6) is 2(x - 1) - 15(y - 1) - (z - 6) = 0
To find the equation of the tangent plane to the surface z = x^2 - 5y^3 at (1, 1, 6), we need to first find the gradient vector of the surface at the given point.
The gradient vector of the surface z = f(x, y) is given by:
∇f(x, y) = <fx, fy, -1>
where fx and fy are the partial derivatives of f with respect to x and y, respectively.
Taking the partial derivatives of z = x^2 - 5y^3 with respect to x and y, we get:
fx = 2x
fy = -15y^2
Therefore, the gradient vector at (1, 1, 6) is:
∇f(1, 1) = <2, -15, -1>
Now, we can use the point-normal form of the equation of a plane to find the equation of the tangent plane. The point-normal form of the equation of a plane is given by:
n . (r - P) = 0
where n is the normal vector to the plane, P is a point on the plane, and r = <x, y, z> is any point on the plane.
At the point (1, 1, 6), the equation of the tangent plane is:
<2, -15, -1> . (<x, y, z> - <1, 1, 6>) = 0
Simplifying this equation, we get:
2(x - 1) - 15(y - 1) - (z - 6) = 0
Therefore, the equation of the tangent plane to z = x^2 - 5y^3 at (1, 1, 6) is:
2(x - 1) - 15(y - 1) - (z - 6) = 0
To learn more about “tangent” refer to the https://brainly.com/question/4470346
#SPJ11
Related Questions
In the figure, a∥b and m∠3 = 34°.
What is the m∠7?
Enter your answer in the box. |__|
Answers
Therefore, In the figure, a∥b angle m∠7 = 34° .
What is angle ?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.
Here,
Given that a and b are parallel lines,
∠3 and ∠7 are corresponding angles and congruent
m∠3 = 34°
thus ,m∠7 =m∠3 = 34°
so, m∠7 = 34°
Therefore, In the figure, a∥b m∠7 = 34° .
To know more about angle , visit
https://brainly.com/question/28451077
#SPJ1
Find the area and perimeter of rectangle DEFG whose
endpoints are D(-3, 1), E(1, 3), F(2, 1), and G(-2, -1)
Answers
The area of rectangle DEFG is 16 square units and its perimeter is 12 units.
To find the area, we can use the formula: Area = length x width We can find the length and width by calculating the distance between the coordinates of opposite sides of the rectangle.
Length = EF =
\( \sqrt{} ((2-1)^2 + (1-3)^2)\)
=
\( \sqrt{} (2 + 4) = \sqrt{} (6)\)
Width = DG =
\( \sqrt{} ((-3+2)^2 + (1+1)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)
The area of rectangle DEFG = length x width =
\( \sqrt{} (6) x \sqrt{} (6)\)
= 6 x 2 = 16 square units.
To find the perimeter, we can add up the lengths of all four sides: Perimeter = DE + EF + FG + GD
DE =
\( \sqrt{} ((1+3)^2 + (-3+(-1))^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)
EF =
\( \sqrt{} ((2-1)^2 + (1-3)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)
FG =
\( \sqrt{} ((2+2)^2 + (1+1)^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)
GD =
\( \sqrt{} ((-2+3)^2 + (-1-1)^2) = \sqrt{} (1 + 4) = \sqrt{} (5)\)
The perimeter of rectangle DEFG =
\( \sqrt{} (20) + \sqrt{} (6) + \sqrt{} (20) + \sqrt{} (5) \)= 12 units.
Hence, The area of the rectangle is 16 square units and the perimeter is 12 units.
Learn more about rectangle here:
https://brainly.com/question/30232870
#SPJ4
what would happen if you put your hand on the stove and got burnt, but put your hand back on 5 more times just to make sure it's actually hot?
Answers
If you put your hand on a hot stove and got burnt, it is a natural response to remove your hand from the stove to prevent further injury. However, if you choose to repeatedly put your hand back on the stove even after being burnt, you will continue to experience pain and potentially cause further damage to your skin and tissues.
Repeatedly exposing yourself to the source of the burn will not change the fact that it is hot and causing damage to your skin. In fact, each time you touch the hot surface, you are likely to make the burn worse, as the heat will continue to damage your skin and tissues.
Additionally, repeated exposure to the hot stove may lead to nerve damage, which can result in a loss of sensation in your hand, making it harder to recognize when you are in danger of burning yourself in the future.
It is important to listen to your body's natural responses to pain and remove yourself from harmful situations. In the case of a burn, it is best to seek immediate medical attention and follow proper first aid procedures to minimize damage and promote healing.
If you are playing a game that has a pair of dice you have to roll, what is the
probability that the sum of the numbers you roll will be a 9?
Probabilities are stated as fractions. For instance, the probability that you will get
heads on a coin flip are "1 out of 2" or 1/2. State your answer as a fraction in
simplest form.
Answers
Answer:
1/9
Step-by-step explanation:
For each of the first die's 6 outcomes, the second die also has a possible 6 outcomes.
6 × 6 = 36
There are 36 different outcomes from
1, 1
1, 2
1, 3
...
6, 6
Many outcomes have the same sum. For example, 3, 4 and 4, 3 both add to 7.
How many outcomes add to 9?
3, 6
4, 5
5, 4
6, 3
4 different outcomes out of a possible 36 different outcomes add to 9.
p(sum of 9) = 4/36 = 1/9
T/F: it is best to plan future activities for the group during the middle of the group
Answers
Answer:
False.
Step-by-step explanation:
It's ok to plan future activities for the group, but it's best to plan in the beginning of the group.
how to prove converse of. basic proportionality theorem
please answer within one hour
Answers
Step-by-step explanation:
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you.
Answer:
two different ways of theoretical and experimental explanation
both are correct
hope they helped you
a ⃗=⟨-9,6⟩ and b ⃗=⟨3,1⟩. What is the component form of the resultant vector 1/3 a ⃗- 2b ⃗ ?
Show all your work.
please answer this, with full work. even if the answer is incorrect the work is the most important part
Answers
The resultant component of the vector addition is (-9, 0).
What is the resultant component of the vectors?The resultant component of the vector is calculated as follows;
a = (-9, 6)
b = (3, 1)
The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)
The result of 2b = 2(3, 1) = (6, 2)
The result of the vector addition is calculated as follows;
1/3a - 2b
= (-3, 2) - (6, 2)
= (-3 -6, 2 -2)
= (-9, 0)
Learn more about vector addition here: https://brainly.com/question/30426215
#SPJ1
If+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answers
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
Learn more on interest here: https://brainly.com/question/2151013
#SPJ12
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answers
(A) x2 + (y – 3)² = 36, is the equation that represents circles with a diameter of 12 units and a center on the y-axis.
What are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So, the standard form for calculating the equation of a circle is as follows:
(x-a)² + (y-b)² = b = r²
Where;
(a, b) is the circle's center.The radius of the circle is denoted by r.Information:
diameter = 12 unitsradius = 12/2 = 6 unitsIf the center is on the y-axis, it will be at (0, 3).
By substituting into the formula, we get (x-0)² + (y-3)² = 6² is equivalent to
x²+ (y-3)² = 36Therefore, the equation that represents circles with a diameter of 12 units and a center on the y-axis is (A) (A) x2 + (y – 3)² = 36.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ9
The correct question is given below:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
a. x2 + (y – 3)2 = 36
b. x2 + (y – 5)2 = 6
c. (x – 4)² + y² = 36
d. (x + 6)² + y² = 144
e. x2 + (y + 8)2 = 36
ab" that goes through points (0,17)
Write an exponential function in the form y
and (2, 153).
What is the answer
Answers
how to factorise by grouping for 7a, d and h
Answers
Step-by-step explanation:
7a
x2 + 4x + ax + 4a
x2 + ax + 4x + 4a
x (x + a) + 4 (x + a)
:(x + 4)(x+a)
7d
x2+2x-ax-2a
x2-ax+2x-2a
x (x-a)+2 (x-a)
:(x+2)(x-a)
7h
x2-2bx-5x+10b
x2-5x-2bx+10b
x (x-5)-2b(x-5)
:(x-2b)(x-5)
Answer:
You have to take out the common terms :
Question A,
\( {x}^{2} + 4x + ax + 4a\)
\( = x(x + 4) + a(x + 4)\)
\( = (x + a)(x + 4)\)
Question D,
\( {x}^{2} + 2x - ax - 2a\)
\( = x(x + 2) - a(x + 2)\)
\( = (x - a)(x + 2)\)
Question H,
\( {x}^{2} - 2bx - 5x + 10b\)
\( = x(x - 2b) - 5(x - 2b)\)
\( = (x - 5)(x - 2b)\)
The point (3,-1) is on a graph of
y = x² + kx -4. What is the value
of k?
A -1
B -4/3
C -2
D-6
Answers
Answer:
Step-by-step explanation: ( 3, 1)
x = 3, y = 1
From the formula, y = x² + kx - 4
1 = 3² + 3k - 4
1 = 9 + 3k - 4
1 = 5 + 3k
-3k = 5 + 1
-3k = 6
Divide both sides by -3
-3k/-3 = 6/ -3
k = -2
what is the closet time to midnight?
A. 11:55AM
B. 12:06AM
C. 11:50AM
D. 12:03AM
Answers
Answer:
11:55 is closest time time to mid night
Option D is correct, 12:03AM is the closet time to midnight.
Midnight is typically defined as the beginning of a new day, precisely at 12:00 AM.
In a 12-hour clock format, AM (ante meridiem) is used to represent the time before noon (from midnight to 11:59 AM), while PM (post meridiem) is used to represent the time after noon (from 12:00 PM to 11:59 PM).
12.06am is 6 minutes past midnight.
11.50am is 10 minutes from midday, or, if you prefer, 11 hours and 55 minutes past midnight.
12.03am is 3 minutes past midnight.
Hence, the closet time to midnight is 12:03 AM.
To learn more on Closet time click:
https://brainly.com/question/31732120
#SPJ2
Find the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares
Answers
The volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.
for given question,
We need to find the volume of the solid whose base is the region bounded between the curve y = x³ and the y-axis from y = 0 to y = 1 and whose cross section taken perpendicular to the y-axis are squares.
Now we rewrite given curve y = x³ in terms of x.
\(x=\sqrt[3]{y}\)
Since the length of the side of each cross sectional square is \(2\sqrt[3]{y}\), the cross sectional area A(y) can be given by
A(y) = \((2\sqrt[3]{y})^2\)
A(y) = \(4y^{\frac{2}{3} }\)
The region is bounded from y = 0 to y = 1
so, the volume V can be found by,
\(V=\int\limits^1_04y^{\frac{2}{3} }~dy\\\\V=4\int\limits^1_0 y^{\frac{2}{3} }~dy\\\\V=4\times \frac{3}{5} \\\\V=\frac{12}{5}\\\\V=2.4\)
Therefore, the volume of the solid whose base is the region bounded between the curve y=x^3 and the y-axis from y=0 to y=1 and whose cross section taken perpendicular to the y-axis are squares is 2.4 cubic units.
Learn more about the volume here:
https://brainly.com/question/12649605
#SPJ4
please help !!
Problem A painter is painting a mural on a wall. He has a 20-foot ladder. He needs to work on
a part of the wall that is 16 feet above the ground. How far from the base of the building should
he place the foot of the ladder to make sure that the ladder reaches his work area? Show your
work
Answers
Answer:
The worker should put the ladder 4 feet away from the wall.
Help please i dint get it pls answer
Answers
Answer: 7%
(Hope this is right.)
Step-by-step explanation:
Let's solve this using the information we have and an equation.
Shane: $32,000 - (Given)
Theresa: 18,000+14x, if x=1,160 - (Given)
---------------------------------------------------------------
Step two: (Theresa) 14(1,160) =16,240 (Algebra)
Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.
---------------------------------------------------------------
Finally,
They're asking for how much more she paid for her car as a percentage of what Shane paid.
34,240-32,000=2,240 and
2,240/32,000=0.07
0.07x100=7
Answer 7% more than what Shane paid.
PLEASE HELP The mean life expectancy of a certain type of light bulb is 860 hours with a standard deviation of 22 hours.
What is the approximate standard deviation of the sampling distribution of the mean for all samples with n = 65?
0.34 h
0.75 h
2.73 h
2.95 h
Answers
Answer: The correct answer is: 2.73 h.
Step-by-step explanation:
I hope this helps! :)
the population of elk in a national forest was measured to be 12,000 in 2003, and was measured again to be 12,700 in 2004. if the population continues to grow linearly at this rate, what will the elk population be in 2014?
Answers
The elk population in 2014 will be 19,700 ,A population is an identified grouping of objects with the purpose of analysis and data collection.
What is population?A population is an identified grouping of objects with the purpose of analysis and data collection. Examples include people and animals. It comprises of a related collection of species that live in a specific area and have the ability to interbreed.
The population increased by 12,700-12,000 = 700 between the two measures, however, it did so over a period of 1 year, from 2004 to 2003. Divide 700 elk by 1
The elk population in 2014 will be 19,700We must first establish the method
2014=700 should add 10 times then we will get the 2014th year population.
so the population of 2014th will 19700
To learn more about population refer to:
https://brainly.com/question/25630111
#SPJ1
What i the lope of the line that pae through the point (7, -4)(7,−4) and (11, -4)(11,−4)? Write your anwer in implet form
Answers
helpppppppppppppppppp
Answers
Answer:
what do you need help with ???
a sample of 800 computer chips revealed that 60% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that above 55% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.01 level to support the company's claim? state the null and alternative hypotheses for the above scenario.
Answers
The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.
Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.
A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion. The test statistic for this test is the z-score, which is calculated as:
\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)
If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.
If we substitute the values, we get:
\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)
The z-score for this assertion is calculated, and we find that it is approximately 2.86.
In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.
Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.
To learn more about hypothesis test refer:
https://brainly.com/question/32068220
#SPJ11
Formulate but do not solve the following exercise as a linear programming problem.
National Business Machines manufactures two models of portable printers: A and B. Each model A costs $120 to make, and each model B costs $140. The profits are $25 for each model A and $40 for each model B portable printer. If the total number of portable printers demanded per month does not exceed 3000 and the company has earmarked not more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profits P in dollars?
Answers
To formulate this problem as a linear programming problem, we need to identify the decision variables, objective functions, and constraints.
Decision Variables:
Let x be the number of model A printers manufactured per month, and y be the number of model B printers manufactured per month.
Objective Function:
The objective is to maximize monthly profits, which can be expressed as P = 25x + 40y.
Constraints:
1. The total number of printers demanded per month cannot exceed 3000, so we have the constraint x + y ≤ 3000.
2. The company has earmarked not more than $600,000/month for manufacturing costs, so the cost constraint is 120x + 140y ≤ 600,000.
3. The number of printers manufactured must be non-negative, so x ≥ 0 and y ≥ 0.
Therefore, the linear programming problem is:
Maximize P = 25x + 40y
Subject to:
x + y ≤ 3000
120x + 140y ≤ 600,000
x ≥ 0, y ≥ 0
Learn more about programming here:
https://brainly.com/question/11023419
#SPJ11
Bro could i get some help
Answers
Answer: wow that’s a lot of stuff
Step-by-step explanation:
Noice profile pic
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once. Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
Answers
Answer:
You would need to know how much money she spent and how much she had left.
Step-by-step explanation:
With this, you could find out how much money she had in total.
Sample Response:
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.
Is the set of polynomials closed under division? Why or why not?
Answers
Hey ✌
Step-by-step explanation:
polynomials are not closed under division.
when u divide polynomials it is possible to get quotients with negative exponents or with fractions that have exponents in the denominator, and neither of these could be included in polynomials.
I hope it helped u
Find the 8th term of the geometric sequence 3, -12, 48, ...
Answers
Answer:
a(8) = -49152
Step-by-step explanation:
Step 1: Find r
-12/3 = 4
Step 2: Write geometric explicit formula
\(a_{n} = 3(4)^{n-1}\)
Step 3: Plug in 8th term for n
\(a_{8} = 3(4)^{7}\)
a(8) = -49152
Alternatively you can find r then multiply 3 by -4 8 times.
Is the height of these students a function of their wrist circumference?
Yes because as wrist circumference increases height also increases.
O Yes because a line can be fit to these data to predict other pairings.
No because the height of 151 cm is paired with two wrist circumferences.
O No because the wrist circumference of 16 cm is paired with two heights,
Answers
hope this helps
Given that a:b = 5:4 and b/c = 7:3 find: a:b:c
Answers
a/b=5/4
a=5k
b=4k
b/c=7/3
b=7x
c=3x
b=4k
b=7x
4k=7x =>
k=7y
x=4y
a/b/c=
=5*7*y/4*7*y/3*4*y=
=35y/28y/12y=
=35/28/12y=
=5/4/12y=
=1,25/12y=
=0.1041666666666667/ y
there may be a mistake in my answer
How far apart are southville and westfield if southville is 57 mi due south of portland and westfield is 76 mi due west of portland?.
Answers
The Answer is 95 miles using distance rule of maths.
What is distance in math?
As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.
So if we mark their position in x-y plane. one is not x line and another one is in y line.
So the coordinates of the points are (57,0) and (0,76)
The distance between them is √(y²+x²)
= √(57²+76²)
=√ (3249 + 5776)
= 95 miles
Hence the distance between them is 95 miles.
Learn more about distance , by the following link.
https://brainly.com/question/17273444
#SPJ4
how would I answer and what would be the answer?
Answers
Answer:
There is a zero at x = 1
Explanation:
The critical points of a function are where the slope of the function is zero.
Now, for our function, the slope is never zero on the given interval. Meaning no point on the function has a horizontal tangent line. This tells us that there is no point within the interval that has a zero slope. Hence, we conclude that the function does not have any critical points in the given interval.
Taking a further look at the graph, however, we see that the function intersects the x-axis at x = 1. Therefore, the function has a zero at x = 0.
Therefore, the fourth answer choice is the correct answer.