1) the equation of the tangent plane at (2,8,5) is [
? ]=0
2)the equation of the tangent plane at (-8,-2,5) is [
? ]=0
Find the equation of the plane tangent to the following surface at the given points. x² + y² -z²-43 = 0; (2,8,5) and (-8, -2,5) 2 X
Answers
The equation of the tangent plane answer: 1) - 2√27x - 8√27y + √27z - 43 = 0 . 2) 8√51x + 2√51y + √51z - 255 = 0
The general equation of the tangent plane is given as z = f(a,b) + f1x + f2y; where (a,b) is the given point and f(a,b) = z1, f1 and f2 are the partial derivatives with respect to x and y, respectively.
Using the given equation; x² + y² -z²-43 = 0
z² = x² + y² - 43
z = ±√(x² + y² - 43)
Therefore; f(x,y) = ±√(x² + y² - 43) at (2,8,5);
f1 = ∂f/∂x = 2x/2√(x² + y² - 43)
f1(2,8) = (2/2√27) = 1/√27
f2 = ∂f/∂y = 2y/2√(x² + y² - 43)
f2(2,8) = (16/2√27) = 4/√27
z1 = f(2,8) = √(2² + 8² - 43) = √23
Equation of the tangent plane:
z - 5 = f1(2,8)(x - 2) + f2(2,8)(y - 8)
⇒ z - 5 = (1/√27)(x - 2) + (4/√27)(y - 8)
⇒ z - 5 = (x - 2 + 4y - 32)/√27
⇒ z - 5 = (x + 4y - 34)/√27
at (-8,-2,5); f1 = ∂f/∂x = 2x/2√(x² + y² - 43)
f1(-8,-2) = (-16/2√51) = -8/√51
f2 = ∂f/∂y = 2y/2√(x² + y² - 43)
f2(-8,-2) = (-4/2√51) = -2/√51
z1 = f(-8,-2) = √((-8)² + (-2)² - 43) = 3
Equation of the tangent plane:
z - 5 = f1(-8,-2)(x + 8) + f2(-8,-2)(y + 2)
⇒ z - 5 = (-8/√51)(x + 8) - (2/√51)(y + 2)
⇒ z - 5 = (-8x - 64 - 2y - 4)/√51
⇒ z - 5 = (-8x - 2y - 68)/√51
Answer: 1) - 2√27x - 8√27y + √27z - 43 = 0. 2) 8√51x + 2√51y + √51z - 255 = 0
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Related Questions
40) Suppose the demand for specialty car license plates is perfectly inelastic and the supply curve for specialty license plates is upward sloping. A tax is imposed on specialty license plates. Which of the following is true? A) Drivers pay the smallest share of the tax. B) Drivers pay none of the tax. C) Drivers pay all of the tax. D) The government pays all of the tax. E) The government collects nothing in tax revenues. 41) Suppose the elasticity of demand for a product is O and elasticity of supply is 1. If the government imposes a tax on the product, then A) buyers and sellers pay exactly the same share of the tax. B) buyers pay all of the tax. C) sellers pay all of the tax. D) buyers pay a smaller share of the tax than do sellers, but both buyers and sellers pay some of the tax. E) because the elasticity of demand is zero, the government collects no revenue from this tax. 42) Suppose the demand for peaches from South Carolina is perfectly elastic. If the supply curve is upward sloping and a tax is imposed on peaches from South Carolina, then A) peach sellers pay all of the tax. B) peach buyers pay all of the tax. C) peach buyers and sellers evenly split the tax. D) the government does not collect any revenue from the tax. E) the tax does not change the equilibrium quantity of peaches.
Answers
40) If the demand for specialty car license plates is perfectly inelastic and the supply curve is upward sloping, then the burden of the tax falls entirely on the consumers (drivers). Therefore, option C) Drivers pay all of the tax is true.
41) If the elasticity of demand for a product is 0 and the elasticity of supply is 1, then the burden of the tax falls entirely on the consumers (buyers). Therefore, option B) Buyers pay all of the tax is true.
42) If the demand for peaches from South Carolina is perfectly elastic and the supply curve is upward sloping, then the burden of the tax falls entirely on the producers (peach sellers). Therefore, option A) Peach sellers pay all of the tax is true.
40) In this scenario, since the demand for specialty car license plates is perfectly inelastic and the supply curve is upward sloping, the correct answer is C) Drivers pay all of the tax. This is because the burden of the tax falls entirely on the consumers with perfectly inelastic demand.
41) With an elasticity of demand of 0 and elasticity of supply of 1, the correct answer is B) buyers pay all of the tax. This is because the inelastic demand means that buyers will absorb the entire tax burden, whereas the elastic supply indicates that sellers can adjust their supply in response to the tax.
42) When the demand for peaches from South Carolina is perfectly elastic and the supply curve is upward sloping, the correct answer is A) peach sellers pay all of the tax. This is because buyers will simply switch to other sources if the price increases due to the tax, so the burden of the tax falls entirely on the peach sellers.
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Write the quotient and remainder when we divide (x^3 -4x^2 + 2x + 5) by (x - 2)
Answers
Answer:
Step-by-step explanation:
Sorry I can't explain how it is done. It is very difficult to explain on paper.
A real estate agent claims that the mean living area of all single-family homes in his county is at most 2400 square feet.A random sample of 50 such homes selected from this county produced the mean living area of 2540 square feet and a standard deviation of 472 square feet.(i) State the null and alternative hypothesis for the test.(ii) Find the value of the test statistic .(iii) Find the p-value for the test.(iv) Using a = .05, can you conclude that the real estate agent’s claim is true? What will your conclusion beif a = .01?
Answers
(i) The null hypothesis is that the mean living area of all single-family homes in the county is equal to or less than 2400 square feet. The alternative hypothesis is that the mean living area of all single-family homes in the county is greater than 2400 square feet.
(ii) The test statistic is calculated using the formula: (sample mean - hypothesized mean) / (standard deviation / square root of sample size). In this case, the test statistic is \(\frac{(2540 - 2400)}{\frac{472}{\sqrt{50} } } =2.44\)
(iii) The p-value is the probability of obtaining a sample mean as extreme or more extreme than the one observed, assuming the null hypothesis is true. Using a t-distribution with 49 degrees of freedom (since we are using a sample size of 50 and estimating the population standard deviation), we can find the p-value to be 0.009.
(iv) Using a significance level of 0.05, we can conclude that the real estate agent's claim is not true, since the p-value is less than 0.05. We reject the null hypothesis and accept the alternative hypothesis that the mean living area of all single-family homes in the county is greater than 2400 square feet. If we use a significance level of 0.01 instead, we still reject the null hypothesis since the p-value is less than 0.01.
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find the solution to mx cx kx=f(t) for an arbitrary function f(t), x(0)=0, x'(0)=0
Answers
Step-by-step explanation:
The given equation `mx cx kx=f(t)` is a second-order linear differential equation with constant coefficients. The general solution to this type of equation is given by the sum of the complementary solution `x_c(t)` and the particular solution `x_p(t)`.
The complementary solution x_c(t) is the solution to the associated homogeneous equation mx cx kx=0. The characteristic equation for this homogeneous equation is mr^2 + cr + k = 0. Solving this quadratic equation gives two roots r_1 and r_2. The complementary solution can then be written as x_c(t) = C_1e^(r_1t) + C_2e^(r_2t).
The particular solution x_p(t) depends on the form of the function f(t). There are several methods for finding the particular solution, such as undetermined coefficients or variation of parameters.
Once the complementary and particular solutions are found, the general solution to the given differential equation is given by x(t) = x_c(t) + x_p(t). The constants C_1 and C_2 can then be determined using the initial conditions x(0)=0 and x'(0)=0.
Without more information about the function f(t), it is not possible to find a more specific solution to the given differential equation.
In APQR, the measure of angle R=90°, RQ = 36, PR = 77, and QP = 85. What ratio
represents the tangent of angle P?
Answers
The ratio of the tangent of angle P of the given problem is: 36/77
How to use trigonometric ratios?We are given the parameters of the right angle triangle as:
R=90°
RQ = 36
PR = 77
QP = 85.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are calculated with respect to sides and angles
The three main trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Thus:
tan P = RQ/PR
tan P = 36/77
Thus, that is the value of tan P
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pls help I really need it too pass I am begging
Answers
Answer:
Lateral : 103.67 in²
Total : 864 in²
Step-by-step explanation: there you go
Jacob would like to purchase a coat and hat for a ski trip. The coat is $62.75, and the hat is $14.25. If the sales tax rate is 8%, then what will be the amount of tax on Jacob’s purchase?
*
1 point
A. $6.16
B. $6.88
C. $7.02
D. $7.44
Answers
Answer:
A. $6.16
Step-by-step explanation:
To calculate the amount of tax on Jacob's purchase, we first need to find the total cost of the coat and hat, and then apply the sales tax rate of 8% to that amount.
The cost of the coat is $62.75, and the cost of the hat is $14.25, so the total cost before tax is:
\(\implies \sf \$62.75 + \$14.25 = \$77.00\)
To calculate the amount of tax, we need to multiply the total cost by the tax rate of 8%:
\(\begin{aligned}\implies \sf \$77.00 \times\: 8\%&=\sf \$77.00 \times \dfrac{8}{100}\\&=\sf \$77.0 \times 0.08\\&=\sf \$6.16\end{aligned}\)
Therefore, the amount of tax on Jacob's purchase is $6.16.
Please help I don't understand I need an answer ASAP
Answers
Answer:
B = 48
Step-by-step explanation:
You are given that the two vertical lines are parallel. That means that the alternate interior angles are equal (they form a Z shape).
So the given is that A = B
A = 5x - 12
B = 2x + 24
Solution
5x - 12 = 2x + 24
5x - 12 = 2x + 24 + 12
5x = 2x + 36
5x - 2x = 36
3x = 36
x = 36/3
x = 12
================
B is
B = 2x + 24
B = 2*12 + 24
B = 24 + 24
B = 48
Answer:
B=48
Step-by-step explanation:
so angle A and B are on what I call the z-angles which are normally equal in that if you view the parallel lines horizontally you will see the form of a z and the corners of it are equal that said you equate both of them to get x
5x-12=2x+24
join like terms
5x-2x=12+24
3x=36
x=12
so to find angle B substitute x with 12
Based on the table and passage, which choice gives
the correct percentages of the purines in yeast DNA?
A) 17.1% and 18.7%
B) 17.1% and 32.9%
C) 18.7% and 31.3%
D) 31.3% and 32.9%
Answers
Correct option is C, 18.7% and 31.3%.
Because adenine and guanine are purines, and because the percentages of adenine and guanine in yeast DNA are mentioned in the table as 31.3% and 18.7%, respectively, and lines 6-7 say that "Two of the possible bases— adenine and guanine—are purines," choice C is the right answer.
The percentages of both purines, adenine and guanine, in yeast DNA are not stated in the other choices, which are A, B, and D.
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Write in slope-intercept form an equation of the line that passes through the given points.
(−2, 3), (2, 7)
Answers
Slope intercept form is y=mx+b.
m (the slope) is 4/4 which is equal to 1
b (the y intercept) is when x is zero meaning that it would be 5
Insert these into the equation:
y=1x + 5
1 x is equal to x so it can be simplified to
y= x + 5
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is y = x + 5
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line y = mx + c
Now,
The equation of the line passes through the points:
(-2, 3) and (2, 7).
This means,
(-2, 3) = (a, b)
(2, 7) = (c, d)
The slope is given as:
Slope:
= (d - b) / (c - a)
= (7 - 3) / (2 + 2)
= 4 / 4
= 1
Now,
The line passes through point (-2, 3) = (x, y) so,
3 = (-2) x 1 + c
3 = -2 + c
c = 3 + 2
c = 5
Now,
m = 1
c = 5
The equation of the line is y = x + 5
Thus,
The equation of the line is y = x + 5
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show that acos(wt)+bsin(wt) can be written in the form
Answers
This form of the equation is useful because it shows that any periodic function of time can be represented as a sum of sine and cosine functions with different amplitudes and phases.
We can show that acos(wt) + bsin(wt) can be written in the form Rsin(wt + φ) where R and φ are constants and R is the amplitude of the wave.
Using the trigonometric identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b), we can write:
acos(wt) + bsin(wt) = R(sin(wt+φ)),
where R = √(a^2+b^2) and φ = tan⁻¹(b/a).
To see how this works, we can use the values of a = 3 and b = 4 as an example:
acos(wt) + bsin(wt) = 3cos(wt) + 4sin(wt)
R = √(a^2+b^2) = √(3^2 + 4^2) = 5
φ = tan⁻¹(b/a) = tan⁻¹(4/3)
So we can rewrite the equation as:
acos(wt) + bsin(wt) = 5sin(wt + tan⁻¹(4/3))
This form of the equation is useful because it shows that any periodic function of time can be represented as a sum of sine and cosine functions with different amplitudes and phases. It is also helpful in analyzing the properties of waves, such as their amplitude and frequency.
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Write a formula for the total cost, (T), in pence, of 2 cups of lemonade and 5 chocolate bars.
Answers
5 chocolate bars: 5(c)
T= 2l + 5
Help! This is due today and I'm stuck on the last problem.
Brainiest for best answer.
NO LINKS! If you put a link, I will report you.
Find the area of the shaded region rounded to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
Square
519450.2
Holes
Semi-circle: 1/2*pi*r^2
diameter = 700/2 = 350 =radius
1/2*pi*350 = 175*pi
Triangle
1/2 b*h
1/2 200*400
100*400
40000
Take out the semi circle and triangle
560000-40000-175*pi
520000-175*pi = 519450.2
5 gallons of water are divided evenly into three buckets how much will be in each bucket? Sol in gallons
Answers
Answer:
1.6 gal
Step-by-step explanation:
\(\frac{5 gal}{3 buckets}\) = 1.66666667
1.6 gal (simplified)
Which graphs represents a function?
Answers
Answer:
1 i think 2 if not
Step-by-step explanation:
Find the value of \(x\)
![Find the value of [tex]x[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/1GkQFmy32mRzOEUew86hqErlAKmdtSJ1.jpeg)
Answers
The value of x in the parallel line is as follows:
1. x = 50
2. x = 55
3. 102 - 2v
How to find angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as alternate interior angles, alternate exterior angles, corresponding angles, vertically opposite angles, linear angles etc.
Therefore, let's use the angle relationship to find the value of x as follows:
1.
m∠1 = m∠8(alternate interior angles)
2x + 25 = x + 75
2x - x = 75 - 25
x = 50
2.
m∠2 = m∠6(corresponding angles)
3x - 10 = 2x + 45
3x - 2x = 45 + 10
x = 55
3.
m∠3 + m∠8 = 180(same side interior angles)
4v - 31 + 2x + 7 = 180
2x = 180 + 31 - 7 - 4v
2x = 204 - 4v
x = 102 - 2v
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Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. What is the median weight of the players?
Answers
Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.
The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.
The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.
In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.
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What is an equation of the line that passes through the points (4, -2) and (8, 3)?
Answers
First, find the slope of the two points.
y2-y1/x2-x1
3+2/8-4
slope=5/3
Then use the point slope formula to create an equation
y-y1=m(x-x1)
y-3=5/3(x-8)
y-3=5/3x-40/3
y= 5/3x - 31/3
The equation of the line that passes through the points (4, -2) and (8, 3) is
y = (5/4)x - 7.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Points:
(4, -2) and (8, 3)
The equation of a line is y = mx + c.
m = (3 + 2)/(8 - 4)
m = 5/4
Now,
(4, -2) = (x, y)
-2 = 5/4 x 4 + c
-2 = 5 + c
c = -2 - 5
c = -7
Thus,
The equation of a line is y = (5/4)x - 7.
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PLEASE OMG HELP FOR POINTSSSS
Answers
Answer:
I think B or D
Step-by-step explanation:
help me withb this qustion
Answers
Answer:
Abigail has 0.5 liters of milk left. This is less than the amount she used. So, the amount she used is greater.
Step-by-step explanation:
1.4
- .9
_____
0.5
John's son will start college in 10 years. John estimated a today's value of funds to finance college education of his son as $196,000. Assume that after-tax rate of return that John is able to earn from his investment is 8.65 percent compounded annually. He does not have this required amount now. Instead, he is going to invest equal amounts each year at the beginning of the year until his son starts college. Compute the annual beginning of-the-year payment that is necessary to fund the estimation of college costs. (Please use annual compounding, not simplifying average calculations).
Answers
John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.
To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.
The present value of an annuity formula is given by:
P = A * [(1 - (1 + r)^(-n)) / r],
where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.
In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:
196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].
Simplifying the expression inside the brackets:
196,000 = A * (1 - 0.469091).
196,000 = A * 0.530909.
Dividing both sides by 0.530909:
A = 196,000 / 0.530909.
A ≈ 369,238.68.
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Expression: a collection of ________, variables, operations, and parentheses
Answers
Expression: a collection of numbers, variables, operations, and parentheses.
What are expressions?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
Given a statement,
The blank of the statement will be filled by the word "numbers" because an expression is a combination of numbers, variables and at least one mathematical operation.
Hence, the answer is numbers.
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544ml^2 is how many liters
show your work
Answers
Answer:
295.936
Step-by-step explanation:
First find out what 544^2 is. That is 295,936. There are 100 ml in 1 liter. So divide 295,936 by 100 to see how many liters are in 295,936 ml.
295,936÷100=295.936
Please help with that question
Answers
Answer:
I know just this solution
A company is designing a new cylindrical water bottle. The volume of the bottle will be 176 cm ^3. The height of the water bottle is 7.8 cm. What is the radius of the water bottle? Use 3.14 for pi
Answers
Step-by-step explanation:
volume = 176 cm³
height = 7.8
radius = ?
pi = 3.14
volume of cylinder = πr²h
176 = 3.14 × r² × 7.8
176 = 24.492 × r²
176/24.4 = r²
7.21 = r²
√7.21 = r². ( Using long division )
r = 2.69 ( approx. )
consider the graph of the linear equatioin 2x-5y=10. the x intercept is, the y intercept is, the slope is
Answers
Answer:
x intercept = (5, 0)
y intercept = (0, -2)
slope = 2/5
Step-by-step explanation:
2x - 10 = 5y
\(\frac{2x-10}{5}\) = y
\(\frac{2}{5}\)x -2 = y
JK has endpoints (-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a
ratio of 2:1.
What are the two possible locations of L?
(-9, 0.5)
(-7, 0.25)
(0, -1)
(-6, 0)
(1, -1.5)
(-4,-0.5)
Answers
If JK has endpoints (-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1 then the possible locations of L is at (-7, 0.25)
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0
L divides JK into two parts with lengths in a ratio of 2:1
so JL:LK is either 2:1 or 1:2
Let us solve the midpoint of JK
Midpoint=(-10+2/2, 1-2/2)
M=(-4,-1/2)
Midpoint of JM is (-10-4/2, 1-1/2/2)
L: (-7, 1/4)
Hence, the possible locations of L is at (-7, 0.25)
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If I ounce is approximately equal to 28.35
grams, which one of the following conversions is
true?
A. 2 ounces is about 54.70 grams
B. 4 ounces is about 12.40 grams
C.6 ounces is about 170.10 grams
D. 8 ounces is about 224.80 grams
Answers
Conversion with option C is true. by conversion of measurements.
What is conversion of measurements?
A unit conversion expresses identical property as a unique unit of measuring. as an example, time is expressed in minutes rather than hours, whereas distance is regenerate from miles to kilometers, or feet, or the other live of length.
Main body:
According to question:
1 ounce = 28.35 grams
We need to check each option to find whether which is correct.
A) 2 ounce = 2 *1 ounce
2 ounce = 2*28.35
= 56.7 grams
but in option it is given 54.70 grams so it if false.
B) 4 ounce = 4 *1 ounce
4 ounce = 2*28.35
= 113.4 grams
so option b is also false
C) 6 ounce = 6*1 ounce
6 ounce = 6*28.35
= 170.1 grams
Hence the correct option is C.
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You are making a picture frame in shop class. Two pieces of wood are cut to form complementary angles so they fit together properly . One angle needs to be (7x +23) and the other angle needs to be (3x +27). What is the measure of the larger angle?
Answers
Answer:
The larger angle is;
\(51^{\circ}\)Explanation:
Given that the two woods are cut to form complementary angles.
Recall that complementary angles add up to 90 degrees.
Given the two angles as;
\((7x+23)^{\circ}+(3x+27)^{\circ}=90^{\circ}\)Solving the equation for x;
\(\begin{gathered} 7x+23+3x+27=90 \\ 7x+3x+23+27=90 \\ 10x+50=90 \\ 10x=90-50 \\ 10x=40 \\ \text{divide both sides by 10;} \\ \frac{10x}{10}=\frac{40}{10} \\ x=4 \end{gathered}\)Since we have the value of x, we can the substitute to find the values of each angle;
\(\begin{gathered} (7x+23)^{\circ} \\ (7(4)+23)^{\circ} \\ (28+23)^{\circ} \\ =51^{\circ} \\ \\ (3x+27)^{\circ} \\ (3(4)+27)^{\circ} \\ (12+27)^{\circ} \\ =39^{\circ} \end{gathered}\)Therefore, form the values of the two angles, the larger angle is;
\(51^{\circ}\)-3(w+1)+8(w-3)=-5w+9+6w
PLEASE HURRY AND ANSWER