z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).
Given the function is z=8-2x²-2y² and point is (5, 3, – 60).
We need to find the equation of the plane tangent to the given surface at the given point. The gradient vector of the function f(x, y, z) is given by(∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k∂f/∂x= -4x and ∂f/∂y= -4y
Therefore, the gradient vector is given by-4xi -4yj + k
Therefore, the equation of the tangent plane is given byz - z1=∇f(x1, y1) . (x - x1)i + ∇f(x1, y1) . (y - y1)j + (-1) [f(x1, y1, z1)]
where (x1, y1, z1) is the given pointWe have f(5, 3, – 60) = 8 – 2(5²) – 2(3²) = – 60
Therefore, the equation of the plane is given byz + 60= (-20i - 12j + k) . (x - 5) - (16i + 24j + k) . (y - 3)
Thus, z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).
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Find the perimeter of a square with a side length of 10 meters
side length of square=10
Now,
perimeter of square =4l
=4×10
=40m
Does anyone know about this question I give brainless If you answer this correctly
Answer:
Side x = 2.12132 = 3√2/2
Step-by-step explanation:
I used a triangle calculator to find side x
Let C be a relation defined on R as follows: For all x,y∈R,xCy iff x 2 +y2 =1. Determine if C is reflexive, symmetric, transitive, or none of these.
The relation C is defined on the set of real numbers (R) as xCy if [tex]x^2[/tex] + [tex]y^2[/tex] = 1 is not reflexive, not symmetric, and not transitive.
To determine if the relation C is reflexive, we need to check if every element x in R is related to itself. However, for any real number x, [tex]x^2[/tex] + [tex]x^2[/tex] = 2[tex]x^2[/tex] ≠ 1. Therefore, C is not reflexive.
For symmetry, we need to check if whenever xCy, then yCx. However, if we take x = 0 and y = 1, we have [tex]x^2[/tex] + [tex]y^2[/tex] = [tex]0^2[/tex]+ [tex]1^2[/tex] = 1, which satisfies the condition for C. But for yCx, we have [tex]y^2[/tex] + [tex]x^2[/tex] = [tex]1^2[/tex] + [tex]0^2[/tex] = 1, which also satisfies the condition. Therefore, C is symmetric.
To test for transitivity, we need to check if whenever xCy and yCz, then xCz. However, if we consider x = 0, y = 1, and z = -1, we have [tex]x^2[/tex] +[tex]y^2[/tex] = [tex]0^2[/tex]+ [tex]1^2[/tex] = 1 and [tex]y^2[/tex] + [tex]z^2[/tex] =[tex]1^2[/tex] + [tex](-1)^2[/tex] = 2. Since 1 + 2 ≠ 1, the condition for transitivity is not satisfied. Thus, C is not transitive.
In conclusion, the relation C is not reflexive, symmetric, or transitive.
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payment stream consists of three payments: $2,500 due today, $3,000 due 100 days from today, and $3,500 due 240 days from today. What single payment, 80 days from today, is economically equivalent to the payment stream if money can be invested at a rate of 5%? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places.)
To find out the single payment that is economically equivalent to the payment stream of $2,500 due today, $3,000 due 100 days from today, and $3,500 due 240 days from today, we have to follow the below-given steps:
Step 1: Calculate the Future Value (FV) of each payment. Let's assume that "P" is the single payment we need to find out and "i" is the annual interest rate (5%)P = FV × [1 / (1 + i/365)^n] where n is the number of days between today and the payment date. For the first payment of $2,500 that is due today, the future value is $2,500 because it is already available today. Hence, no calculation is required for it. For the second payment of $3,000 that is due 100 days from today, Future Value (FV) = $3,000 × [1+(0.05/365)]^100 ≈ $3,093.29For the third payment of $3,500 that is due 240 days from today, Future Value (FV) = $3,500 × [1+(0.05/365)]^240 ≈ $3,701.85
Step 2: Calculate the Present Value (PV) of the payment stream by discounting each FV to 80 days from today. The formula for the present value of a future amount is PV = FV × [1 / (1 + i/365)^n] where "n" is the number of days between the date of the future amount and the date on which it is to be discounted. Here, we need to discount all three payments to 80 days from today. The number of days between today and 80 days from today is 80. So, we put n = 80 in the above formula.
For the first payment of $2,500 that is already available today, there is no need for any discounting. Hence, its present value is the same as its future value, i.e., $2,500.For the second payment of $3,093.29 that is due 100 days from today, Present Value (PV) = $3,093.29 × [1 / (1 + 0.05/365)^80] ≈ $2,893.16For the third payment of $3,701.85 that is due 240 days from today, Present Value (PV) = $3,701.85 × [1 / (1 + 0.05/365)^80] ≈ $3,243.11
Step 3: Add up the present values of all three payments to find the present value of the payment stream Present Value of the payment stream = $2,500 + $2,893.16 + $3,243.11 = $8,636.27
Step 4: Calculate the single payment that is economically equivalent to the payment stream by calculating its future value at the end of 80 days. FV = PV × (1 + i/365)^n where n = 80, i = 0.05, and PV = $8,636.27FV = $8,636.27 × (1 + 0.05/365)^80 ≈ $9,040.07Therefore, the single payment that is economically equivalent to the payment stream is $9,040.07.
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Paola wants to measure the following dependent variable: happiness. How could you measure happiness in a way:
a) physiological?
b) observation?
c) self-report? Search for a scale that already exists.
What is the scale called? :
APA citation:_____
1. She would use Facial electromyography
2. She would use smiling
3. She would use Subjective Happiness Scale
How do you measure happiness?It is common practice to evaluate subjective experiences, including happiness, using self-report measures. The Subjective Happiness Scale (SHS) is a popular tool for gauging happiness.
The SHS is a self-report survey that asks participants to rate how much they agree with statements about their personal experiences of happiness. It consists of four things and is frequently utilized in studies.
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Help pleas ? Brainliest as prize
Answer:
9
Step-by-step explanation:
There are 9 x's above 1 letter mailed.
Solve for z.
x + y + z = 4
4x - y - z = 1
x + z = 2
Answer:
z= 4-x-y
z= -1+4x-y
z= 2-x
Step-by-step explanation:
z = 2-x
y = -1-z +4x
substitute
x -1 -2+x +4x + 2 -x = 4
-1 + 5x = 4
5x = 5
x = 1
z = 1
1+y+1 = 4
y = 2
If the volume of the cylinder is 502.4 in?, what is the radius of
the base of the cylinder? Use 3.14 for i and enter your answer
as a whole number.
h=10 in
r= in.
Answer:
radius of the base of cylinder = 4 in
Step-by-step explanation:
Volume of cylinder = pi x r² × h
502.4 = 3.14 x r² x 10
502.4 = 31.4 x r²
r² = 502.4/31.4
r² = 16
r = 4 in
A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure below. Of the following, which is closest to the volume of the grain silo, in cubic feet?
A) 261.8
B) 785.4
C) 916.3
D) 1047.2
Answer:
A. 261.8
Step-by-step explanation:
espero ayudar sorry
Which table represents a linear equation
the price of a jacket was reduced from $50 to $30. by what percentage was the price of the jacket reduced?
Answer:
the jacket price was reduced by 40%.
Step-by-step explanation:
if $50 is 100% then every one dollar is 2%.
Percentage of the reduction of price of the jacket is 40%.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100.
Percentage is usually denoted by the symbol '%'.
We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Given that,
Original price of the jacket = $50
Let x be the percentage of reduction of the price of the jacket.
50 - (x × 50) = 30
50x = 50 - 30
50x = 20
x = 20 / 50
x = 0.4
Percentage = 0.4 × 100 = 40%
Hence the percentage reduction is 40%.
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Find z1/z2 in polar form. The angle is in degrees. z1= 15 cis (83) and z2 = 6 cis (114).
To find the division of z1 by z2 in polar form, where the angles are given in degrees, we have z1 = 15 cis (83°) and z2 = 6 cis (114°). The polar form of the division of z1 by z2 is 2.5 cis (329°).
To divide complex numbers in polar form, we can divide their magnitudes and subtract their angles. Let's start by dividing the magnitudes:
|z1/z2| = |z1|/|z2| = 15/6 = 2.5
Next, we subtract the angles:
θ = θ1 - θ2 = 83° - 114° = -31°
Since the angle is negative, we add 360° to it to get a positive angle in the standard range:
θ = -31° + 360° = 329°
Therefore, the division of z1 by z2 in polar form is given by:
z1/z2 = 2.5 cis (329°)
So, the polar form of the division of z1 by z2 is 2.5 cis (329°).
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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
[infinity] (n − 1)!
5n
n = 0
lim n → [infinity]
an + 1
an
=
Using the Ratio Test the series ∑(n³ / [tex]4^n[/tex]) converges. Option A is the correct answer.
To determine the convergence or divergence of the series ∑(n³ / [tex]4^n[/tex]), we can apply the Ratio Test.
The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms in a series is less than 1, then the series converges. If the limit is greater than 1 or it does not exist, the series diverges.
Let's apply the Ratio Test to the given series:
lim n → ∞ |([tex]a_n[/tex] + 1) / [tex]a_n[/tex]| = lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) / (n³ / [tex]4^n[/tex])|
We simplify the expression by multiplying by the reciprocal:
lim n → ∞ |((n + 1)³ / [tex]4^{(n + 1)[/tex]) × ([tex]4^n[/tex] / n³)|
Next, we simplify the expression inside the absolute value:
lim n → ∞ |((n + 1)³ × [tex]4^n[/tex]) / ([tex]4^{(n + 1)[/tex] × n³)|
Now, we can cancel out the common factors:
lim n → ∞ |(n + 1)³ / (4 × n³)|
Simplifying further:
lim n → ∞ |(n + 1) / (4n)|³
Taking the limit as n approaches infinity:
lim n → ∞ |(1 + 1/n) / 4|³
Since the limit of the absolute value of the ratio is less than 1 (as n approaches infinity), the series converges.
Therefore, the answer is:
A. Converges
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The question is -
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
∑ n = 1 to ∞ (n³ / 4^n)
lim n → ∞ |(a_n + 1) / a_n| = _______
A. Converges
B. Diverges
which angle pair represents corresponding angles?
options on picture
Answer: b
Step-by-step : not needed
The discrete-time system is described by yik-11 + 2y[k] = Fiki, with fiki = [k] and y(0) = 0. Solve the above equation iteratively to determine yll] and y[2] values.
Value of y[1] = 0.5 and y[2] = 0.5.
The given discrete-time system is:
y[k-1] + 2y[k] = [k]with y(0) = 0.
Substituting k = 0 in the above equation:
y[-1] + 2y[0] = [0] y[-1] = 0
Substituting k = 1 in the given equation:
y[0] + 2y[1] = [1]
Substituting the value of y[0] from the above equation in this equation, we get:
2y[1] = [1] - y[0]
Substituting the value of y[0] = 0 in the above equation:
2y[1] = [1]y[1] = [1]/2 = 0.5
Substituting k = 2 in the given equation:
y[1] + 2y[2] = [2]
Substituting the value of y[1] from the above equation in this equation, we get:
2y[2] = [2] - y[1]
Substituting the value of y[1] = 0.5 in the above equation:
2y[2] = [2] - 0.5y[2] = [2]/2 - 0.5 = 0.5
Therefore, y[1] = 0.5 and y[2] = 0.5.
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hlp help help plsssssssssssss
Answer:
A
Step-by-step explanation:
Think about the square root of 64, which is 8. It will only be slightly higher than 8, which will not even be .5, so 8 is the closest number.
Solve for x.
x = ln e
x =
Answer:
x = 1
Step-by-step explanation:
Mhanifa can you please help? This is due soon. Look at the picture attached. I will mark brainliest!
Answer:
84° 125°Step-by-step explanation:
Sum of the interior angles of a regular polygon:
S(n) = 180°(n - 2), where n- number of sidesExercise 4Pentagon has sum of angles:
S(5) = 180°(5 - 2) = 540°Sum the given angles and find x:
x° + 122° + 100° + 90° + 144° = 540°x° + 456° = 540°x° = 540° - 456°x° = 84°Exercise 5Hexagon has sum of angles:
S(6) = 180°(6 - 2) = 720°Sum the given angles and find x:
x° + 110° + 160° + 105° + 105° + 115° = 720°x° + 595° = 720°x° = 720° - 595°x° = 125°How is the dispersion of a Normal distribution compare to the dispersion of a T - distribution, Normal Distribution is more dispersed than the T distribution Normal Distribution is less dispersed than the T distribution Normal Distribution is dispersed in the same way as the T distribution
The dispersion of a Normal distribution is less dispersed than the T-distribution.
The dispersion of a distribution is measured by the standard deviation (or variance) of the distribution.
For a Normal distribution, the standard deviation is always known.
On the other hand, for a t-distribution, the standard deviation of the population is not known and is estimated using the sample standard deviation.
This means that the t-distribution has more uncertainty, which leads to more dispersion compared to the Normal distribution.
The t-distribution is often used when the sample size is small or when the population standard deviation is unknown. As the sample size increases, the t-distribution approaches the Normal distribution.
Therefore, for large sample sizes, both distributions become more or less similar.
In conclusion, the Normal distribution is less dispersed than the t-distribution.
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PLSS HELPPP NO BOTS OR I WILL REPORT BUT PLS HELP ASAPP!! The graphs below of a function true or false?
which of the following equations are linear? a. y = 6x 8 b. y 7 = 3x c. y – x = 8x 2 d. 4y = 8
A linear equation is an equation in which the highest power of an unknown quantity is 1. Among the given options, the equation y = 6x + 8 is linear.
Hence, the correct option is a. y = 6x + 8.
An equation is linear if and only if it can be written in the form y = mx + c, where m and c are real numbers. In the given options, the equation y = 6x + 8 can be written in the form y = mx + c where m = 6 and c = 8, so it is linear. On the other hand, the equation y – x = 8x2 can be rearranged to give y = 8x2 + x, so the highest power of x is 2. Hence, this equation is not linear.Similarly, the equation 4y = 8 can be rearranged to give y = 2, which is a constant, and so it is also not linear.Finally, the equation y7 = 3x is not linear because the exponent 7 on y is greater than 1 and makes the equation non-linear. Therefore, the correct answer is option a. y = 6x + 8.
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Determine the integral of 8 (3x − 2)³ dx
The integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C, where C is the constant of integration.
To find the integral of 8(3x - 2)³ dx, we can apply the power rule of integration. According to the power rule, the integral of xⁿ dx is (xⁿ⁺¹ / (n + 1)) + C, where n is a constant and C is the constant of integration.
In this case, we have (3x - 2)³ as the integrand. We can rewrite it as 8(3x - 2)³ to simplify the expression. Since 8 is a constant multiplier, it can be factored out of the integral.
Using the power rule, we integrate each term separately. The integral of (3x - 2)³ is [(3x - 2)⁴ / 4] + C, where C is the constant of integration. Multiplying by the constant 8, we get 8[(3x - 2)⁴ / 4] + C.
Simplifying further, we can simplify the expression to 2(3x - 2)⁴ + C, where C is the constant of integration.
Therefore, the integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C.
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EASY POINTS!!
PLS ADD A DISC!!
All interior angle degrees must add up to 180 degrees.
the little square means that it is a right angle (90 degrees)
30 + 90 = 120
Y = 60
(a) Calculate sinh (log(6) - log(5)) exactly, i.e. without using a calculator Answer: (b) Calculate sin(arccos(76)) exactly, i.e. without using a calculator.
(a) The exact value of sinh(log(6) - log(5)) is 11/60.
To calculate sinh(log(6) - log(5)), we can use the identity: sinh(x) = ([tex]a^n[/tex] - [tex]e^-x[/tex])/2
So, substituting x = log(6) - log(5), we get:
sinh(log(6) - log(5)) = ([tex]e^(log(6)[/tex] - log(5)) - [tex]e^-(log(6)[/tex] - log(5)))/2
= (([tex]e^log(6)[/tex])/([tex]e^log(5)[/tex]) - ([tex]e^-log(6)[/tex])/([tex]e^-log(5)[/tex]))/2
= ((6/5) - (5/6))/2
= (36/30 - 25/30)/2
= 11/60
Therefore, sinh(log(6) - log(5)) = 11/60.
(b) The exact value of sin(arccos(76)) is undefined.
To calculate sin(arccos(76)) exactly, we can use the Pythagorean identity [tex]sin^2[/tex](x) + [tex]cos^2[/tex](x) = 1.
Let's assume arccos(76) = x. Applying the cosine function to both sides, we have cos(arccos(76)) = cos(x).
Since arccos and cosine are inverse functions, cos(arccos(76)) simplifies to 76.
Now, using the Pythagorean identity, we can calculate sin(x):
sin(x) = sqrt(1 - [tex]cos^2[/tex](x)) = sqrt(1 - 76^2) = sqrt(1 - 5776) = sqrt(-5775).
The square root of -5775 is an imaginary number, which cannot be expressed exactly without using complex numbers or numerical methods.
Therefore, the exact value of sin(arccos(76)) cannot be determined without using a calculator or numerical methods.
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Find a85 of the sequence 4,9,14,19,….
Answer: 424
Step-by-step explanation:
Solve for x: 3x + 2 = 2x + 8.
Answer:
x = 6
hope this is the answer you are looking for
Step-by-step explanation:
Answer:
X=6
Step-by-step explanation:
Firstly subtract 2x from both sides = x+2=8
Then subtract 2 from both sides and you'll get x=6.
What additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply. B ≅ P and BC ≅ PQ A ≅ T and AC = TQ = 3. 2cm A ≅ T and B ≅ P A ≅ T and BC ≅ PQ AC = TQ = 3. 2 cm and CB = QP = 2. 2 cm
Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:
Option 1: B ≅ P and BC ≅ PQ
To prove that two triangles are congruent using AAS (Angle-Angle-Side) or ASA (Angle-Side-Angle) postulates, we need specific conditions met. Let's examine the given options:
1. B ≅ P and BC ≅ PQ:
This condition satisfies the AAS postulate since we have two angles and a corresponding side that are congruent.
2. A ≅ T and AC = TQ = 3.2 cm:
This condition satisfies the ASA postulate since we have two angles and the included side that are congruent.
3. A ≅ T and B ≅ P:
This condition alone does not satisfy either the AAS or ASA postulate, as we need to have at least one side congruent or an included side congruent to prove congruence.
4. AC = TQ = 3.2 cm and CB = QP = 2.2 cm:
This condition alone does not satisfy either the AAS or ASA postulate, as we need to have congruent angles as well.
Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:
- Option 1: B ≅ P and BC ≅ PQ
This satisfies the AAS postulate, and with the given information, we can conclude that the triangles are congruent.
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which expression is equivlent to 12(2x-3y+4)
Answer:
24x-36y+48
hope this helps :)
24x - 36y + 48 is equivalent to 12(2x-3y+4)
Yezenia is filling up her outdoor swimming pool to get ready for summer time. She leaves the garden hose running for 1000 minutes in order to fill the pool, which has a volume of 15,460 gallons. What is the approximate rate at which water leaves the garden hose?
Answer:
15.46 gallons per minutes
Step-by-step explanation:
Garden hose was running for 1000 minutes
Volume of the pool = 15,460 gallons
What is the approximate rate at which water leaves the garden hose?
Rate at which water leaves the garden hose = Volume of the pool / running time of the hose
= 15,460 gallons / 1000 minutes
= 15.46 gallons per minutes
Rate at which water leaves the garden hose = 15.46 gallons per minutes
Someone please help me.
Felipe's age is ≥ 5
Step-by-step explanation:
Difference of F's age and 4: f - 4
Twice: 2 (f -4) ≥ 2
2f - 8 ≥ 2
2f ≥ 10
f ≥ 5
Answer:
Step-by-step explanation: