F(x,y)=eâ8xâx2+8yây2. find and classify all critical points of the function. if there are more blanks than critical points, leave the remaining entries blank.

Final answer:

The volume of the ellipsoid x²+y²+9z²=64 is 1024π/3 cubic units.

Explanation:

To find the volume of the ellipsoid given by the equation x²+y²+9z²=64, we can use the formula for the volume of an ellipsoid, which is V = (4/3)πa×b×c, where a, b, and c are the semi-axes of the ellipsoid. In our case, the ellipsoid can be rewritten to show its semi-axes clearly by dividing the equation by 64, which gives us (x²/64) + (y²/64) + (z²/(64/9)) = 1, indicating that our semi-axes are a = b = 8 and c = 8/3. Plugging these values into our volume formula gives us V = (4/3)π×8×8×(8/3), which simplifies to V = 1024π/3 cubic units.

The most effective way to show that 10C2 = 10C8 is to solve for the values of each combination. To solve for the values, we have to make use of the combination formula:

nCr = n! / r! (n – r)!

where n is the total sample size and r is the selected sample size

Calculating the value of 10C2:

10C2 = 10! / [2! (10 – 2)!]

10C2 = 10! / (2! * 8!)

10C2 = 45

Calculating the value of 10C8:

10C8 = 10! / [8! (10 – 8)!]

10C8 = 10! / (8! * 2!)

10C8 = 45

Therefore,

10C2 = 10C8

Answer:

Yes bc I want you to have some money

Step-by-step explanation:

Answer: The correct option is A., i.e, Slope of Function B = 2 x Slope of Function A.

Explanation:

The given function is,

[tex]f(x)=x-9[/tex]

It can be written as,

[tex]y=x-9[/tex]

It is the slope intercept form like y=mx+c, where m is the slope. On comparing the f(x) with the slope intercept form, we get the slope of f(x) is 1.

The graph of function g(x) passing through the point (-1,-3) and (2,3).

If a line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of line is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{3-(-3)}{2-(-1)}=\frac{3+3}{2+1}= \frac{6}{3} =2[/tex]

The slope of g(x) is 2.

Since slope of f(x) is 1 and the slope of g(x) is 2, so we can say that the slope of function B is twice of slope of function A.

Slope of Function B = 2 x Slope of Function A

Therefore, the first option is correct.

The answer is A... yeet                                      

the answer would be the third choice which is N(0, z)

Answer with explanation:

Vertices of Rhombus, KM LN, are : K (w,0), M (w,v) , L (u,z) and N (?).

N (?)= (x,y)

Diagonals of Rhombus Bisect each other.Diagonal, KL and MN will Bisect each other.

Mid Point Formula of Line Joining , (m,n ) and (r,s) is :

            [tex]=(\frac{m+r}{2},\frac{n+s}{2})[/tex]

Mid Point of KL is

         [tex]=(\frac{w+u}{2},\frac{0+z}{2})[/tex]

Mid Point of MN is

         [tex]=(\frac{w+x}{2},\frac{v+y}{2})[/tex]

So, Mid point of KL = Mid Point of MN

[tex](\frac{w+u}{2},\frac{0+z}{2})=(\frac{w+x}{2},\frac{v+y}{2})\\\\ \frac{w+u}{2}=\frac{w+x}{2}\\\\x=u\\\\\frac{0+z}{2}=\frac{v+y}{2}\\\\y=z-v[/tex]

So, coordinates of Point N,can be = (u, z-v).

None, of the Option,matches with the given option.

If you will Write the rhombus as,K L MN,then also you will not get answer which matches with the options.

The total distance Mary would have to travel considering she needs to return home for her shoes is 25km.

This math problem involves the calculation of distances within a commute. Here's how we can provide a solution:

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Answer:

The correct option is 2.

Step-by-step explanation:

Steps for construction of a circle inscribed in a circle:

1. Draw a circle using compass.

2. Draw a diameter of that circle, using the scale.

3. Place the compass on a end point of diameter and draw a full circle, without changing the span on compass.

4. Mark the points of intersection of the two circle.

5. Using scale connect both points of intersection.

6. Using the scale connect each in intersection point with the second end point of diameter.

The diagram below shows the partial construction of a circle inscribed in a circle. Therefore the correct option is 2.

Answer:

$165

Step-by-step explanation:

In 1 years, you will have $165.00 of simple interest.

Calculations: The Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods.  Where r is in decimal form; r=R/100; r and t are in the same units of time.

The accrued amount of an investment is the original principal P plus the accumulated simple interest, I = Prt, therefore we have:

A = P + I = P + (Prt), and finally A = P(1 + rt)

Calculate Total Amount Accrued (Principal + Interest), solve for A

A = P(1 + rt)

Calculate Principal Amount, solve for P

P = A / (1 + rt)

Calculate rate of interest in decimal, solve for r

r = (1/t)(A/P - 1)

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = (1/r)(A/P - 1)

Final answer:

The simple interest earned on a $3000 deposit at a 5.5% annual interest rate for one year is $165. This is found using the simple interest formula: Interest = Principal x Rate x Time.

Explanation:

To calculate the amount of simple interest earned on a $3000 deposit at an interest rate of 5.5% per annum for one year, we use the simple interest formula: Interest = Principal  x Rate  x Time.

In this case:

Principal (P) is $3000,

Rate (R) is 5.5% per annum, or 0.055 when expressed as a decimal,

Time (T) is 1 year.

So, the interest earned can be calculated as follows:

Interest = $3000  x 0.055 x 1

Interest = $165

Therefore, the amount of simple interest earned on the $3000 deposit after one year is $165.

Answer:

Quotient of 22x²y²÷11x²y² is:

2

Step-by-step explanation:

If a number p is divided by b then,

if p could be written as p=qb+r then q is the quotient and r is the remainder

Here, p=22x²y²

and b=11x²y²

22x²y²= 2(11x²y²)+0

⇒ q=2 and r=0

⇒ quotient=2

Hence, quotient of 22x²y²÷11x²y² is:

2

Answer:

B-60

Step-by-step explanation:

The  area of the trapezoid is 60 square units

The formula for finding the area of a trapezoid is expressed as:

A = 0.5(a+b)h

Given the following parameters

a = AD = √4² + 6²

AD = √16+36
AD = √52

For the length of BC
a = AD = √6² +10²

AD = √36+100
AD = √136
Calculate the height of the trapezium (10, 6) and (8, 12)

H = √6² +2²

H =  √40

Substitute

A = 1/2(7.21+11.66)*6.33

A = 60 square units

Hence the  area of the trapezoid is 60 square units

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Final answer:

The equation of the circle with diameter endpoints (-1,-4) and (3,2) is (x - 1)^2 + (y + 1)^2 = 13, found by calculating the center at (1, -1) and the radius as sqrt(52)/2.

Explanation:

To find an equation of the circle whose diameter has endpoints at (-1,-4) and (3,2), we need to determine the center and radius of the circle. The center of a circle is the midpoint of the diameter, and the radius is half the length of the diameter.

First, we calculate the midpoint (which will be the center of the circle) using the formula: (x1 + x2)/2, (y1 + y2)/2. For the given points (-1,-4) and (3,2), the midpoint is ((-1 + 3)/2, (-4 + 2)/2), which simplifies to (1, -1). So, the center of the circle is (1, -1).

To find the radius, we use the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2). The distance between the two points is sqrt((3 - (-1))^2 + (2 - (-4))^2), which simplifies to sqrt(4^2 + 6^2) = sqrt(16 + 36) = sqrt(52). The radius is half of the diameter, so r = sqrt(52)/2.

The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Substituting the values we found, we get (x - 1)^2 + (y + 1)^2 = (sqrt(52)/2)^2, which simplifies to (x - 1)^2 + (y + 1)^2 = 13. This is the equation of the circle.

Apex Answer: Overdraft fee

Answer: KP=15

Step-by-step explanation:

HM/KP = 7/5.

HM = KP+6, so:

(KP+6)/KP =7/5.

cross multiply

5(KP+6) = 7KP

5KP + 30 = 7KP

30 = 2KP and KP = 15

Hope this helps, have a BLESSED and wonderful day! :-)

-Cutiepatutie <3 :-)

Max and Jen ate a total of 1 3/20 pies together.

To find out how many pies Max and Jen ate all together, we need to add the fractions of the pies that each of them ate.

Max ate 2/5 of a pie and Jen ate 6/8 of a pie. To add these fractions, we need to find a common denominator. The common denominator of 5 and 8 is 40.

Multiplying the numerator and denominator of 2/5 by 8, we get 16/40. Multiplying the numerator and denominator of 6/8 by 5, we get 30/40.

Now we can add the fractions: 16/40 + 30/40 = 46/40.

Since 46/40 is an improper fraction, we can simplify it to a mixed number by dividing the numerator by the denominator. 46 divided by 40 is 1 with a remainder of 6, so the mixed number is 1 6/40.

However, we can simplify the fractional part of the mixed number further. Both 6 and 40 are divisible by 2, so we can divide both the numerator and denominator by 2: 6 divided by 2 is 3, and 40 divided by 2 is 20. Therefore, the simplified mixed number is 1 3/20.

Therefore, Max and Jen ate a total of 1 3/20 pies together.

Final answer:

Max ate 2/5 of a pie and Jen ate 6/8 of a pie. The total is 1 and 6/40 pies.

Explanation:

To find out how many pies Max and Jen ate all together, we need to add the fractions of pies they each ate. Max ate 2/5 of a pie and Jen ate 6/8 of a pie. To add these fractions, we need to have a common denominator.

To find the common denominator, we can multiply the denominators together. In this case, the common denominator would be 5 * 8 = 40.

Now, we can convert both fractions to have a denominator of 40.

Max's fraction becomes 16/40 and Jen's fraction becomes 30/40.

Finally, we add the two fractions together:

16/40 + 30/40 = 46/40.

So, Max and Jen ate a total of 46/40 or 1 and 6/40 pies all together.

The outfielder throws the ball approximately 168 ft to the pitcher.

The outfielder throws the ball to the pitcher at an angle of 32° to the right of the pitcher's mound. To find the distance the outfielder throws the ball, we need to break down the component of the throw in the direction perpendicular to the path of the ball. This can be done by finding the horizontal component of the throw.

To find the horizontal component, we can use the equation:

horizontal component of throw = distance * cos(angle)

Substituting the given values, we have:

horizontal component of throw = 195 ft * cos(32°)

Calculating this, we find that the horizontal component of the throw is approximately 168 ft.

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Answer:

C

2, 2, 25, 25, 26, 26, 27, 28, 28, 30

Minimum: 2

Maximum: 30

Median: 26

Lower quartile: 25

Upper quartile: 28

Step-by-step explanation:

To find the probability of Jessica winning more games than Susan in a card game, we need to calculate the probabilities for each outcome.

To determine the probability that Jessica will have won more games than Susan, we need to calculate the probability of each possible outcome.

Given that Susan wins 60% of the time, the probability of Susan winning a game is 0.6 and the probability of Jessica winning a game is 0.4.

To calculate the probability of Jessica winning more games, we can use combinations. In this case, we need to find the sum of the probabilities of Jessica winning 0, 1, 2, 3, 4, 5, 6, 7, and 8 games out of 9.

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