Find the local maxima, local minima, and saddle points, if any, for the function z = 5x3 + 5x²y + 4y2. (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (*, *,*), (*, *, *)... Enter DNE if the points do not exist.)

The value of the integral is 15.87.

The given integral is:∫∫R 10(x+y) dAwhere R={(x,y)∣16≤x²+y²≤25,x≤0} in rectangular coordinates.In rectangular coordinates, the equation of circle is x²+y² = r², where r is the radius of the circle and the equation of the circle is given as: 16 ≤ x² + y² ≤ 25 ⇒ 4 ≤ r ≤ 5We need to evaluate the integral over the region R using rectangular coordinates and integrate first with respect to x and then with respect to y.∫∫R 10(x + y) dA = 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) (x+y) dx dy...[since x < 0]

Now, integrating ∫(x+y) dx we get ∫(x+y) dx = (x²/2 + xy)Therefore, 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) (x+y) dx dy = 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) [ (x²/2 + xy) ] dy dx= 10∫ from 4 to 5 [∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy] dxNow integrating with respect to y we get∫(x²/2 + xy) dy = (xy/2 + y²/2)

Putting the limits and integrating we get10∫ from 4 to 5 [∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy] dx = 10∫ from 4 to 5 [(∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy)] dx = 10∫ from 4 to 5 [(x²/2)[y]^(-√(16-x²) )_(^(-√(25-x²))] + [(xy/2)[y]^(-√(16-x²) )_(^(-√(25-x²)))] dx = 10∫ from 4 to 5 [-(x²/2)√(16-x²) + (x²/2)√(25-x²) - (x/2)(16-x²)^(3/2) + (x/2)(25-x²)^(3/2) ] dxNow integrating with respect to x, we get10∫ from 4 to 5 [-(x²/2)√(16-x²) + (x²/2)√(25-x²) - (x/2)(16-x²)^(3/2) + (x/2)(25-x²)^(3/2) ] dx = [ (10/3) [(25/3)^(3/2) - (16/3)^(3/2)] - 5√3 - (5/3)[(25/3)^(3/2) - (16/3)^(3/2) ] ]Ans: The value of the integral is 15.87.

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Answer:

No no don't click the link

Answer:

The biggest difference between exponential and linear functions is that linear functions change at a constant rate, while exponential functions change at a rate proportional to it's value, or exponent.

Basically, that's also what separates exponential functions from all others. It's the only function that changes at a rate proportional to its exponent.

Step-by-step explanation:

Answer:

216

Step-by-step explanation:

Answer:

72yd

Step-by-step explanation:

Hope that helps

hsobsnsjns

Answer:

1666.70

Step-by-step explanation:  10,000/6=1666.70

Answer: the answer is C 126°

The function g(x) = (3)ˣ has a unique fixed on [0,1]

From the question, we have the following parameters that can be used in our computation:

g(x) = (3)ˣ

The above function is an exponential function with the following features

Initial value = 1

Rate = 3

using the above as a guide, we have the following:

x = 0 in [0, 1]

So, we have

g(0) = (3)⁰

Evaluate

g(0) = 1

See that g(0) = 1 i.e. [0. 1]

Hence, the function has a unique fixed on [0,1]

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The molarity of the diluted solution is approximately 0.220 M.

The concentration of a solute in a solution is measured by its molarity. The amount of solute that dissolves in one liter (L) of solution is the number of moles. One of the most used units of concentration is t, represented by the symbol M. Number of moles of solute contained in 1 liter of solution is how it is defined.

To calculate the molarity of a solution, you need to use the formula:

M₁V₁ = M₂V₂

Substituting these values into the formula:

(1.0 M)(121 ml) = M₂(550.0 ml)

Rearranging the equation to solve for M₂:

M₂ = (1.0 M)(121 ml) / (550.0 ml)

M₂ = 121 / 550 ≈ 0.220 M

Therefore, the molarity of the diluted solution is approximately 0.220 M.

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Answer:

Simplifying

logx + -4 = 0

Reorder the terms:

-4 + glox = 0

Solving

-4 + glox = 0

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '4' to each side of the equation.

-4 + 4 + glox = 0 + 4

Combine like terms: -4 + 4 = 0

0 + glox = 0 + 4

glox = 0 + 4

Combine like terms: 0 + 4 = 4

glox = 4

Divide each side by 'lox'.

g = 4l-1o-1x-1

Simplifying

g = 4l-1o-1x-1

Answer:

[tex]x=40000[/tex]

Step-by-step explanation:

[tex]log(x)-log(4)=4\\log(\frac{x}{4})=4\\\frac{x}{4} = 10^4 \\x=4*10^4=40000[/tex]

Given the function: f(x,y) = 3x^7 + 4y^7 + 12To verify that f_xy = f_yx, we need to find the partial derivatives of the given function with respect to x and y. We can find them as follows: ∂f/∂x = 21x^6 ∂f/∂y = 28y^6

Now, to verify that f_xy = f_yx, we need to find f_xy and f_yx. We can find them as follows: f_xy = ∂^2f/∂y∂x = ∂/∂y(∂f/∂x) = ∂/∂y(21x^6) = 0 (since we have no y terms in the derivative of ∂f/∂x) f_yx = ∂^2f/∂x∂y = ∂/∂x(∂f/∂y) = ∂/∂x(28y^6) = 0 (since we have no x terms in the derivative of ∂f/∂y)Since f_xy = f_yx = 0, we can say that f_xy = f_yx.

Therefore, the value of fx is 21x^6 and the value of fy is 28y^6. Hence, the value of fxy is 0 and fyx is also 0.

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Answer:

180in3 (180 inch cubed)

Step-by-step explanation:

12 x 5 x 3

Answer: I would assume the answer would be 180

Step-by-step explanation: The formula for volume is Length x Width x Height. So multiply all the number above and the answer will be 180

Answer:

232cm

Step-by-step explanation:

A cheese usually has the shape of a cuboid.

Characteristics of a Cuboid

The amount of paper that would be needed to cover the block of cheese can be determined by calculating the perimeter of the block of cheese which is shaped as a cuboid

Perimeter of a cuboid = 4 x (length + breadth + height)

4 x (30 + 20 + 8) = 232cm

Answer:

x=-2

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

The value of 'm' for which (x + 4) is a factor of the polynomial [tex]5x^3 + 18x^2 + mx + 16[/tex] is -4.

To find the value of 'm' for which the expression (x + 4) is a factor of the polynomial[tex]5x^3 + 18x^2 + mx + 16[/tex], we can apply the factor theorem. According to the factor theorem, if (x + 4) is a factor of the polynomial, then the polynomial evaluated at (-4) should be equal to zero.

Substituting (-4) into the polynomial, we get:

[tex]5(-4)^3 + 18(-4)^2 + m(-4) + 16 = 0[/tex]

-320 + 288 + (-4m) + 16 = 0

-16 + (-4m) = 0

Simplifying the equation, we have:

-4m - 16 = 0

-4m = 16

m = 16 / -4

m = -4

Therefore, the value of 'm' for which (x + 4) is a factor of the polynomial [tex]5x^3 + 18x^2 + mx + 16[/tex] is -4.

By substituting -4 for 'm' in the given polynomial, we obtain:

[tex]5x^3 + 18x^2 - 4x + 16[/tex]

When this polynomial is divided by (x + 4), the remainder will be zero, confirming that (x + 4) is indeed a factor.

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Answer:

197.9

Step-by-step explanation:

The formula for circumference is 2(pi)r   and r is the radius

The diameter is two times the size of the radius, so by dividing the diameter by two, you can get the radius

So, r=63/2

r= 31.5

That means that 2(pi)(31.5) is the circumference

2(pi)(31.5) = 197.9 (rounded to the nearest tenth)

The coefficient of restitution between the ball and the ground is 0, indicating a completely inelastic collision.

The coefficient of restitution (e) is a measure of the elasticity or bounciness of a collision between two objects. It is defined as the ratio of the relative velocity of separation after the collision to the relative velocity of approach before the collision.

In this case, the ball is dropped vertically from a height of 1 m and returns to a height of 0.6 m. We can assume that the collision with the ground is approximately elastic, meaning that kinetic energy is conserved.

When the ball hits the ground, its initial velocity is zero, and the final velocity after the collision is also zero since it momentarily comes to rest before bouncing back up. Therefore, the relative velocity of separation is zero.

The relative velocity of the approach is the velocity just before the collision. Since the ball is dropped vertically, its velocity just before hitting the ground is given by the equation:

[tex]v = \sqrt(2gh)[/tex]

where v is the velocity, g is the acceleration due to gravity (approximately[tex]9.8 m/s^2[/tex]), and h is the initial height (1 m).

Plugging in the values:

[tex]v = \sqrt(2 * 9.8 * 1)[/tex]

[tex]= \sqrt(19.6)[/tex]

≈ 4.427 m/s

Therefore, the relative velocity of the approach is approximately 4.427 m/s.

Since the relative velocity of separation is zero, we can calculate the coefficient of restitution (e) as:

e = 0 / 4.427

= 0

Therefore, the coefficient of restitution between the ball and the ground, in this case, is 0, indicating a completely inelastic collision where the ball comes to a stop upon hitting the ground and does not bounce back.

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The total vertical distance traveled by the rubber ball, assuming it bounces indefinitely, is approximately 85.71 feet.

To find the total vertical distance traveled, we need to sum up the heights achieved by the ball during each bounce. The ball initially drops from a height of 26 feet, so we start with this value. On each bounce, the ball rebounds up 62% of its previous height. This means that after the first bounce, the ball reaches a height of 26 feet * 0.62 = 16.12 feet.

For subsequent bounces, we continue to multiply the previous height by 0.62 to find the new height. Therefore, after the second bounce, the height becomes 16.12 feet * 0.62 = 9.99 feet.

We can see that the heights achieved during each bounce form a geometric sequence with a common ratio of 0.62. The sum of an infinite geometric sequence can be calculated using the formula,

Sum = a / (1 - r), first term is a and 'r' is the common ratio is r.

In this case, 'a' is the initial height of 26 feet and 'r' is 0.62. Plugging these values into the formula, we get,

Sum = 26 / (1 - 0.62) = 26 / 0.38 ≈ 68.42 feet.

Therefore, adding all the distances,

Distance = 68.42 + 9.99 + 16.12

Distance = 85.71 feet, total vertical distance traveled by the rubber ball, rounded to two decimal places, is approximately 85.71 feet.

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Answer:

2.2

Step-by-step explanation:

Answer:

11/5

Step-by-step explanation:

The outcome of the race between Alpha and Beta, as described by their parametric equations, is that Beta moves faster but loses. Although Beta has a higher speed, Alpha consistently maintains a higher vertical position, leading to Alpha winning the race.

To determine the outcome of the race between Alpha and Beta, let's compare their positions using the given parametric equations:

Alpha's position:

[tex]x_{alpha} = 3t - 4sin(t)\\y_{alpha}= 3 - 3cos(t)[/tex]

Beta's position:

[tex]x_{beta} = 3t - 4sin(t)\\y_{beta} = 3 - 4sin(t)[/tex]

From the equations, we can see that the x-coordinate of both Alpha and Beta is the same, given by 3t - 4sin(t). Therefore, their horizontal positions are identical throughout the race.

To determine the vertical positions, we compare their y-coordinates. Alpha's y-coordinate is given by 3 - 3cos(t), while Beta's y-coordinate is given by 3 - 4sin(t).

Since cos(t) ranges from -1 to 1, and sin(t) ranges from -1 to 1, we can observe the following:

For Alpha, the y-coordinate (3 - 3cos(t)) ranges from 0 to 6, inclusive.

For Beta, the y-coordinate (3 - 4sin(t)) ranges from 2 to 4, inclusive.

Based on the range of their y-coordinates, we can conclude that Beta remains at a higher position throughout the race. Therefore, the correct answer is:

(D) Beta moves faster but loses.

Despite Beta moving faster, it loses the race because Alpha consistently maintains a higher vertical position.

Therefore, the outcome of the race between Alpha and Beta, as described by their parametric equations, is that Beta moves faster but loses. Although Beta has a higher speed, Alpha consistently maintains a higher vertical position, leading to Alpha winning the race.

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Answer: b im pretty sure hope this helps :)

Step-by-step explanation:

Answer:

A: x = -4

B: a = -7 (I'm assuming the '-' in front of 49 was supposed to be an '=')

Step-by-step explanation:

A: You need to group the like terms together, and isolate the variable, which in this case is x.

Take the 7 over to the other side, so the equation looks a little bit like this.

3-7 = x.

3-7 is -4, so we've gotten our answer.

x = -4.

B: -7a = 49.

When two negative numbers are multiplied together, the product becomes positive.

49 is 7x7.

-7 times -7 would be 49.

So, in this situation, a would be -7.

a = -7.

Answer:

a) The person who washed the most of the laundry is Mrs Smith

b) 4/15 of the laundry is left to wash

Step-by-step explanation:

Mrs. Smith washed 2/5 of her laundry. Her son washed 1/3 of it.

a) Who washed most of the laundry?

We convert the fraction of laundry each person washed to decimal

Mrs Smith = 2/5 = 0.4

Her son = 1/3 = 0.333

Therefore, the person who washed the most of the laundry is Mrs Smith

b) How much of the laundry still needs to be washed?

Let us total laundry = 1

=1 - ( 2/5 + 1/3)

Lowest Common Denominator is 15

=1- (3 × 2 + 5 × 1/15)

= 1 - (6 +5/15)

=1 - 11/15

= 4/15

Answer:

67 degrees for both of the other angles or 46 degrees and 88

Step-by-step explanation:

An isosceles triangle has two angle that are the same size so it could only be these.

Answer:

The expected value of x ; E(x) = 1

Step-by-step explanation:

F(x) = 1/8 for 0 ≤ x ≤ 4

To prove that it is a probability density function we will find E(x )

attached below is the required prove

It is proven that F(x) = 1/8 for 0 ≤ x ≤ 4 is  probability density function

The expected value of X = 1

9514 1404 393

Answer:

  (x -y -1)(x +y)

Step-by-step explanation:

The expression can be factored by grouping.

  x^2 -y^2 -x -y = (x^2 -y^2) -(x +y)

  = (x -y)(x +y) -1(x +y)

  = (x -y -1)(x +y)

_____

It is useful to know that a difference of squares is factored as ...

  a^2 -b^2 = (a -b)(a +b)

Answer:

x = 10.52 m

Step-by-step explanation:

Given that,

Length of a park = 90 m

Width of a park = 60 m

Area, A = 9000 m²

A uniform strip borders all four sides of the park for parking. We need to find the width of the strip. Let it is x. Now the area becomes,

(90+2x)(60+2x) = 9000

[tex]4x^2 +120x +180x =5400 = 9000\\\\x=10.52\ m[/tex]

So, the width of the strip is equal to 10.52 m.

Answer:

Since I do not know the context of the question I will list answers I think it could be based on what you asked:

1. 3.72 x 0.6 = 2.232

2. 3.72 ÷ 0.6 = 6.2

3. 3.72% of 0.6 = 0.02232

The answer is probably the first one. I can't give a definite solution without knowing the exact question being asked, sorry!

Answer:

Fibonacci

Step-by-step explanation:

the Fibonacci sequence