Given mn, find the value of x.
149⁰

The rate at which the diameter decreases when the diameter is 10 cm is -0.00798 cm/min.

To find the rate at which the diameter decreases, we can use the relationship between the surface area and the diameter of a sphere.

The surface area of a sphere is given by the formula:

A = \(4\pi r^2\), where A is the surface area and r is the radius (which is half the diameter).

Differentiating both sides of the equation with respect to time t, we get:

dA/dt = 8πr(dr/dt).

We are given that the surface area decreases at a rate of \(1 cm^2/min\), so dA/dt = \(-1 cm^2/min\). We want to find dr/dt when the diameter is 10 cm, which means the radius is r = 10/2 = 5 cm.

Substituting these values into the equation, we have:

-1 = 8π(5)(dr/dt).

Simplifying, we get:

-1 = 40π(dr/dt).

Now, solving for dr/dt:

dr/dt = -1 / (40π).

Using a calculator, this evaluates to approximately -0.00798 cm/min.

Therefore, when the diameter is 10 cm, the rate at which the diameter decreases is approximately -0.00798 cm/min. Note that the negative sign indicates the decrease in diameter.

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Answer:

6.82

Step-by-step explanation:

We are given two paraboloids as:z = (-9/2)(x^2 + y^2)andz = 5 - 2(x^2 + y^2)The volume of the solid enclosed between the two paraboloids is given byV = ∫∫R[(5 - 2(x^2 + y^2)) - (-9/2)(x^2 + y^2)] d\(z = (-9/2)(x^2 + y^2)andz = 5 - 2(x^2 + y^2)\)A

where R is the region in the xy-plane that is bounded by the circular region of radius a centered at the origin.We can rearrange the equation and simplify it as follows:V = ∫∫R (23/2)x^2 + (23/2)y^2 - 5 dAWe will use polar coordinates (r, θ) to evaluate the integral, and the limits of integration for the radius will be 0 and a, and the limits of integration for the angle will be 0 and 2π.

Hence, we can rewrite the integral as:V = ∫[0, 2π] ∫[0, a] (23/2)r^2 - 5r dr dθEvaluating this integral:V = ∫[0, 2π] [23/6 * a^3 - 5/2 * a^2] dθV = 4π [23/6 * a^3 - 5/2\(V = ∫[0, 2π] ∫[0, a] (23/2)r^2 - 5r dr dθ Evaluating this integral:V = ∫[0, 2π] [23/6 * a^3 - 5/2 * a^2] dθV = 4π [23/6 * a^3 - 5/2 * a^2]V = (46/3)πa^3 - 10πa^2\) * a^2]V = (46/3)πa^3 - 10πa^2Hence, the volume of the solid enclosed between the two paraboloids is (46/3)πa^3 - 10πa^2.The explanation has a total of 152 words.

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Answer:

Step-by-step explanation:

When each of the dimensions is multiplied by 1/3, the result is a rectangle that is ...

   (12 mm)·(1/3) by (15 mm)·(1/3) = 4 mm by 5 mm

The result is ...

  a smaller rectangle with length 4 millimeters and width 5 millimeters

__

The perimeter of the smaller rectangle has the same ratio to the original that the side lengths do.

The new perimeter will be 1/3 times the perimeter of the original rectangle.

The change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.

For a known length and width of a rectangle, the expression for calculating the perimeter of a rectangle is 2(L × w).

From the given information:

A rectangle's length = 12 mm, and width = 15 mm

Therefore, we can deduce that the change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.

This is because by using the scale factor:

\(\mathbf{\dfrac{1}{3}(12) \times \dfrac{1}{3}(15)}\)

We can get the value for the length and width of the new smaller rectangle as 4 mm and 5 mm respectively.

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(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

Step-by-step explanation:

4in

Answer:

Y=1.50

Step-by-step explanation:

For the graph chart the x as the table says and the y as 1.50 for one then keep adding 1.50 for the others

1) 4x1.50= 6.00

2)5.00/1.50= 3 and 1/3

The equations 12x = 9x^2 + 4, 2x^2 = 6x - 5, and -x^2 - 10x = 34 all have two complex solutions and no real solutions.

The equation 3x^2-5x=-8 has two complex solutions and no real solutions. Let's solve it step-by-step:
1. Start by rearranging the equation in standard quadratic form: 3x^2 - 5x + 8 = 0.
2. Now, we need to use the quadratic formula to find the solutions. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a),
where a, b, and c are the coefficients of the quadratic equation.
In our case, a = 3, b = -5, and c = 8.
3. Substitute the values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4*3*8))/(2*3).
Simplifying further:
x = (5 ± √(25 - 96))/(6).
x = (5 ± √(-71))/(6).
4. Since we have a negative value under the square root, we can conclude that the solutions are complex.
5. To express the solutions in complex form, we can write them as follows:
x = (5 ± i√71)/(6),
where i represents the imaginary unit (√(-1)).
Therefore, the equation 3x^2-5x=-8 has two complex solutions and no real solutions. The solutions are x = (5 + i√71)/(6) and x = (5 - i√71)/(6).
Now let's check the other equations:
1. 12x = 9x^2 + 4:
This equation is a quadratic equation in the form ax^2 + bx + c = 0. By rearranging it, we get 9x^2 - 12x + 4 = 0. Applying the quadratic formula, we find two complex solutions, which are x = (2 + i√2)/3 and x = (2 - i√2)/3.
2. 2x^2 = 6x - 5:
Again, rearranging the equation gives us 2x^2 - 6x + 5 = 0. Applying the quadratic formula, we find two complex solutions, which are x = (3 + i)/2 and x = (3 - i)/2.
3. -x^2 - 10x = 34:
By rearranging the equation, we get -x^2 - 10x - 34 = 0. Applying the quadratic formula, we find two complex solutions, which are x = (-5 + i√79)/(-1) and x = (-5 - i√79)/(-1).
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we assume the height of the triangle is x,

so the base length will be x+4

the triangle area will be area = 1/2 ( base * height)

48 = 1/2 (x + 4) x

96 = x2 + 4x

96 + 4 = x2 + 4x + 4

100 = (x + 2)2

10 = x + 2 (for the square 100, we ignore the -10, minus is meaningless in length )

x = 8

x + 4 = 8 + 4 = 12

so the height for the triangle is 8 unit, base is 12 unit,

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The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).

Let's simplify the given expression step by step using the given terms:
Expression:

\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)

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The dimensions of diameter of the circle is 6 inches which Jessa used to draw her circle.

The circumference of a circle is stated by the formula -

C = 2πr, where r refers to radius of the circle. Calculating radius now.

18.84 = 2πr

Rewriting the equation for radius of circle

r = 18.84/2×3.14

Performing division on Right Hand Side of the equation

r = 3 inches

As known, diameter is double the radius. Hence, diameter of the circle = 2×3

Performing multiplication on Right Hand Side of the equation

Diameter of the circle = 6 inches

Thus, the correct answer is A 6.

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The complete question is -

9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi.

A 6

B 15.7

C 3

D 9.42

The base case (n = 1) does not satisfy the divisibility condition. Therefore, we cannot prove that 8 | 52n + 7 for all n ≥ 1 using mathematical induction.

To prove that 8 divides (is divisible by) 52n + 7 for all n ≥ 1 using mathematical induction, we will follow the steps of the induction proof.

Step 1: Base case

We start by checking if the statement holds true for the base case, which is n = 1.

For n = 1:

52n + 7 = 52(1) + 7 = 59

We can observe that 59 is not divisible by 8. Therefore, the base case is not satisfied, and the statement does not hold for n = 1.

Step 2: Inductive hypothesis

Assume that the statement holds true for some arbitrary positive integer k, denoted as P(k):

8 | 52k + 7

Step 3: Inductive step

We need to prove that the statement also holds for k + 1.

For n = k + 1:

52n + 7 = 52(k + 1) + 7 = 52k + 52 + 7 = 52k + 59

Now, let's consider the expression 52k + 59. We know that 8 | 52k + 7 (according to our inductive hypothesis).

To prove that 8 | 52k + 59, we need to show that the difference between these two expressions is divisible by 8.

(52k + 59) - (52k + 7) = 52k + 59 - 52k - 7 = 52

Since 52 is divisible by 8 (52 = 8 * 6), we can conclude that 8 | 52k + 59.

Step 4: Conclusion

Since we have shown that if the statement holds for k, then it also holds for k + 1, we can conclude that the statement "8 | 52n + 7 for all n ≥ 1" is true by mathematical induction.

However, it's important to note that the initial statement is incorrect. The base case (n = 1) does not satisfy the divisibility condition. Therefore, we cannot prove that 8 | 52n + 7 for all n ≥ 1 using mathematical induction.

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The required value of partial derivative of the given function is,

fy(3,1/6) ≈ 1.607.

To find fy,

We have to take the partial derivative of f with respect to y while holding x constant.

Using the chain rule, we have,

⇒ f(x, y) = y sin⁻¹(xy)

⇒ ∂f/∂y = sin⁻¹(xy) + y d/dy[sin⁻¹(xy)]

             = sin⁻¹(xy) + y / √(1 - (xy)²)  x

So, to find fy(3,1/6),

Substitute x = 3 and y = 1/6,

⇒ fy(3,1/6) = sin⁻¹(3/6) + (1/6) / √(1 - (3/6)²) x 3

                 = sin⁻¹(1/2) + 1/2

                 ≈ 1.107 + 0.5

                 ≈ 1.607

Therefore,

fy(3,1/6) ≈ 1.607 is the required value.

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Answer:

8/5

Step-by-step explanation:

Answer

C. 49 fl oz

Step-by-step explanation:

I took the quiz.

Answer:

(x-2,y+1)

Step-by-step explanation:

from point (1, 3) to (-1, 4).

x=1 to x=-1

x-2=-1

1-2=-1

from y=3 to y=4

y+1=4

3+1=4

Answer:

717.25 that's the answer

5738 divided by 8 but you only want the R and the R is 2869

Answer:

the answer is 90

Step-by-step explanation:

hope it helps

have a nice day ^_^

Answer:

It is 90 degrees.

Step-by-step explanation:

It is one fourth of 360 degrees, which is 90 degrees.

Hope that helps!

Answer:

  A) 2x^2 -12x +13

  B) terms {2x^2, -12x, 13}; coefficients {2, -12, 13}; constants {13}

Step-by-step explanation:

A) Using the distributive property, we get ...

  -2x +3 +2x^2 -10x +10

  = 2x^2 -12x +13

__

B) Terms: {2x^2, -12x, 13}

  Factors: There are no overall factors. Each term has factors ...

     2x^2 has factors {2, x, x}

     -12x has factors {-1, 2, 2, 3, x}

     13 has factors {1, 13} (it is prime)

  Coefficients: {2, -12, 13} . . . see note below

  Constants: {13}

_____

Additional comment

We have listed the prime factors of each term, any subset can be multiplied to be a factor of the term. For example, 2·3 = 6 is a factor of -12x.

Please note that some sources do not consider a constant (13) to be a coefficient. You will need to refer to your curriculum materials to see what your author says about that.

Answer:

x = 88; y = -4

Step-by-step explanation:

2(x+2y) = 160 --> x + 2y = 80

--> 1x + 4y - x - 2y = 72 - 80

--> 2y = -8 --> y = -4

--> x = 88

Answer:

  about 0.19 m

Step-by-step explanation:

You want the side of a cube with the same volume as a cuboid of dimensions 0.24 m by 0.19 m by 0.15 m.

The volume of the rectangular prism is ...

  V = LWH = (0.24)(0.19)(0.15) m³

The volume of a cube is ...

  V = s³

So, the side length of a cube is ...

  s = ∛V

For a cube of the same volume as the rectangular prism, the side length is ...

  s = ∛((0.24×0.19×0.15) ≈ 0.19 . . . . meters

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a. The assumption that more is better is satisfied for both goods in the given utility function U(x, y) = 3x + y.

b. The marginal utility of x diminishes as the consumer buys more x.

c. The marginal rate of substitution (MRS) of x for y is 3.

d. The MRS of x and y is constant as the consumer substitutes x for y along an indifference curve.

e. On a graph, a typical indifference curve will exhibit a diminishing MRS. Additionally, a second indifference curve U2 > U1 can be drawn.

a. The assumption that more is better is satisfied for both goods because the utility function U(x, y) = 3x + y implies that increasing the quantities of both goods x and y will lead to higher utility.

b. The marginal utility of x diminishes as the consumer buys more x. This is because the marginal utility of x (MUx) is given as 3, which is a constant value. As the consumer consumes more units of x, the additional satisfaction derived from each additional unit of x decreases, leading to a diminishing marginal utility.

c. The marginal rate of substitution (MRS) of x for y is 3. MRSxy represents the rate at which the consumer is willing to trade off one good (x) for another (y) while keeping the utility constant. In this case, the MRSxy is constant and equal to the ratio of the marginal utilities, which is 3 (MUx / MUy = 3/1 = 3).

d. The MRS of x and y is constant as the consumer substitutes x for y along an indifference curve. The given utility function does not exhibit changing MRS as the consumer substitutes one good for another along an indifference curve. The MRS remains constant at 3, indicating a consistent trade-off rate between x and y.

e. On a graph, a typical indifference curve for the utility function U(x, y) = 3x + y will exhibit a diminishing MRS. This means that as the consumer moves along the indifference curve, the slope (MRS) will decrease, reflecting a decrease in the rate at which the consumer is willing to trade off x for y. Additionally, a second indifference curve U2 > U1 can be drawn, representing higher levels of utility. The specific shapes and positions of the indifference curves will depend on the values of x and y chosen for each curve.

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Answer:

21

Step-by-step explanation:

5 bushes ×6 pounds is =30 pounds

30pounds + 96pounds = 126pounds

126pounds ÷6 = 21bushes

Old Macdonald had 21 bushes before summer

Answer:

90

Step-by-step explanation:

In order to find the average of something, you add all the numbers and then divide it by how many numbers there were.

69+68+100+105=360

360 ÷ 4 = 90

John's average is 90.

Brainliest please?

Answer:

D. 1x9x4

Step-by-step explanation:

V= l x w x h

A y-intercept is the value at which x = 0.

(4,0) is not a y-intercept because x = 4.

(-1, 1) is not a y-intercept because x = -1.

(0,0) is a y-intercept because x = 0.

(0, -7) is a y-intercept because x = 0.

(-2, 2) is not a y-intercept because x = -2.

(0, -0.25 is a y-intercept because x = 0.

Answer:

here's the answer

Step-by-step explanation:

Answer:

Exact Form:

51/4

Decimal Form:

12.75

Mixed Number Form:

12 3/4

Step-by-step explanation: