Hadley's parents want to build a fence around her play area. The perimeter of the play area is 186 feet. The width is two times the length. Use the formula for the perimeter of a rectangle as one of your equations. What is the length and width of the play area?

Answer and Step-by-step explanation:

We want to prove that 0.5555... = 5/9.

First, let's set 0.555... equal to x:

x = 0.555...

Now multiply this by 10:

10x = 5.555...

Now subtract the original from this new one:

   10x = 5.555...

-       x = 0.555...

______________

     9x = 5

Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.

We now have 9x = 5, so divide both sides by 9:

x = 5/9, as desired

The divergence of the vector field F = ⟨z, y, x⟩ can be found by taking the partial derivatives of each component with respect to its corresponding variable and summing them up.

Let's denote the partial derivative with respect to x as ∂/∂x, y as ∂/∂y, and z as ∂/∂z. Then the divergence (div(F)) is given by:

\(\[\text{div}(F) = \frac{\partial}{\partial x}(x) + \frac{\partial}{\partial y}(y) + \frac{\partial}{\partial z}(z).\]\)

Taking the partial derivatives, we get:

\(\[\text{div}(F) = 1 + 1 + 1 = 3.\]\)

(b) The Divergence Theorem states that for a vector field F and a closed surface S bounding a region in space, the flux of F through S is equal to the triple integral of the divergence of F over the enclosed region. In this case, the surface S is the solid sphere defined by \(x^2 + y^2 + z^2\) ≤ 36.

To evaluate the flux of F through S, we need to compute the triple integral of the divergence of F over the region enclosed by S. Since the divergence of F is constant and equal to 3, the triple integral simplifies to:

\(\[\iiint\limits_V \text{div}(F) \, dV = \iiint\limits_V 3 \, dV,\]\)

where V represents the region enclosed by S.

To sketch the region of integration, visualize a solid sphere centered at the origin with a radius of 6 (since \(x^2 + y^2 + z^2\) ≤ 36). The region of integration encompasses the volume inside this sphere.

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According to the sample data, the best conclusion supported by the sample data is that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds. The answer is (D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

The conclusion that is best supported by the sample data is that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds, which is based on the fact that the sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds.

Therefore, options A and C are incorrect. The sample data does not provide enough information to determine the average weight of all fish in the pond, so option B is also incorrect.

The correct answer is D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds. This conclusion is supported by the sample data because the study specifically included a sample of 150 largemouth basses, of which 30% weighed more than 2 pounds. The other options are not supported by the sample data because the study does not include data on any other types of fish or the average weight of all fish in the pond.

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Answer:

Based on the alternating series test, we can conclude that the series Σ((-1)^n)/(2^(5+n)) converges.

Step-by-step explanation:

To determine if the series Σ((-1)^n)/(2^(5+n)) converges or diverges, we can use the alternating series test.

The alternating series test states that if a series has the form Σ((-1)^n)*b_n or Σ((-1)^(n+1))*b_n, where b_n is a positive sequence that decreases monotonically to 0, then the series converges.

In the given series, we have Σ((-1)^n)/(2^(5+n)). Let's analyze the terms:

b_n = 1/(2^(5+n))

The sequence b_n is positive for all n and decreases monotonically to 0 as n approaches infinity. This satisfies the conditions of the alternating series test.

Therefore, based on the alternating series test, we can conclude that the series Σ((-1)^n)/(2^(5+n)) converges.

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Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

Answer:

If the question is supposed to be solved using the pythagorean thorem, y≈64.35

Answer:

59

Step-by-step explanation:

Answer:

Growth

Step-by-step explanation:

This function is growth because the base (1.23) is greater than 1

If it were less than 1, it would be decay

Answer:no idea mate sorry

Step-by-step explanation:

Answer:

Acute

Step-by-step explanation:

Answer:

380.8cm³

Step-by-step explanation:

Volume of a Cylinder is: \(V=\pi r^2h\)

'r' is the radius.

'h' is the height.

We are given a height of 9.9 cm and a diameter of 7cm.

The radius is half the diameter.

Divide 7 by 2:

\(7/2=3.5\)

The radius is 3.5 cm.

Solve for The Volume (Using 3.14 for pi):

\(V=3.14*3.5^2*9.9\\\rightarrow3.5^2=12.25\\V=3.14 * 12.25 * 9.9\\V=38.465 * 9.9\\\boxed {V=380.8035}\)

380.8035 ≈ 380.8

The volume of the cylinder should be 380.8cm³.

Answer:

x = 6

Step-by-step explanation:

tan(53) = 8/x

=> x = 8/tan(53) = 8/(4/3) = 6

The graph of f(x) is concave down for x < -1/2.

To determine when the graph of a function is concave down, we need to examine the second derivative of the function. Let's calculate the second derivative of f(x) = 2xex:

First, find the first derivative of f(x):

f'(x) = (2xex)' = 2ex + 2xex = 2ex(1 + x)

Now, let's find the second derivative of f(x):

f''(x) = (2ex(1 + x))' = (2ex)'(1 + x) + 2ex(1 + x)'

= 2eˣ(1 + x) + 2ex

= 2eˣ + 2xeˣ + 2ex

= 4xeˣ + 2eˣ

To determine when the graph of f is concave down, we need to find where the second derivative, f''(x), is negative.

Setting f''(x) < 0 and solving for x:

4xeˣ + 2eˣ < 0

2eˣ(2x + 1) < 0

To satisfy this inequality, either 2eˣ < 0 or (2x + 1) < 0.

However, since eˣ is always positive, the inequality 2eˣ< 0 cannot be satisfied.

Therefore, to determine when the graph of f(x) = 2xex is concave down, we need to solve (2x + 1) < 0:

2x + 1 < 0

2x < -1

x < -1/2

Thus, the graph of f(x) is concave down for x < -1/2.

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The derivative of the function g(x) = \(5√x + e^(3x)ln(x) is g'(x) = (5/2)x^(-1/2) + (3e^(3x)ln(x) + e^(3x)*(1/x)).\)

To find the derivative of the function g(x) = 5√x + e^(3x)ln(x), we can differentiate each term separately using the rules of differentiation.

The derivative of the first term, 5√\(x^n\)x, can be found using the power rule and the chain rule. The power rule states that the derivative of \(x^n\) is \(n*x^(n-1),\)and the chain rule is applied when differentiating composite functions.

So, the derivative of \(5√x is (5/2)x^(-1/2).\)

For the second term, \(e^(3x)ln(x)\), we use the product rule and the chain rule. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by (u'v + uv'), where u' and v' are the derivatives of u and v, respectively.

The derivative of \(e^(3x) is 3e^(3x),\) and the derivative of ln(x) is 1/x. Applying the product rule, the derivative of \(e^(3x)ln(x) is (3e^(3x)ln(x) + e^(3x)*(1/x)).\)

Finally, adding the derivatives of each term, we get the derivative of the function g(x):

g'(x) = \((5/2)x^(-1/2) + (3e^(3x)ln(x) + e^(3x)*(1/x))\)

Therefore, the derivative of the function g(x) = \(5√x + e^(3x)ln(x) is g'(x) = (5/2)x^(-1/2) + (3e^(3x)ln(x) + e^(3x)*(1/x)).\)

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'Find the derivative of the function. 3x g(x) = 5√x + e³x In(x)

The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.

Equivalent ratios can be described as ratios that have the same values when compared to each other. For example, 8/16, 4/8 and 1/2 re equivalent ratios because:

8/16 = 1/2

4/8 = 1/2

Therefore, 8:16 = 4:8 = 1:2.

Given the table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, the ratio is: 3:4.

This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.

Therefore:

6/8 = 3/4

9/12 = 3/4

6/8 = 9/12 = 3/4

This implies that 6:8, 9:12 and 3:4 are all equivalent ratios.

Therefore, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.

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Answer: the first answer choice is the answer i think it is at least

Step-by-step explanation:

Answer:

c(x)

Step-by-step explanation:

c(x) increases by the same interval, 2.5, every time

a(x) is a negative exponential function

b(x) is a positive exponential function

Answer:19 dimes 1 necke

Answer:

11/10°C

Step-by-step explanation:

7 x 3/10 = 21/10

Temperature at Midnight = -1°C

Temperature at 7.00am = 21/10 + (-1°C)

= 11/10°C

Answer:

2

Step-by-step explanation:

Its has tei wholes......

Answer:it has two holes

Step-by-step explanation:

Answer:

It’s B

Step-by-step explanation:

Answer:

i think the answer is c because it has to do with the congruence of porportional relationships

Step-by-step explanation:

The values of d that make the inequality 9d > 9 true are given as follows:

2, 4, 11.

Hence the equivalent inequality is given as follows:

d > 1.

The inequality in the context of this problem is defined as follows:

9d > 9.

(an inequality is solved similarly to an equality, isolating the desired variable, the difference is that the solution is composed by infinity values on an interval instead of a finite number of exact values).

To solve the inequality, we solve it similarly to an equality, isolating the desired variable d, hence the solution is given as follows:

d > 9/9 -> division is the inverse operation of multiplication.

d > 1.

The > symbol means that the solution is composed by values that are greater than 1, hence the options are 2, 4, 6 and 11.

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Answer:

since there are 30 students as a whole and 20 boys make up part of the class, you can assume that there are 10 girls in the class. since the mean mark for boys is 62 I think the mean mark for girls would be 8%

Step-by-step explanation:

In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

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Answer:

7. B 8. C 9. C

Step-by-step explanation:

7. y is greater than because the area above the line is shaded and since the line is dashed there it's not greater than or equal to.

8. C provides the correct y values for all of the x values.

9. The point (6, 3) produces -3 ≥ -8 which is the only one that is correct out of all the points provided.

The  integral using spherical coordinates ∫∫∫D (x² + y² + z²) ⁵/² dV  is 4π/7.

Using spherical coordinates for ∫∫∫D (x² + y² + z²)^(5/2) dV inside the unit sphere centered at the origin is equal to (4π/7).

To evaluate the integral, we first convert it to spherical coordinates:
∫∫∫D (ρ²)^(5/2) ρ²sin(φ) dρ dφ dθ.

Next, we set the limits of integration: ρ goes from 0 to 1, φ goes from 0 to π, and θ goes from 0 to 2π.

Now we have:
∫₀¹ ∫₀^π ∫₀^2π ρ^(10) sin(φ) dρ dφ dθ.

Integrate each variable separately:
(∫₀¹ ρ^(10) dρ) (∫₀^π sin(φ) dφ) (∫₀^2π dθ).

After integration, we get:
[(ρ^(11)/11) |₀¹] [(-cos(φ)) |₀^π] [(θ) |₀^2π] = (1/11)(2)(2π).

Simplifying, we get (4π/7) as the answer.

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Three different whole numbers whose sum and product are equal are 1, 2, and 3.

1 + 2 + 3 = 6

1 x 2 x 3 = 6

As demonstrated above, the sum and product of 1, 2, and 3 is the same.

Hope this helps!! :)

Answer:

1 2 and 3

Step-by-step explanation:

given the sequence: -23, -18, -13,-8, ...

A) the common difference = -18 - (-23) = 5

B) Write an equation to represent the sequence.

The equation is = (-23) + 5 ( n - 1)

C) Find the 13th term

a13 = (-23) + 5 ( 13 - 1 ) = -23 + 5 * 12 = 37

The rate at which the y-coordinate of the jogger is changing is \({-\frac{3}{4}}\) times the rate at which the x-coordinate of the jogger is changing.

Given information:

Radius of the circular track = 75 ft

Coordinates of the jogger: (45, 60)

We know that the coordinates of a point in the Cartesian plane can be represented as (x, y), where x represents the horizontal displacement and y represents the vertical displacement.

Let us now consider a jogger who runs around a circular track of radius 75 ft, with the center of the track being the origin. Therefore, the horizontal and vertical displacements of the jogger will be its coordinates, respectively.

Let us now consider a right-angled triangle with the hypotenuse representing the radius of the circular track, and the vertical and horizontal sides representing the y and x coordinates of the jogger, respectively. Since the radius of the circular track is constant, we can use the Pythagorean theorem to relate x and y.

Since we know that the radius of the track is 75 ft, we can say that:

\(\[x^2 + y^2 = 75^2\]\)

Differentiating with respect to time t, we get:

\(\[\frac{d}{dt}(x^2 + y^2)\)

= \(\frac{d}{dt}(75^2)\]\\\2x \cdot \frac{dx}{dt} + 2y \cdot \frac{dy}{dt} = 0\]\)

Now, since we are given that the jogger's coordinates are (45, 60), we can substitute these values to obtain:

\(\[2(45) \cdot \frac{dx}{dt} + 2(60) \cdot \frac{dy}{dt} = 0\]\)

On solving, we obtain:

\(\[\frac{dy}{dt} = -\frac{3}{4}\cdot \frac{dx}{dt}\]\)

Hence, the rate at which the y-coordinate of the jogger is changing is \({-\frac{3}{4}}\) times the rate at which the x-coordinate of the jogger is changing.

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Answer:

1.64

Step-by-step explanation:

3.28 divided by 2 equals 1.64