What must be the contact area between a suction cup (completely evacuated) and a ceiling if the cup is to support the weight of an 80.0-kg student?

To solve this problem, all we have to do is to use the formula below, plug in the value of the parameter λ, then calculate for the median distance. The formula is:

Median = ln 2 / λ

Substituting:

Median = ln 2 / 0.01357

Median = 51.08 m

Answer:

Option B.

Step-by-step explanation:

We need [tex]2\frac{3}{4}[/tex] wheelbarrows of sand for 8 wheelbarrows of concrete.

That means ratio between sand and concrete is [tex]2\frac{3}{4}:8[/tex]

Or [tex]\frac{11}{4}:8[/tex]

Now we have to calculate the amount of sand to make 248 cubic feet of concrete.

If the amount of sand required is x cubic feet then the ratio of sand and concrete will be x : 248.

Since both the ratios should be same therefore,

[tex]\frac{x}{248}=\frac{\frac{11}{4} }{8}[/tex]

[tex]\frac{x}{248}=\frac{11}{32}[/tex]

x = [tex]\frac{11\times 248}{32}[/tex]

x = [tex]\frac{2728}{32}[/tex]

x = [tex]\frac{341}{4}[/tex]

  = [tex]85\frac{1}{4}[/tex] cubic feet

Option B will be the answer.

Answer:

[tex]150.72 feet^2[/tex] is the difference in the area covered.

Step-by-step explanation:

A lawn sprinkler sprays water 8 feet at full pressure, P.

A lawn sprinkler rotates 360 degree which means area covered by sprinkler is of circular shape. Since the sprinkler is in center and sprays the the water 8 feet away in all the direction while rotating.

Radius of the circle = 8 feet

Maximum pressure = P

As we know that higher the pressure higher will the force by which water will move out of the sprinkler. And with more force, sprinkler will able to spray water farther.

So we this we can say that pressure of the sprinkler is directly proportional to the radius of the circle in which water sprayed

[tex]pressure\propto Radius[/tex]

[tex]P\propto r[/tex]

[tex]\frac{P_1}{r_1}=\frac{P_2}{r_2}=constant[/tex]

[tex]P_1=P.P_2=P-50\%\times P=0.5 P[/tex]

[tex]r_1=8 feet.r_2=?[/tex]

[tex]r_2=\frac{0.5 P\times 8 feet}{P}=4 feet[/tex]

Area when , [tex]r_1= 8 feet[/tex] (Area of circle=[tex]\pi (radius)^2[/tex])

[tex]A=\pi r_1^{2}=\pi (8 feet)^2[/tex]

Area when ,[tex]r_2= 4 feet[/tex]

[tex]A'=\pi r_1^{2}=\pi (4 feet)^2[/tex]

Difference in Area = A- A'

[tex]\pi (8 feet)^2-\pi(4 feet)^2=\pi(48 feet^2)=150.72 feet^2[/tex]

[tex]150.72 feet^2[/tex] is the difference in the area covered.

Answer:

x= 2 vertex: (2,4)

Step-by-step explanation:

just did the assignment

Answer:

10 times greater

Step-by-step explanation:

700÷70=10

Step 1: The intersection curve is only at the origin.

Step 2: Set up the volume integral over the sphere region.

Step 3:Evaluate the integral to find the volume: [tex]\(V = 216\pi\sqrt{2}\).[/tex]

To find the volume of the solid enclosed by the cone [tex]\(z = x^2 + y^2\)[/tex] and the sphere[tex]\(x^2 + y^2 + z^2 = 72\),[/tex] we'll first find the intersection curve of the cone and the sphere in cylindrical coordinates, then set up the triple integral to find the volume.

Step 1: Finding the intersection curve:

The cone equation in cylindrical coordinates becomes [tex]\(z = r^2\)[/tex] and the sphere equation remains the same as [tex]\(r^2 + z^2 = 72\).[/tex]

To find the intersection, we set these two equations equal to each other:

[tex]\[r^2 = r^2 + z^2\][/tex]

Substitute [tex]\(z = r^2\)[/tex] from the cone equation:

[tex]\[r^2 = r^2 + (r^2)^2\][/tex]

[tex]\[r^2 = r^2 + r^4\][/tex]

[tex]\[r^4 = 0\][/tex]

From this, we see that the only solution is (r = 0), which corresponds to the point at the origin.

Step 2: Setting up the integral for volume:

We'll integrate over the region where the cone lies within the sphere, which is the entire sphere. In cylindrical coordinates, the limits of integration are [tex]\(0 \leq r \leq 6\)[/tex] (since the sphere has radius [tex]\(\sqrt{72} = 6\)) and \(0 \leq \theta \leq 2\pi\).[/tex]

The limits for \(z\) are from the cone to the sphere, so it's from [tex]\(r^2\) to \(\sqrt{72-r^2}\).[/tex]

Thus, the volume integral is:

[tex]\[V = \iiint_{E} r \, dz \, dr \, d\theta\][/tex]

Where (E) is the region enclosed by the cone and the sphere.

Step 3: Evaluate the integral:

[tex]\[V = \int_{0}^{2\pi} \int_{0}^{6} \int_{r^2}^{\sqrt{72-r^2}} r \, dz \, dr \, d\theta\][/tex]

Let's evaluate this integral step by step:

[tex]\[V = \int_{0}^{2\pi} \int_{0}^{6} (r\sqrt{72-r^2} - r^3) \, dr \, d\theta\][/tex]

[tex]\[V = \int_{0}^{2\pi} \left[-\frac{1}{4}(72-r^2)^{3/2} - \frac{1}{4}r^4\right]_{0}^{6} \, d\theta\][/tex]

[tex]\[V = \int_{0}^{2\pi} \left[-\frac{1}{4}(0)^{3/2} - \frac{1}{4}(6^4) - \left(-\frac{1}{4}(72)^{3/2} - \frac{1}{4}(0)^4\right)\right] \, d\theta\][/tex]

[tex]\[V = \int_{0}^{2\pi} \left[\frac{1}{4}(72)^{3/2}\right] \, d\theta\][/tex]

[tex]\[V = \frac{1}{4}(72)^{3/2} \int_{0}^{2\pi} 1 \, d\theta\][/tex]

[tex]\[V = \frac{1}{4}(72)^{3/2} \cdot 2\pi\][/tex]

[tex]\[V = 36\pi \sqrt{72}\][/tex]

[tex]\[V = 36\pi \times 6\sqrt{2}\][/tex]

[tex]\[V = 216\pi\sqrt{2}\][/tex]

So, the volume of the solid enclosed by the cone and the sphere is [tex]\(216\pi\sqrt{2}\).[/tex]

To solve this problem, let us first calculate for the Perimeter of the other octagon. The formula for Perimeter is:

Perimeter = n * l

Where n is the number of sides (8) and l is the length of one side. Let us say that first octagon is 1 and the second octagon is 2 so that:

Perimeter 2 = 8 * 16.35 in = 130.8 inch

We know that Area is directly proportional to the square of Perimeter for a regular polygon:

Area = k * Perimeter^2

Where k is the constant of proportionality. Therefore we can equate 1 and 2 since k is constant:

Area 1 / Perimeter 1^2 = Area 2 / Perimeter 2^2

Substituting the known values:

392.4 inches^2 / (87.2 inch)^2 = Area 2 / (130.8 inch)^2

Area 2 = 882.9 inches^2

Therefore the area of the larger octagon is about 882.9 square inches.

The total surface area of the cylinder is approximately 1187.72 cm², the volume is approximately 3077.2 cm³, and the cost to cover it with gift wrap at $3 per square centimeter is $3,558.76.

The surface area of a cylinder is calculated using the formula: Surface Area = 2πr(height) + 2πr². With a diameter of 14 cm, the radius (r) is half of that, which is 7 cm. Plugging in the values, the surface area is 2π(7 cm)(20 cm) + 2π(7 cm)².

For part b, once we have calculated the surface area, we can determine the cost to cover the cylinder using the given price per square centimeter. If S represents the total surface area, the cost will be $3 times S.

The volume of the cylinder can be found with the formula V = πr²h, and using the radius of 7 cm and a height of 20 cm, we get the volume V = π(7 cm)²(20 cm).

Performing these calculations:

Using 3.14 for π, we get:

Answer:

since he missed b ill answer it for your b is 24 because when you look at the grragh  it goes from 0 then to 24 so its unit rate would be 24

Step-by-step explanation:

The unit rate of fragrance A is; $ 26, and the unit rate of fragrance B is; $ 24. Hence Fragrance A has the greater unit rate.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

According to the condition the rate of the fragrance A will be;

78/3 = 156/6

= 234/9

= 26 $ per bottle

According to the graph the price of the fragrance B will be;

24/4 = 48/2

=24 $ per bottle

Therefore, the unit rate of fragrance A is; $ 26, and the unit rate of fragrance B is; $ 24.

Hence, Fragrance A has the greater unit rate.

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The solution is $ 153

The change in the net working capital is $ 153

What is Net Working Capital?

The difference between a company's current assets and current or short-term liabilities is known as net working capital, or working capital.

Cash flow will have an operational origin, when there is a net decrease in working capital

Working Capital = Current Assets - Current Liabilities

Given data ,

Let the change in net working capital be A

Now , the equation will be

Working Capital at the beginning = Current Assets - Current Liabilities

Substituting the values in the equation , we get

Working Capital at the beginning = 316 - 220

Working Capital at the beginning = $ 96

And ,

Working Capital at the end = Current Assets - Current Liabilities

Substituting the values in the equation , we get

Working Capital at the end = 469 - 260

Working Capital at the end = $ 209

So ,

The change in net working capital A = Working Capital at the end - Working Capital at the beginning

Substituting the values in the equation , we get

The change in net working capital A = 209 - 96

The change in net working capital A = $ 153

Therefore , the value of A is $ 153

Hence , change in the net working capital is $ 153

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Answer:

inceases by factor four

Step-by-step explanation:

The area of the larger square is 4 times larger than the area of the smaller square. The area of the big hexagon is 12 sq. in.

The area of the larger square is 4 times larger than the area of the smaller square. This is because the area of a square is proportional to the square of its side length.

In this case, the side length of the larger square is twice the side length of the smaller square, so the area of the larger square is 2² times greater than the area of the smaller square.

Given that the area of the small hexagon is 3 sq. in, the area of the big hexagon can be found by multiplying the area of the small hexagon by the square of the scale factor:

Area of big hexagon = (scale factor)² * Area of small hexagon = 2² * 3 sq. in = 12 sq. in

Final answer:

The sales tax rate is found by dividing the amount of sales tax by the cost of the item before tax and then multiplying by 100. In this case, the sales tax rate is 5%.

Explanation:

To find the sales tax rate of an item, you need the amount of sales tax paid and the cost of the item before tax. The formula to calculate the sales tax rate is:

sales tax rate = (amount of sales tax \/ cost of the item before tax) \ 100

Applying the formula, we have:

sales tax rate = ($22.50 \/ $450) \ 100

sales tax rate = 0.05 \ 100

sales tax rate = 5%

Therefore, the sales tax rate for the item is 5%.

The least common multiple of 2, 10 and 6 by using the definition of multiple is 30.

The lowest possible number that  can be divisible by all the given numbers is called as  least common multiple (LCM). It is the smallest multiple which is common in all the numbers.

The least common multiple of 2, 10 and 6 can be calculated as:

The multiples of 2 are: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34.........

The multiples of 10 are: 10,20,30,40,50,60,70.............

The multiples of 6 are: 6,12,18,24,39,36,42,48,54,60,66...........

The lowest common multiple among 2,10,6 is 30.

Thus, the least common multiple of 2, 10 and 6 is 30.

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Answer:

$735

Step-by-step explanation:

$180/week * 2 weeks = $360 for 2 weeks

$0.75/mile * 500 miles = $375

$360 + $375 = $735 for 2 week trip of 50 miles

According to budgeting guidelines often referred to as the 20/30/50 rule, no more than 20% of your net income should be spent on debt repayments. Therefore, the maximum amount spent on credit payments for a $1,500 monthly income should be $300.

The best practice for budgeting recommends that no more than 20% of your net monthly income should be spent on debt repayments, including credit payments. This is commonly referred to as the 20/30/50 rule. Therefore, given a monthly net income of $1,500, the maximum amount spent on credit payments should be 20% of $1,500, which equals to $300.

Here's how you would calculate it:

So, the correct answer is B. $300.

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we know that

The x-intercept is the value of x when the the value of y is equal to zero

and

The y-intercept is the value of y when the the value of x is equal to zero

In the graphed function we have that

the value of x when the the value of y is equal to zero is [tex]-1[/tex]

therefore

the x-intercept is equal to the point [tex](-1,0)[/tex]

the value of y when the the value of x is equal to zero is [tex]-3[/tex]

therefore

the y-intercept is equal to the point [tex](0,-3)[/tex]

the answer is

x-intercept = (–1, 0)

y-intercept = (0, –3)