Calculate the value of X. C is the center of the circle.

The walls of the archway are approximately 8.9 apart.

To find the distance between the walls of the archway, we need to find the horizontal distance where the function f(x) intersects the x-axis. This is because the archway's walls are vertical, and their distance apart is the same as the horizontal distance between the points where the archway meets them.

To find the x-intercepts of the function f(x) = -0.5x^2 + 10, we need to set f(x) = 0 and solve for x:

0 = -0.5x^2 + 10

0.5x^2 = 10

x^2 = 20

x = ±√20

Since the archway is a physical object, we can discard the negative value for x, which means the archway meets the walls at x = √20 feet.

To find the distance between the walls of the archway, we can double this value:

2√20 ≈ 8.94

Then it's concluded that the walls of the archway are approximately 8.9 feet apart.

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The derivative of the function f(x) = (x³ - 5x)(2x-1) after simplification is 6x⁴ - 10x³ - 10x².

We apply the product rule and simplify to determine the derivative of,

f(x) = (x³ - 5x)(2x-1).

The product rule is used to determine the derivative of the given function f(x),

h(x) = a.b, then after applying product rule,

h'(x) = (a)(d/dx)(b) + (b)(d/dx)(a).

Applying this for function f,

f'(x) = 6x⁴ - 25x² - 10x³ + 15x²

f'(x) = 6x⁴ - 10x³ - 10x².

Therefore, f'(x) = 6x⁴ - 10x³ - 10x² is the derivative of f(x) after simplifying the function.

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The volume of the sphere that lies between the two cones is approximately 43.53 cubic units.

To find the volume of the sphere that lies between the given cones, we first need to determine the limits of integration.

Since the sphere has a radius of 6 (since x² + y² + z² = 36), we can use spherical coordinates to express the volume as an integral. Let's first consider the cone z = √3x² + 3y².

In spherical coordinates, this is equivalent to z = ρcos(φ)√3, where ρ is the radial distance and φ is the angle between the positive z-axis and the line connecting the origin to the point.

Similarly, the cone z = √(x²+y²)/3 can be expressed in spherical coordinates as z = ρcos(φ)/√3.

Since we're only interested in the volume of the sphere between these cones, we can integrate over the limits of ρ and φ that satisfy both inequalities.

The limits of ρ will be 0 (the origin) to 6 (the radius of the sphere).

To find the limits of φ, we need to solve for the intersection points of the two cones.

Setting the two equations equal to each other, we get:

ρcos(φ)√3 = ρcos(φ)/√3

Solving for φ, we get:

tan(φ) = 1/√3 Using the inverse tangent function, we find that: φ = π/6, 7π/6

So the limits of integration for φ will be π/6 to 7π/6.

Finally, we need to integrate over the full range of θ (the angle between the positive x-axis and the line connecting the origin to the point).

This will be 0 to 2π.

Putting it all together, the volume of the sphere between the two cones is:

∫∫∫ ρ^2sin(φ) dρ dφ dθ

With limits of integration:

0 ≤ ρ ≤ 6 π/6 ≤ φ ≤ 7π/6 0 ≤ θ ≤ 2π

Evaluating this integral gives:

V = 288π/5 - 216√3π/5

So the volume of the sphere that lies between the two cones is approximately 43.53 cubic units.

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The value of FE comes out to be 35.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The measure of an angle is typically given in degrees or radians, and it describes the amount of rotation needed to move one of the rays or line segments to coincide with the other. Angles are used in many areas of mathematics, physics, engineering, and other sciences to describe and analyze various phenomena.

Parallel lines have the same slope and will never meet, no matter how far they are extended. Parallel lines are important in geometry and other areas of mathematics, as well as in engineering, architecture, and other fields where precise measurements and constructions are required.

[tex]4x-1/x+5 = 60/24\\5x+25= 8x-2\\27= 3x\\x=9[/tex]

Therefore FE= 4×(9)-1

=35

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The frequency table shows that 152 female students chose website design out of a total of 362 female students, which is about 0.421 or 42%.

The frequency table shows that out of the total 362 female students attending the technology summer camp, 152 chose website design, which is a design class. This means that the percentage of female students who chose a design class is 152/362 = 0.4202 or about 42%.

However, the camp counselor says that about 68% of female students chose a design class. It is unclear where the counselor obtained this information from as it is not reflected in the frequency table. It is possible that the counselor gathered this information from a different survey or observation.

On the other hand, the camp director's statement is more accurate as it is based on the frequency table.

The frequency table shows that 152 female students chose website design out of a total of 362 female students, which is about 0.421 or 42%. It is important to rely on data and accurate information when making statements or drawing conclusions.

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The height of the tree is approximately 20.1 feet.

To determine the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the length of the shadow) of a right triangle.

tan(35°) = height of tree / 35 feet shadow

Rearranging this formula, we get:

height of tree = 35 feet shadow x tan(35°)

Plugging in the given values and using a calculator, we get:

height of tree = 35 x tan(35°) ≈ 20.1 feet

Therefore, the height of the tree is approximately 20.1 feet.

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In the proportion,  the cost of 0.7kg apple is Rs.62.65 .

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here cost of 1kg apples = 89.50

Then cost of 0.7 kg apple = x.

Now using proportion,

=> 1   = 89.50

   0.7=  x

=> x = [tex]\frac{89.50\times0.7}{1}[/tex]

=> x = 62.65.

Hence the cost of 0.7kg apple is Rs.62.65 .

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The total length of the race is approximately 28.24 miles.

To determine the total length of the race, we can use the given information: Piotr has completed 24 miles, which represents 85% of the race. We can set up a proportion to find the total length. Let 'x' represent the full length of the race:

(24 miles) / x = 85% / 100%

To solve for 'x', we can first convert the percentage to a decimal by dividing 85 by 100, resulting in 0.85:

24 / x = 0.85

Next, we can cross-multiply:

0.85 * x = 24

Now, we can solve for 'x' by dividing both sides by 0.85:

x = 24 / 0.85

x ≈ 28.24 miles

Therefore, the total length of the race is approximately 28.24 miles. Piotr has completed 85% of this distance, which means he has run 24 miles and has around 4.24 miles remaining to finish the race.

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Answer:

1email is given by its boss and another email is given by its assistent

Applying the triangle inequality theorem, the possible length of side AC is: C. 18 inches.

The triangle inequality theorem states that lengths of the two sides of a triangle, when added together must be greater than the third side of any given triangle.

Therefore, to determine the possible length of side AC, we can use the triangle inequality theorem, stated above and applying this to triangle ABC, we have the following:

AC < AB + BC

AC < 12 + 20

AC < 32

This implies that, length of side AC must be less than 32 inches. Thus, the answer is: C. 18 inches.

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The center of mass of the metal plate with density rho(x,y) = αx+ βy g/cm2 must lie on the line x + y = 7/6.

To find the center of mass of the metal plate, we need to calculate the coordinates of its centroid (X, Y). The coordinates of the centroid are given by:

X = (1/M) ∬(R) x ρ(x,y) dA, Y = (1/M) ∬(R) y ρ(x,y) dA

where M is the total mass of the plate, R is the region of integration (0 ≤ x ≤ 1, 0 ≤ y ≤ 1), and dA is the differential area element.

We can calculate the total mass M of the plate as follows:

M = ∬(R) ρ(x,y) dA = α/2 + β/2 = (α + β)/2

Using the given density function, we can calculate the integrals for X and Y:

X = (1/M) ∬(R) x ρ(x,y) dA = (2/αβ) ∬(R) x(αx+βy) dA = (2/3)(α+β)

Y = (1/M) ∬(R) y ρ(x,y) dA = (2/αβ) ∬(R) y(αx+βy) dA = (2/3)(α+β)

Thus, the coordinates of the centroid are (X, Y) = ((2/3)(α+β), (2/3)(α+β)).

Now, if we substitute X + Y = (4/3)(α+β) into the equation x + y = 7/6, we get:

x + y = 7/6

2x + 2y = 7/3

2(x+y) = 4/3(α+β)

x+y = (2/3)(α+β)

which shows that the centroid lies on the line x + y = 7/6. Therefore, the center of mass must also lie on this line.

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If 1/6 of the boys joined the basketball team, there are 160 boys in the soccer team.

If 1/6 of the boys joined the basketball team, then 5/6 of the boys did not join the basketball team. Similarly, if 2/9 of the boys joined the soccer team, then 7/9 of the boys did not join the soccer team.

Let's first find out how many boys did not join the soccer team:

7/9 x 540 = 380

Therefore, 380 boys did not join the soccer team.

To find out how many boys did join the soccer team, we can subtract the boys who did not join from the total number of boys:

540 - 380 = 160

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Using area formula for rectangles, we can find the new area of the rectangle to be 7350m².

The new dimensions are:

Length = 105m

Breadth = 70m

A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Each rectangle's two defining characteristics are its length and breadth. A rectangle's longer and shorter sides are its width and length, respectively.

Here in the question,

Dimensions of the rectangle are as follows:

Length, l = 42m.

Width, w = 28m.

Scale factor here is 1: 5/2

Now,

Let the new width be x.

The new width will be:

28/x = 1/ (5/2)

Cross multiplying:

⇒ 28 × 5/2 = x

⇒ x = 70m.

So, new width = 70m.

Now, let new length be x.

So,

42/x = 1/ (5/2)

Cross multiplying:

⇒ x = 42 × 5/2

⇒ x = 105m.

So, the new length = 105m.

Now new area will be:

70 × 105

= 7350m².

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The temperature of 80°F is equivalent to 48°C.

To convert 80°F to Celsius degrees using the formula C = (F - 32), we substitute the given Fahrenheit temperature into the formula.

C = (80 - 32) = 48

Therefore, the temperature of 80°F is equivalent to 48°C.

The Celsius scale is commonly used in scientific and international contexts, while the Fahrenheit scale is more prevalent in the United States. The conversion formula allows us to convert temperatures between these two scales.

Rounding to the nearest tenth of a degree, we find that 48°C remains unchanged.

It's worth noting that the Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C at standard atmospheric pressure. In contrast, on the Fahrenheit scale, water freezes at 32°F and boils at 212°F.

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The maps scale is 1 inch = 6 miles. This means that for every inch on the map, it represents 6 miles in real-life distance.

To determine the scale, we need to know the relationship between the distance on the map and the actual distance. In this case, the distance on the route map between Hugo's house and his work is 3 inches, and the actual distance he travels by bus is 18 miles.

To find the scale, we can set up a proportion using the given information:

(distance on the map in inches) / (actual distance in miles) = (1 inch) / (x miles)

Now, we can plug in the known values:

(3 inches) / (18 miles) = (1 inch) / (x miles)

To solve for x, we can cross-multiply:

3 inches * x miles = 18 miles * 1 inch

3x = 18

Now, divide both sides by 3:

x = 6

So, the scale of the map is 1 inch = 6 miles.

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False. Cultural traits that are diffused from one group are not always changed or adopted over time by the people in the receiving culture.

This is because different cultures have their own unique values, beliefs, and practices that may not align with the diffused cultural trait. Additionally, some cultural traits may be seen as a threat to the receiving culture and therefore not adopted.
Moreover, not all diffused elements of culture are successfully integrated into other cultures. Some may be rejected outright, while others may only be partially integrated or adapted to fit the receiving culture. It's important to note that cultural diffusion is a complex and ongoing process that involves a multitude of factors, including social, economic, and political influences, as well as individual attitudes and beliefs.

Therefore, the success of cultural diffusion and integration can vary greatly from one context to another.

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Answer:

Another vehicle has a mass of 1290 kg and uses diesel fuel. 1 L of petrol has a mass of 737 g. 1L of diesel has a mass of 820g.

Answer:

12(8) + (1/2)(13)(20) + (1/4)π(8^2)

= 96 + 130 + 4π = 226 + 16π ft^2

= about 276.27 ft^2

The solution to the problems are given below:

Giving each of the letters numbers based on their numerical position on the English alphabet, we can solve below:

n (14) + e (5) = 14 + 5 = 19

t (20) - j (10) = 20 - 10 = 10

d (4) x e (5) = 4 x 5 = 20

p (16) / b (2) = 16 / 2 = 8

It can be seen that with the letter e for example is the 5th letter of the alphabet and the value is used to compute the addition of the problem.

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Using the given function, we can plug in x=3 and t=5 to find the concentration of the drug in the blood:

C = f(x,t) = 26te^-(5-x)
C = f(3,5) = 26(5)e^-(5-3)
C = f(3,5) = 130e^-2

Using a calculator, we can simplify this to:

C = f(3,5) ≈ 32.22 mg/liter

Therefore, the concentration of the drug in the blood 3 hours after injection with a dosage of 5 mg is approximately 32.22 mg/liter.
Hi! To find the concentration C at f(3,5), you'll need to plug in the values for x and t into the given function f(x,t) = 26te^-(5-x).

So, f(3,5) = 26(5)e^-(5-3) = 130e^(-2).

Now, calculate the exponential value: e^(-2) ≈ 0.1353.

Finally, multiply this value by 130: 130 * 0.1353 ≈ 17.589.

Thus, f(3,5) = 17.589 mg/liter (rounded to 3 decimal places).

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To find the volume of the cone, we first need to find its radius. Since the pyramid is contained within the cone such that the vertices of the base of the pyramid are touching the edge of the cone, the diagonal of the square base of the pyramid is equal to the diameter of the base of the cone. The diagonal of the square base of the pyramid is:

d = √(10^2 + 10^2) = √200 = 10√2 cm

Therefore, the diameter of the base of the cone is 10√2 cm, and the radius is 5√2 cm.

The volume of the cone can be calculated using the formula:

V = (1/3)πr^2h

where r is the radius of the base of the cone and h is the height of the cone.

Substituting the given values, we get:

V = (1/3)π(5√2)^2(20)

V = (1/3)π(50)(20)

V = (1/3)(1000π)

V = 1000/3 * π

Using 3.14 as the decimal approximation for π, we get:

V ≈ 1046.35 cubic centimeters

Therefore, the volume of the cone is approximately 1046.35 cubic centimeters. The answer is A.

The amount of time it would take for the ball to reach its maximum height is 2.1825 seconds.

Based on the information provided, we can logically deduce that the height (h) in feet, of this ball above the​ ground is related to time by the following quadratic function:

Next, we would determine the maximum height of this ball by taking the first derivate in order to determine the time (t) it takes as follows;

h(t) = -16t² + 90t

h'(t) = -32t + 90

90 = 32t

t = 90/32 = 2.1825 seconds.

h(2.1825) = -16(2.1825)² + 90(2.1825)

h(2.1825) = 120.21 feet.

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The containment area is shrinking at a rate of 280π m²/min when the diameter is 80m and the radius is decreasing at a constant rate of 7m/min.

Let's begin by first finding the radius of the containment area when its diameter is 80m.

The diameter of the containment area is 80m, so its radius is half of that:

[tex]r = 80m / 2 = 40m[/tex]

Now, we need to find the rate at which the containment area is shrinking when the radius is decreasing at a constant rate of 7m/min.

We can use the chain rule of differentiation to find this rate:

[tex]dA/dt = dA/dr * dr/dt[/tex]

where A is the area of the containment, t is time, r is the radius of the containment, and dA/dt and dr/dt are the rates of change of A and r with respect to time, respectively.

We know that dr/dt = -7 m/min (negative because the radius is decreasing), and we can find dA/dr by differentiating the formula for the area of a circle with respect to r:

A = π[tex]r^2[/tex]

[tex]dA/dr = 2πr[/tex]

So, when r = 40m, we have:

[tex]dA/dt = dA/dr * dr/dt[/tex]

= (2πr) * (-7)

= -280π [tex]m^2[/tex]/min

Therefore, the containment area is shrinking at a rate of 280π m^2/min when the radius is decreasing at a constant rate of 7m/min and the diameter of the containment area is 80m.

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|r| = 7/80 < 1, the series is convergent. The sum = 0/(1-7/80) = 0. the sum of the geometric series is 0.

The geometric series with first term 0 and common ratio 7/80 is given by 0, 7/80, (7/80)², (7/80)³, ... In general, the nth term is (7/80)ⁿ⁻¹.

To determine whether this series is convergent or divergent, we can use the formula for the sum of an infinite geometric series:

sum = a/(1-r)

where a is the first term and r is the common ratio. In this case, a = 0 and r = 7/80.

If |r| < 1, then the series converges to the sum given by the above formula. If |r| ≥ 1, then the series diverges.

In this case, |r| = 7/80 < 1, so the series is convergent. The sum is given by:

sum = 0/(1-7/80) = 0

Therefore, the sum of the geometric series is 0.

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The speed of Fred's snowmobile was 30 miles per hour.

This is calculated by dividing the distance traveled by the time taken for each journey, which gives a speed of 30 mph for both the outward and return journeys.

To find Fred's speed, we can use the formula speed = distance/time. We know that Fred traveled a distance of 360 miles in 12 hours on the outward journey, so his speed was 360/12 = 30 mph.

Similarly, on the return journey, he traveled the same distance of 360 miles, but it took him 15 hours, so his speed was again 360/15 = 24 mph.

However, we are asked to find his constant speed, so we take the average of the two speeds, which gives us (30 + 24)/2 = 27 mph. Therefore, Fred's snowmobile was traveling at a constant speed of 30 mph on both journeys.

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The equation would be: y = 3 + x

To include the terms you mentioned, we can set up an equation to represent the relationship between the number of weeks Stacy volunteers (x) and the number of cards she has (y).

Since Stacy starts with 3 collector's cards and receives 1 more card each week she volunteers, the equation would be:

y = 3 + x

In this equation, x represents the number of weeks Stacy volunteers, and y represents the total number of collector's cards she has.

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The solutions for the cube function are x=64 or x= -64.

The main power rules are presented below.

The question gives the equation [tex]x^{2/3}[/tex]=16, you can rewrite it as: [tex]\sqrt[3]{x^2}[/tex]=16.

For eliminating the cubic root, you should apply the power 3 ib both sides. See:

[tex](\sqrt[3]{x^2})^3[/tex]= 16³

x²= 4096

Finally, you have x=64 or x=-64

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