Let R be the region bounded by y= square root of 25-x^2 and y=0. Find the volume of the solid of revolution obtained by revolving R about the x-axis.

The runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

What is the coefficient?

A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c, the coefficient is 14. In the term g, the coefficient is 1.

A) The mechanical energy lost due to friction can be calculated as follows:

Initial kinetic energy of the runner: KE = 0.5 * m * v² = 0.5 * 80 kg * (4.7 m/s)² = 140.29 J

The force of friction acting on the runner is given by:

[tex]friction_{force} = friction_{coefficient} * normal_{force}[/tex]

where,

[tex]friction_{coefficient} = 0.70[/tex]

[tex]and normal_{force} = m * g (g = 9.8 m/s^{2} )[/tex]

The normal force is given by:

[tex]normal_{force} = m * g = 80 kg * 9.8 m/s^{2} = 784 N[/tex]

Therefore, the force of friction acting on the runner is: [tex]friction_{force} = 0.70 * 784 N = 548.8 N[/tex]

The work done by friction is given by:

[tex]W = friction_{force} * distance[/tex]

Since the speed of the runner is reduced to zero, the work done by friction is equal to the change in kinetic energy:

[tex]W = KE_{final} - KE_{initial}[/tex]

= 0 - 140.29 J = -140.29 J

So, the mechanical energy lost due to friction is 140.29 J.

B) The distance the runner slides can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.

The work done by friction is given by: W = friction_force * distance

Since the friction force is constant, the work done by friction is equal to the change in kinetic energy:

[tex]W = KE_{final} - KE_{initial}[/tex]

= 0 - 140.29 J = -140.29 J

Rearranging this equation and substituting in the known values, we get:

[tex]distance = -W / friction_{force}[/tex]

= -140.29 J / 548.8 N = 0.255 m or 25.5 cm

Hence, the runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.

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The strand of straight hair would be most accurately classified as a ray.

The definition of ray in math is that it is a part of a line that has a fixed starting point but no endpoint.

Given is the strand of straight hair.

Considering the strand of hair to be straight. We can call it as a ray as ray originates from one point and extends away from that point towards infinity.

Therefore, the strand of straight hair would be most accurately classified as a ray.

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Answer:

To find Sally's yearly salary, we can use the information that her budget for food is 1/8 of her yearly salary and her total food bill for the year is $12,500. Let's call Sally's yearly salary "S".

Since 1/8 of Sally's yearly salary is dedicated to food, we can write:

S * 1/8 = $12,500

To solve for S, we can divide both sides of the equation by 1/8:

S = $12,500 * 8 = $100,000

So, Sally's yearly salary is $100,000.

Step-by-step explanation:

Answer:

The Islamic month of Ramadan in 2017 began on Friday, 26 May, which was the 146th day of the year. There are 365 days in a year, so this was approximately 0.4 of the year.

Step-by-step explanation:

The region has a 318.0863 square foot size, as stated in the sentence.

The diameter or extent of a circular is its circumference. A straight line connecting a spot on one length of the circular to a position at the other end, going through the middle, is the diameter.

Diameter of the circle is 26 feet , so radius of the circle is r

= 26/2

= 13 feet

Central angle of the sector is [tex]\frac{5 \pi}{8} \text { radians. }[/tex]

We know that area of a sector of circle of radius r and central angle θ is

[tex]A=\frac{1}{2} \theta r^2[/tex]

Therefore, area of the sector is

A = 1/2 × 5π/8 × 13² = 318.0863 square feet

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The sum is x/(x+5) + (x+10)/(x+1).

The difference is x/(x+5) - (x+10)/(x+1).

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Here, we have

Given: x/(x+5) + (x²+20x+100)/(x²+11x+10)

Sum:

= x/(x+5) + (x²+20x+100)/(x²+11x+10)

= x/(x+5) + (x+10)²/(x+1)(x+10)

=  x/(x+5) + (x+10)/(x+1)

Hence, the sum is x/(x+5) + (x+10)/(x+1).

Now, the difference:

= x/(x+5) - (x²+20x+100)/(x²+11x+10)

= x/(x+5) - (x+10)²/(x+1)(x+10)

= x/(x+5) - (x+10)/(x+1)

Hence, the difference is x/(x+5) - (x+10)/(x+1).

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A) True. Both the given statement about simple interest and compound interest is True.

Simple interest is computed on a loan's principal, or initial loan amount.

Compound interest is often referred to as "interest on interest" since it is calculated using both the principal and the accrued interest from prior periods.

Formula for simple interest - S.I. = (P × T × R) ⁄ 100

Formula for compound interest - C.I. = P(1+R⁄100)t − P

If interest is computed on a compound basis rather than a simple basis, the amount of interest that must be paid on a loan can vary significantly. Positively, the power of compounding can work in your favor when it comes to investments and can be a significant contributor to wealth accumulation.

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The series must converge to a finite value.

The proof is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The partial sums of the series satisfy the inequality s(n) ≥ 1000 for all n.

This means,

The sum of the series is bounded from below by 1000.

Now,

All terms of the series are positive, the sum of the series must either converge to a finite value or diverge to infinity.

For the sake of contradiction,

The series diverges to infinity.

Then for any M > 0, there exists an integer N such that,

a(N) + a{N+1} + a{N+2} + ... > M

This means,

The partial sums of the series start at index N.

i.e

s(N), s{N+1}, s(N+2), ... also diverge to infinity.

This contradicts the fact that they are all bounded from below by 1000.

Thus,

The series must converge to a finite value.

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The sample proportion for successes that estimates the percentage of people who own a tablet computer from Horace's survey of 400 individuals is 48.75%.

The sample proportion shows the percentage or proportion of successes or expected outcomes in a sample.

The sample proportion is given as the quotient resulting from the division operation between the successes (numerator) and sample size (denominator), and multiplied by 100.

The Sample Size = 400

The number of tablet computer owners in the sample = 195

The sample proportion = Number of Success/Sample Size x 100

= 195/400 x 100

= 48.75%

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The exact values for the following:

Sec(0) = -2.2417

Csc(0) = -1.1173317211

Tan(0) = 2.00630902786

Cot(0) = 0.4984

Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

Given:

0 = 17/4.

Then the exact values for the following:

Sec(0) = 1 / cos(17/4) = -2.2417

Csc(0) =  1/ sin(17/4) = -1.1173317211

Tan(0) =  tan(17/4) = 2.00630902786

Cot(0) =  1/ tan(17/4) = 0.4984

Therefore, the exact values are given above.

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The amount of paper, he will need for the bulletin board is 30.875 square feet.

The required amount of ribbon is 22.5 feet.

The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

Kyle puts ribbon around his rectangular bulletin board and covers it in a paper board measuring 4[tex]\frac{3}{4}[/tex] feet by 6[tex]\frac{1}{2}[/tex].

That means,

the perimeter of the paper board = the perimeter of the rectangular bulletin board

The perimeter of the rectangular bulletin board = 2(4[tex]\frac{3}{4}[/tex] + 6[tex]\frac{1}{2}[/tex])

The perimeter of the rectangular bulletin board = 45/2 feet

The perimeter of the rectangular bulletin board = 22.5 feet.

The amount of paper = (4[tex]\frac{3}{4}[/tex] x 6[tex]\frac{1}{2}[/tex]) = 30.875 square feet.

Therefore, the required amount of ribbon is 22.5 feet.

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The solution of x in the equation is (-5.855, 2.435)

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

sec(3x - 15) = csc(14x + 3)

Next, we split the equation as follows

y = sec(3x - 15)

y = csc(14x + 3)

Next, we solve the equation graphically

When the graph is plotted, we have one of the points of intersection to be:

(x, y) = (-5.855, 2.435)

Hence, the solution is (-5.855, 2.435)

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Answer: [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

We can use the pythagorean theorem to solve this.

We will call the length of the unknown side x for now.

Using the theorem, we will get to:
[tex]8^2-4^2=x^2[/tex]

[tex]64 - 16 = x^2[/tex]

[tex]48 = x^2[/tex]

[tex]x = \sqrt{48}[/tex]

In simplest radical form, it will be:

[tex]4\sqrt{3}[/tex]

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the third side, then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]

As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.

To calculate simple interest, divide the original by the loan rates, the length of time, and other variables. The marketing equation is simple gain = principal + interested + hours. It is easier to compute interest with this system. The method that is most frequently used to calculate this is as a percentage of the principle amount. If someone borrows $100 from a buddy and promises to return him with 5% interest, he may only pay his portion of the 100% interest. $100 (0.05) = $5. You must pay interest on any further borrowings as well as any loans you put out. Interest is frequently calculated as a measure of the entire amount of the loan. This percentage represents the loan's interest rate.

given that,

Simple interest = $12,000 × 0.05 × 13/52 = $150

Simple discount note = ($12,000 - $150) × 13/52 = $2962.5

Effective rate of interest = $150 / $2962.5

Effective rate of interest = 0.0506 or 5.06%

As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.

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Answer:

see below

Step-by-step explanation:

dogs = x

cats = y

x+y =39

x- y = 13

so add the 2 equations together you get 2x = 52 so x = 26

y = 13

Step-by-step explanation:

let the length of rectangle be x

let the breadth of rectangle be x - 4m

the perimeter of rectangle=40m

solution,

perimeter of rectangle=40m

2(l+b)=40m

2(x+x-4)=40m

2(2x-4)=40m

4x-8=40m

4x=40+8

or,4x=48

or,x=48/4

•°•, x=12

so,

length of rectangle=x=12

breadth of rectangle=x-4

= 12-4

=8

For the Propositional Function each proposition ∀x∀y P(x,y) is false.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

It is given that Propositional function -

P(x,y) : x ≥ y

Universal quantifier x Universal quantifier y Propositional function

∀x∀y P(x,y)

For every positive integer = every positive integer ≥ every positive integer

But this is false.

Example - x = 1 and x = 2

x < y

Therefore, the given statement is false.

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Let P(x,y) be the propositional function x≥y. The domain of discourse is Z+×Z+. Tell whether each proposition is true or false.

∀x∀yP(x,y)

The function below that models the location of the car if it is d miles from the garage h hours after starting towards the garage is option a d = 26 - 35h.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

The distance travelled by the car is given as:

26 miles away from its destination. Let d be the destination the we have the distance in miles as:

26 - d

The formula of the speed is:

Speed = distance / time

35 = (26 - d) / h

Rearranging the equation, we have:

d = 26 - 35h

Hence, the function below that models the location of the car if it is d miles from the garage h hours after starting towards the garage is option a d = 26 - 35h.

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Probability that it is Saturday is 1/2 as it is on weekend. We can calculate this using Conditional Probability formula.

Given that a day of the week is randomly selected and that it is on the weekend, the probability of it being Saturday can be calculated as follows:

There are two days in a week that are on the weekend: Saturday and Sunday.

If we know that a day is on the weekend, the probability of it being Saturday is equal to the number of Saturdays on the weekend divided by the total number of weekend days. This is because there are two equally likely outcomes for the weekend (Saturday and Sunday), and we are interested in only one of them.

We can find this out by using formula:

P(A|B) = P(A and B) / P(B), where A and B are two events.

So, the probability of selecting Saturday, given that it is on the weekend, is 1/2. In other words, if we randomly select a day of the week and it is on the weekend, there is a 50% chance that it will be Saturday.

This can be written as P(Saturday|Weekend) = 1/2.

Therefore, probability = 1/2

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Step-by-step explanation:

a=3, u= 5, t=7 (given)

v=u+at

v = 5+ 3×7 = 5+21= 26

v=26

The substitute a = 3, u = 5, t = 7 into the formula v=u+at. The value of V would be 26.

Given, a = 3, u = 5, t = 7

To find, v=u+at or v = u + (a × t)

= 5 + (3 × 7)

= 5 + 21

= 26

Thus, v = 26.

By substituting a = 3, u = 5, t = 7 into the formula v=u+at the value of V would be 26.

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In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

aX1 + bX2 ≤ c

where a, b, and c are constants.

The first constraint, 1.5X1 + 2.5X2 ≤ 80, is already in standard form.

The second constraint, 2X1 + 1.5X2 ≤ 70, can be rewritten in standard form as follows:

-2X1 - 1.5X2 ≤ -70

You can now write the problem in the following standard form:

Maximize Z = 5X1 + 4X2

Subject to:

1.5X1 + 2.5X2 ≤ 80

-2X1 - 1.5X2 ≤ -70

X1, X2 ≥ 0

In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.

This means that if you produce 40 units of X1 and 0 units of X2, you will achieve the highest possible value of Z.

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36/25 scoops needed for the recipe if the we have a scoop that holds 2/5 cup, and a recipe calls for 3 3/5 cups of water.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have given that baker has 2/5 cup, and a recipe calls for 3 3/5 cups of water

3 3/5 = 18/5

we only has a 18/5 cup water.

Scoops we will need for the recipe = (18/5)/(2/5) = 36/25

Thus, we will need 36/25 scoops for the recipe.

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9  scoops would we need to use.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

2/5 cup of water can be hold by a scoop.

So, 1 cup of water hold 5/2 scoop

and, 18/5 cup of water can be hold by

=5/2 x 18/5

=18/2

= 9 scoops

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The value of the function F(0) will be -1 / 4.

The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are indicated by letters like f, g, and h.

Given that the function is f(n) = 4f(n-1) + 5 and the value of f(1) is 4.

The value of f(0) will be calculated as:-

f(n) = 4f(n-1) + 5

f(1) = 4f(1 - 1 ) + 5

f(1) = 4f(0) + 5

4 = 4f(0) + 5

f(0) = -1 / 4

Therefore, the value of the function F(0) will be -1 / 4.

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Answer:

arcsin (1°/245°) + 4.963586

Step-by-step explanation:

Rewrite the angle as a sum or difference with its reference angle

simplify the expression using the general reduction formula

Remove the parentheses

Simplify using exponent rule with same exponent (ab)n

Simplify using exponent rule with same exponent

Calculate the approximate value

Calculate

Calculate the sum or difference

As a result, the answers are 2, 1, 1 for Systems A, B, and C, respectively.

An equation, in its most basic form, is a mathematical statement that states that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

The number of real solutions for each system of equations can be determined by counting the number of points where the lines or curves intersect.

System A:

The equation x² + y² = 17 defines a circle with center at the origin and radius √17. The equation y = -1/2x defines a line. Since the circle and line intersect at two points, the system of equations has two real solutions.

Number of real solutions for System A: 2

System B:

The equation y = x² defines a parabola. The equation 7x + y = -6x + 5 defines a line. Since the parabola and line intersect at exactly one point, the system of equations has one real solution.

Number of real solutions for System B: 1

System C:

The equation y = 2x² + 9 defines a parabola. The equation 8y - 17 = 0 defines a line. Since the parabola and line intersect at exactly one point, the system of equations has one real solution.

Number of real solutions for System C: 1

So the answer is 2, 1, 1 for System A, B, C respectively.

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