Rearrange the formula V = 1 3 πr2h for h.

3f(2) =  12

Complete question: How do you Evaluate 3f(2) if f(x) = x²?

The given function is:

f(x) = x²

To find f(2), substitute x = 2 into the function f(x):

f(2)  =  2²

f(2)  =  4

3f(2)  =  3 (4)

3f(2)  =  12

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Answer:

[tex]r[/tex]≈[tex]5.2 in[/tex]

Step-by-step explanation:

It is given that a circle is required to inscribe an equilateral triangle with an area of [tex]35.074 in^2[/tex] and an altitude of [tex]7.794 in[/tex],

Also, we know that the centroid divides the altitude into 2:1 form, thus

[tex]r=\frac{2}{3}(h)[/tex]

Substituting the value of an altitude, we have

[tex]r=\frac{2}{3}(7.794)[/tex]

[tex]r=5.196 in[/tex]

[tex]r[/tex]≈[tex]5.2 in[/tex]

Therefore, the radius of the circle is [tex]5.2 inches[/tex].

Answer:

James is 12 years old

Joe is 22 years old

Step-by-step explanation:

Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times James's age.

LEt x be the age of James

x+10 be the age of Joe

In 8 years,  James age becomes x+8

In 8 years, Joe's age becomes x+10+8 = x+18

Twice Joe's age is equal to 3 times of James's age

2(x+18)= 3(x+8)

2x+ 36=3x+24

Subtract 2x from both sides and subtract 24 from both sides

x=12

James is 12 years old

Joe is x+10 = 22 years old

Final answer:

To solve for K in the equation F=9/5(K−273.15)+32, subtract 32 from both sides, multiply by 5/9, and then add 273.15 to isolate and solve for K.

Explanation:

When solving the equation F=9/5(K−273.15)+32 for K, the goal is to isolate K on one side of the equation. To achieve this, follow these steps:

This formula allows you to convert a temperature from Fahrenheit to Kelvin.

The domain of the function f(x) = x5 ln x consists of all positive real numbers since the natural logarithm is undefined for zero and negative numbers.

The domain of a function consists of all possible input values (x-values) where the function is defined. In the case of the function f(x) = x5 ln x, we need to consider where this function is defined.

The domain for a function that involves a natural logarithm (ln), like this one, is always x > 0. This is because the natural logarithm, or ln, is undefined for values of x <= 0. In other words, we can't take a natural logarithm of zero or a negative number.

Therefore, the domain of the function f(x) = x5 ln x is x > 0. All positive real numbers are included in the domain, while zero and negative numbers are excluded.

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The solution is Option D.

The quadratic equation which has a leading coefficient of 2 and a constant term of -3 is A = 2x² + 3x - 3

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

a) Let the equation be f ( x ) = 2x³ - 3

The equation is not a quadratic equation

b) Let the equation be f ( x ) = -3x² - 3x + 2

The quadratic equation does not have a constant term of -3

c) Let the equation be f ( x ) = -3x³ + 2

The equation is not a quadratic equation

d) Let the equation be f ( x ) = 2x² + 3x -3

Now , the quadratic equation is of the form ax² + bx + c = 0 and has a leading coefficient of 2 and constant term of -3

Hence , the quadratic equation is f ( x ) = 2x² + 3x -3

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A person who has reached the age of 35 has lived approximately 1,103,760,000 seconds. This is calculated by multiplying the number of seconds in a year by 35.

To calculate how many seconds a person has lived by the age of 35, we need to calculate the number of seconds in a year and multiply that by 35. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year. Therefore, there are approximately 31,536,000 seconds in a year. If we multiply that by 35, we find that a 35-year-old person has lived approximately 1,103,760,000 seconds.

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Answer:

As per the statement: Sandy is observing the velocity of a runner at different times.

Also, after one hour, the velocity of the runner is 4 km/h. and after two hours, the velocity of the runner is 2 km/h..

(A)

Let x represents the time in hours and y represents the velocity of the runner(in km/hr)

Then, we have two points from the given statement:

(1, 4) and (2, 2)

An equation of line for two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by;

[tex]y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

For the given two points (1, 4) and (2, 2) we have an equation:

[tex]y-4 = \frac{2-4}{2-1}(x-1)[/tex]

[tex]y-4 = \frac{-2}{1}(x-1)[/tex]

or

[tex]y-4 = -2(x-1)[/tex]

Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]

[tex]y-4 = -2x + 2[/tex]

Add 4 on both sides we get;

[tex]y-4 +4= -2x + 2+4[/tex]

Simplify:

[tex]y= -2x + 6[/tex]

Add 2x on both sides we get;

[tex]y + 2x=-2x+6+ 2x[/tex]

Simplify:

[tex]y + 2x = 6[/tex]

[Since, standard form for linear equations in two variables is Ax+By=C]

Therefore, an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times is:

[tex]2x+y= 6[/tex] ; where x represents the time in hours and y represents the velocity of the runner.

(B)

Equation in part A

It is given as;  [tex]2x+y= 6[/tex]          .....[1]

To graph this equation; for the first 4 hours.

x                  y = -2x+6

1                  4

2                 2

3                 0

4                 -2

Now, using these points (1, 4) , (2, 2) , (3, 0) and (4, -2) plot the graph as shown below in the attachment.

Answer:

It's the first one

Step-by-step explanation:

Using a calculator or long division, the square root of 658 is approximately 25.66.

To find the square root of 658, we can use a calculator or the long division method.

Using the long division method:

Step 1: Guess a number whose square is close to 658. Let's start with 25, since [tex]\(25^2 = 625\)[/tex], which is close to 658.

Step 2: Divide 658 by 25. [tex]\(658 \div 25 = 26.32\)[/tex]

Step 3: Take the average of the quotient and the divisor: [tex]\((25 + 26.32) \div 2 = 25.66\)[/tex]

Step 4: Repeat steps 2 and 3 using the new guess until the desired level of accuracy is achieved.

By repeating these steps, we'll get closer to the square root of 658. However, using a calculator will give a more accurate result.

Answer:

a. 5712.04

b. 5712.04

c. 79.97

d. 878.71

e. 12.30

f. 67.67

Step-by-step explanation:

B- 17136.12 /30= 5712.04  

C- 5712.0r x 0.014 =79.97  

D- 712.04 x 29= 20,649.16  

   5723.04 x 1 = 5712.04  

                         = 26,361.20/ 30  

                               =878.71  

E- 878.71(0.014)= 12.30  

F- 79.97 -12.30 = 67.67

Helene will accrue a finance charge on her credit card due to not fully repaying her balance. With her APR, the monthly interest is 1.4%, which is then applied to her $5,712.04 balance after making the car down payment. This example illustrates how credit card interest is calculated and applied.

Given Helene's credit card's Annual Percentage Rate (APR) of 16.8%, the total credit card balance after making the $5,000 down payment on a car will be $5,712.04. The APR is divided into 12 months to get the monthly interest rate. Therefore, the monthly interest rate is 16.8 / 12 = 1.4%. The finance charge for the next billing cycle will be 1.4% of  $5,712.04.

Additionally, considering that Helene does not fully repay her balance, she is always subject to a finance charge, which is the cost of borrowing money. The interest cost is calculated by applying the interest rate to the balance left over at the end of the billing cycle.

This scenario is a real-world example of credit card finance and illustrates how credit card interest is computed and applied each billing cycle.

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His cost per wear

He will have 240 wears in 5 years

$180 in dry cleaning and $200 for cost of the suit.

$380 total investment

$1.58/per wear

The total investment for the suit is $380 and the cost per wear is $1.58.

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.

We have,

Jason decides to invest in a new two-piece suit which will cost him $200.

So, the total amount he invested

= $180 in dry cleaning + $200 for cost of the suit.

= $380

and, the cost per wear is

= 380/ 240

= $1.58

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Kym is wrong because the ratio means that 50% of the students in the cafeteria were boys.

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value.

Number of boys = (25 /50) x 50 = 25

Percentage of the number of boys = (25/50) x 100 = 50%

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Kym is incorrect because the ratio of boys to girls being 25:25 means there are equal numbers of boys and girls. Therefore, boys make up 50% of the students, not 25%.

Kym's explanation is incorrect because the ratio of boys to girls being 25:25 means that the number of boys is equal to the number of girls.
Specifically, this ratio can be simplified to 1:1. Since there are 50 students in total and the number of boys and girls is equal, there must be 25 boys and 25 girls.
Therefore, boys make up 25 out of the 50 students, which is actually 50%, not 25%.

The total number of students= 50.

Understand that a ratio of 25:25 means equal parts of boys and girls.

Simplify the ratio 25:25 to 1:1.

The number of boys: 50 students \/ 2 = 25 boys.

The percentage of boys,
(25 boys \/ 50 total students) * 100 = 50%.

Thus, boys constitute 50% of the student population, not 25%.

Answer:

Step-by-step explanation: