Suppose f and g are continuous functions such that g(3) = 6 and lim x → 3 [3f(x) + f(x)g(x)] = 54. find f(3).

Area of circle is 345.4 cm²

Given that;

Angle of sector = 45°

Area of sector = 13.75π cm²

Find:

Area of the circle

Computation:

Area of sector = [tex]\frac{\theta}{360}[/tex][Area of circle]

13.75π = [tex]\frac{\theta}{360}[/tex][Area of circle]

13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]

13.75(3.14) = [tex]\frac{45}{360}[/tex][Area of circle]

43.175 = 0.125[Area of circle]

Area of circle = 345.4 cm²

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The parking cost for the specified duration would be $6.70.

The parking fee consists of a base charge of $1.50 for the first hour. In this case, the car is parked for 5.5 hours (from 12:45 pm to 6:15 pm). The first hour is covered by the base charge, and the remaining 4.5 hours are billed as subsequent half-hours. For each half-hour, there is an additional charge of 55 cents. So, for the subsequent 4.5 hours, the additional charge is calculated as follows:

[tex]\[4.5 \times \$0.55 = \$2.475.\][/tex]

Adding this to the base charge:

$1.50 + $2.475 = $3.975.

Therefore, the total parking cost for the specified duration is $1.50 (for the first hour) + $2.475 (for the subsequent 4.5 hours), resulting in a final cost of $6.70.

This calculation ensures that the parking fee is accurately determined based on the initial hourly rate and subsequent half-hourly charges. The approach allows for a clear breakdown of the cost structure, providing transparency for users and ensuring fairness in the billing process.

A parking lot implements a fee structure of $1.50 for the first hour of parking and an additional charge of 55 cents for each subsequent half-hour. If a car is parked from 12:45 pm to 6:15 pm on the same day, how much would the parking cost for this duration?

When factoring an expression, we need to identify the Greatest Common Factor of the expression (GCF). By definition, GCF is the product of prime factors involved with its Lowest Exponent.

We need to divide each term by the GCF to get the expression inside the parenthesis.

[tex] 30a^6-24a^2\\ GCF\; is \; 6a^2\\ \\ 30a^6-24a^2=6a^2(\frac{3a^6}{6a^2} -\frac{24a^2}{6a^2} )=6a^2(5a^4-4)\\ ---------------------\\ \\ 16a^5-20a^3\\ GCF \; is \; 4a^3\\ \\ 16a^5-20a^3=4a^3(\frac{16a^5}{4a^3} -\frac{20a^3}{4a^3})=4a^3(4a^2-5) \\ ---------------------\\ \\ 12a^3+8a\\ GCF \; is \; 4a\\ \\ 12a^3+8a=4a(\frac{12a^3}{4a}+\frac{8a}{4a})=4a(3a^2+2)\\ ---------------------\\ 24a^4+18\\GCF \; is \; 6\\\\24a^4+18=6(\frac{24a^4}{6} +\frac{18}{6})=6(4a^4+3) \\ --------------------- [/tex]

Conclusion:

From above we can conclude that the below expressions are factored completely

[tex] 16a^5-20a^3=4a^3(4a^2-5)\\ \\ 24a^4+18=6(4a^4+3) [/tex]

Answer:

50 square units.

Step-by-step explanation:

Eng2021

Answer:

k = 22.5; xy = 22.5

your welcome

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Answer:

Option B is correct.

Obtuse triangle.

Step-by-step explanation:

Acute triangle:

In acute triangle, all angles are less than 90 degree.

Obtuse triangle:

In obtuse triangle, the triangle has an angle more than 90 degree.

Right triangle.

In right triangle, it has a right angle 90 degree.

Isosceles triangle.

In isosceles triangle, it can be acute, right or obtuse depends only on the apex angle.

Therefore, the triangle whose angles are all more that 90 degree is, Obtuse triangle.

59 degrees Fahrenheit is equivalent to 15 degrees Celsius.

We have,

To convert a temperature in Fahrenheit to Celsius, you can use the formula:

°C = (°F - 32) x (5/9)

Let's apply this formula to convert 59 degrees Fahrenheit to Celsius:

°C = (59 - 32) x (5/9)

Simplifying the equation:

°C = 27 x (5/9)

°C = 135/9

°C = 15

Therefore,

59 degrees Fahrenheit is equivalent to 15 degrees Celsius.

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The correct option is:    The range and domain of the graph are the same.

Explanation

Given function is:   [tex]f(x) = -\sqrt{-x}[/tex]

The inside term of a square root can't be negative, it will be always 0 or positive. That means,  [tex]-x \geq 0[/tex] or [tex]x\leq 0[/tex]

So, the Domain of the function is : "All real numbers such that [tex]x\leq 0[/tex]"

Now, if x=0, then f(x) =0 and if x is any negative number, then f(x) will be also negative.

That means, the Range of the function: "All real numbers such that [tex]f(x)\leq 0[/tex]"

So, the range and domain of the function are the same.

Answer:

Joe Don actually ran 113.2 yards

Step-by-step explanation:

Length of the football field = 100 yd

Width of the football field = 53 yd

The football field is rectangular in shape. So in order to find the diagonal of the field, we need to split it up into two right triangles.

In one of the right triangles, the length and width becomes the two sides of it and diagonal is the third side.

In order to find the third side (diagonal), we need to apply the Pythagoras theorem.

So,

Diagonal² = 100² + 53²

Diagonal² = 10000 + 2809

Diagonal² = 12809

Taking square root on both sides

[tex]\sqrt{Diagonal^{2} } =\sqrt{12809}[/tex]

Diagonal = 113.17 yd

Diagonal = 113.2 yd (approx)

Thus Joe Don actually ran 113.2 yards

Answer:

25, 2, & 3 are rational numbers

π is a irrational number.

Explanation:

I think we need to find out the irrational number.

Here we learn main difference between rational and irrational number.

Rational Number:

All numbers whose written in fraction form where numerator and denominator are whole number.

All the whole numbers are rational number.

For example: 2 (because we can write 2 as [tex] \frac{2}{1} [/tex]), [tex] \frac{5}{6} [/tex] etc

0.666666.... (endless repeating digits)

In given question: 25, 2 and 3 are rational numbers

Irrational Numbers:

All numbers that are not rational are considered irrational. An irrational number can be written as a decimal form, but not as a fraction form.

An irrational number has endless non-repeating digits to the right of the decimal point.

π = 3.141592...... (endless non repeating digits)

√2 =1.414213... (endless non repeating digits)

Answer:

25, 2, 3

Step-by-step explanation:

A rational number is a terminating decimal or a non-terminating, repeating decimal.

25, 2, and 3 are terminating decimals, so they are rational.

values could she use for a, b, and c a = 4 b = -13 c = 3

Step-by-step explanation:

We have been given the equation

4x²=13x-3

Subtract 4x²  to both sides of the equation

0=-4x²+13x-3

Multiply both sides of the equation by -1

4x²-13x+3=0

The general equation of a quadratic equation is ax²+ bx +c=0

Comparing this equation with above equation 4x²-13x+3=0

a = 4

b = -13

c = 3

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There are 10 different ways to select a committee of 2 people from a group of 5 candidates.

To calculate the number of ways to select a committee of 2 people from a group of 5 candidates, we can use the combination formula. The number of combinations of n items taken r at a time is given by the formula:

nCr = n! / (r!(n-r)!)

Here, n is the total number of candidates (5) and r is the number of people to be selected for the committee (2). Plugging in the values, we get:

5C2 = 5! / (2!(5-2)!)

Simplifying this expression:

5C2 = (5 * 4) / (2 * 1)

Therefore, there are 10 different ways to select the committee.

The formula for the growth rate is given by

[tex] y=a(b)^x [/tex]

Now when b is greater than 1 , then it is increasing function

and when b is less than 1 , then it is decreasing function.

Now in the function

[tex] 22000(.88)^{(x+2)} [/tex]

here value of b is 0.88 , which is less than 1 , so it is decreasing function

And decay rate is given by

1-r = 0.88

Subtract 1 from both sides

-r = 0.88-1

-r = -0.12

r = 0.12

or r= 12%

It means it is decreasing at a rate of 12%

Hence Option C is correct

C.The price of the boat decreases by 12% every year.

Answer:

Step-by-step explanation:

The periodic interest rate refers to the rate that it's charged after certain fixed period, can be yearly, monthly, daily. In this case, the periodic interest rate is due in 2 weeks.

Now, to find this interest rate, we just have to divide the fee by the loan and see what percentage represents

[tex]\frac{\$80}{\$500}=0.16[/tex]

Then, we multiply by 100 to obtain the percentage

[tex]0.16(100)= 16\%[/tex]

Therefore, the interest rate is 16%

Answer:

Sample Response: Replace the word "is" with an equals sign. Replace the word "product" with a multiplication sign. Replace the words "a number" with the variable n, to represent the unknown value. The equation is 63 = 9n.

The statement 'Sixty-three is the product of nine and a number' translates to the equation 63 = 9 × n. The variable n represents the unknown number that, when multiplied by nine, equals sixty-three.

To translate the statement "Sixty-three is the product of nine and a number" into an equation using  n for the variable, we can use the following steps:

1. Identify the unknown number: Let's denote the unknown number as  n

2. Express the known quantities: We know that "Sixty-three" is equal to the product of "nine" and the unknown number  n .

3. Write the equation: The statement can be translated into the equation:

[tex]\[ 63 = 9 \times n \][/tex]

In this equation:

-  63  represents the product of  9  and  n .

-  9  represents the known quantity.

-  n represents the unknown number we are trying to find.

So, the equation [tex]\( 63 = 9 \times n \)[/tex]expresses the statement "Sixty-three is the product of nine and a number" using the variable  n .

The solutions for a are a=1 and a=−13. So the correct answer is A. -13 and 1.

To solve the equation [tex]\( (a+6)^2 = 49 \)[/tex], follow these steps:

1. Take the square root of both sides:

[tex]\[ \sqrt{(a+6)^2} = \sqrt{49} \][/tex]

2. Consider both positive and negative roots:

[tex]\[ a + 6 = \pm 7 \][/tex]

3. Solve for ( a ):

For ( a + 6 = 7 ):

[tex]\[ a = 7 - 6 = 1 \][/tex]

For ( a + 6 = -7 ):

[tex]\[ a = -7 - 6 = -13 \][/tex]

So, the solutions for ( a ) are ( a = 1 ) and (a = -13).

Therefore, the correct answer is A. -13 and 1.

Answer:

The age you are when you purchase life insurance is the biggest factor in how much you will have to pay. The premium amount typically increases about 8% to 10% for every year of age. The older you are, the more expensive you are to insure. When you are in your 40s, your rates increase from 5%-8% and when you are over 50, your rates increase by 9%-12% each year.

Step-by-step explanation:

Answer:

The Life insurance premium totally depends on your age when you will be purchasing it.

Step-by-step explanation:

Age is a significant factor in purchasing the policy. Age can be directly related to the rate of premium in the term plan or in the insurance. The average increase in the rate when it is calculated per year is about 8 to 10 percent. {Told by Ted Bernstien}.

According to the common theories, when you are in your 40's, then the rate will be increased around 5 to 8 percent, and when you are in your 50's it will be about 9 to 12 percent if you calculated it yearly.

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