assume the series can be integrated term by term. use this fact and the result from part a) to find the fourier cosine series of the function f(x)

By using the PEMDAS order of operations, we get 3(6+7) = 39.

The equation be 3(6+7) then the correct answer is 34.

The order of operations exists as a law that describes the proper sequence of stages for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).

Given: 3(6+7)

By using the PEMDAS order of operations, we get

(6+7) = 13

Then we get

3(6+7) = 3 \(*\) 13

= 39.

Therefore, the value of 3(6+7) = 39.

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if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

\(\mathsf {SA = 112 in.^{2} }\)

Step-by-step explanation:

\(\textsf {Formula used :}\\\implies \textsf {SA = 2(length * width + width * height + length * height) }\)

\(\textsf {Given :}\\\textsf {Length = 5 in.}\\\textsf {Width = 4 in.}\\\textsf {Height = 4 in.}\)

\(\textsf {Solving :}\)

\(\implies \mathsf {SA = 2 (5 * 4 + 4 * 4 + 5 * 4)}\)

\(\implies \mathsf {SA = 2 (20 + 16 + 20)}\)

\(\implies \mathsf {SA = 2 (56)}\)

\(\implies \mathsf {SA = 112 in.^{2} }\)

The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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The value of x in the given equation is 302.9.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

2500 / 233 = 3250 / x

cross multiply both sides

2500 * x = 3250 * 233

2500x = 757250

x = 757250 / 2500

x = 302.9

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Translation: Solve the equation to calculate the value of the variable and thus answer the question

Answer:

5: 4

6: 20

7: $3.20

8: 92

9: 22

10: $11.60

Step-by-step explanation:

6. remove 3 from 83, you will have 80 and then divide by 4 = 20 students in a class.

7. Subtract 8.80 from 24.80, you will get 16 dollars. Do 16 ÷ 5 = 3.2 as the cost of each pencil.

9. 94- 6 = 88 so, 88 ÷ 4 = 22.

10. 13.40 -7.60 = 5.8 as his weekly allowance.

I hope it helps.

Answer:

7(5y+7)

Step-by-step explanation:

7×5y=35y

7×7=49

so its 7(5y+7)

9514 1404 393

Answer:

  A.  $45

Step-by-step explanation:

12 hours is 5 more than 7 hours.

Hank will be paid 5 × $9 = $45 if he spends 12 hours working outside.

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

11x-1

Step-by-step explanation:

Area =length x width

so multiply (2x+3) and (3x+1) to get 11x-1

Answer:

its 5;11

Step-by-step explanation:

GIVE 5 STAR AND THQANKS YOU GET A ON TEST

Answer:

Ryan: (100/13)(1/1,609.34)(3,600) =

17.21 miles per hour

Ryan is faster than Juan, by about 2.21 miles per hour

Answer:

17°

Step-by-step explanation:

A right angle equals 90°, so we add 73 and 90 together to get 163. But a triangle has 180°, so we subtract 163 from 180 to get our answer.

180-163 = 17°

Answer:

224

Step-by-step explanation:

360.-136.

Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:

9. B. 32 millimeters

10. C. 7 inches

11. C. 56.24 millimeters

13. B. 14.13 square feet

Step-by-step explanation:

9. Radius of a circle or any circular shape = ½ of its diameter

Diameter of the disk = 64 millimeters

Radius of the disk = ½(64) = 32 millimeters

10. Width of the cooler = 6 in.

Length = 8 in.

Volume = 336 in.³

Height = ?

Formula for volume of a rectangular prism = L*W*H

Plug in the values

336 = 8*6*H

336 = 48*H

Divide both sides by 48

336/48 = H

H = 7 inches

11. A dime has a circular shape

The circumference of the dime = circumference of a circle = πd

Where,

d = 17.91 millimeters

π = 3.14

Plug in the values

C = 3.14 × 17.91 = 56.2374

≈ 56.24 millimeters (nearest hundredth)

12. Area of the top of the desk = area of semicircle = ½ × πr²

Where,

r = ½(6) = 3 ft

π = 3.14

Plug in the values

Area = ½ × 3.14 × 3² = ½ × 3.14 × 9

Area = 14.13 square feet

Answer:

{7, 9}

(Numbers from 1 to 10 equal to or greater than 7 are 7 and 9)

Step-by-step explanation:

We have to find the set of whole number greater than and equal to 7 from 1 to 10,

Now, From 1 to 10, the odd numbers are, 1,3,5,7,9,

And of these, 7 and 9 are equal to or greater than 7

So, we get the set,

{7, 9}

Answer:

4.9 feet

Step-by-step explanation:

First, we need to determine the height of the building using the following:

\(L^2 = H^2 + B^2\)

Where

H = Height of the building

L = Length of the first ladder = 20ft

B = Distance from the base of the building = 10ft

So, we have:

\(20^2 = H^2 + 10^2\)

\(400 = H^2 + 100\)

\(H^2 = 400 - 100\)

\(H^2 = 300\)

\(H = \sqrt{300\)

Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:

\(L_2^2 = H^2 + B_2^2\)

Where

\(L_2 = 18\) --- Length of the second ladder

\(H = \sqrt{300\) ----- Height of the building

So, we have:

\(18^2 = \sqrt{300}^2 + B_2^2\)

\(324 = 300 + B_2^2\)

\(B^2_2 = 324 - 300\)

\(B^2_2 = 24\)

Solving for B2, we have:

\(B_2 = \sqrt{24\)

\(B_2 = 4.9\)

No.

Since w = 8, you must replace the variable with the number associated to it.

So, it would be 5 + 8 = 58

5 + 8 is not equal to 58, it is equal to 13.

If you wanted to find out what w was, simply subtract 5 on both sides.

w = 58 - 5

Answer:

If they water the plants in the garden together then it will take about 15 minutes because when they do it seperatly it takes about 30 minutes. So if they do it together, they are cutting work in half. And half of 30 is 15.

Step-by-step explanation:

32 rounded is 30.

25 rounded is 30.

30/ 2 = 15

Answer:

To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:

0.05 x 3.8 = 0.19

So, 0.19 gallons of engine oil should be added to the jerry can.

The final value is 13.43, which represents the product of 5.48 and 2.45.

We have,

The concept being demonstrated here is the multiplication of two decimal numbers.

When multiplying decimal numbers, we follow these steps:

- Ignore the decimal points and multiply the numbers as if they were whole numbers.

In this case, we multiply 548 by 245, which gives us 134,260.

- Determine the total number of decimal places in the original numbers.

In this case, the original numbers have a total of four decimal places (two decimal places each).

- Place the decimal point in the product so that it has the same number of decimal places as the total from step 2.

In this case, we need to place the decimal point two places from the right, giving us 1,342.60.

- Round the final result if necessary.

In this case, rounding to two decimal places gives us 1,342.60 rounded to 13.43.

Therefore,

The final value is 13.43, which represents the product of 5.48 and 2.45.

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Answer:

x + 9

Step-by-step explanation:

The sum of x and 9,

x + 9

Answer:

(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Step-by-step explanation:

i literally just learned this today so here we go:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:

(x - (-7))^2 + (y - (-4))^2 = r^2

(x + 7)^2 + (y + 4)^2 = r^2

We also know that the circle contains the point (-1, -8).

We can substitute these values for x and y, and solve for r:

(-1 + 7)^2 + (-8 + 4)^2 = r^2

36 + 16 = r^2

r^2 = 52

Substituting this value of r^2 into the equation for the circle, we get:

(x + 7)^2 + (y + 4)^2 = 52

Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Answer:

See answers below.

Step-by-step explanation:

Large Rectangle:  length x width = (x + 3)(x - 4) =

                                        x² - 4x + 3x - 12

                                           x² - x - 12

Smaller Rectangle:  length x width = (x)(3) = 3x

Shaded Region: shaded area =  lg. rectangle minus small rectangle

                             A = (x² - x - 12) - 3x  

                             A = x² - 4x - 12

Solve for x, if shaded reion's area is 48 square units:      

                          48 = x² - 4x - 12

                                  x² - 4x - 12 -48 = 0

                                  x² - 4x - 60 = 0

                                  (x - 10)(x + 6) = 0

                                   x - 10 = 0   or   x + 6 = 0

                                   x = 10    or    x = -6

                                               But x represents a length, so x cannot be -6.

                                  x = 10

Answer:

2x^3+x^2-7x+3

Step-by-step explanation:

To do this you have to multiply the first term in the first parenthesis so you would multiply 2x by x^2 x and -3 so you get 2x^3+2x^2-6x  for the first part and then you would multiply -1 by the terms again so you would get -x^2-x+3 so you would get 2x^3+2x^2-6x-x^2-x+3 then you would add add teh like terms together so you get 2x^3+x^2-7x+3 as the final answer