An engineer designs a satellite dish with a parabolic cross-section. The dish is 15 ft. wide at the opening and the depth is 4 feet. Find the position of the light source (the focus). How far is it from the deepest part of the dish?

Answer:

$990 per unit.

Step-by-step explanation:

The Unit Cost (C) and Unit Revenue R from the production and sale of x units are related by the function:

[tex]C=\dfrac{R^2}{220000} +3221[/tex]

We are required to find the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is ​$1,000.

Rate of Change of C,

[tex]\dfrac{dC}{dt}=\dfrac{R}{110000} \dfrac{dR}{dt} \\\dfrac{dC}{dt}=\$9, R=\$1000\\9=\dfrac{1000}{110000} \dfrac{dR}{dt}\\\dfrac{dR}{dt}=9 \div \dfrac{1000}{110000}\\=9 X \dfrac{110000}{1000}\\\dfrac{dR}{dt}=\$990 $ per unit$[/tex]

The Revenue is changing at a rate of $990 per unit.

The problem is solved by first finding the derivative of the given equation to determine the rate of change. Given that the cost per unit is changing by $9, we substitute this in the derivative equation to get the revenue. Real-world applications of such problems help understand the concepts of marginal revenue and marginal cost.

As per the equation C = R2/220000 + 3221, we first need to find the derivative to determine the rate of change. So, C'(R) = 2R/220000 where C' represents the derivative of the cost with respect to revenue.

Given that the cost per unit is changing by $9, we can represent this as C' = 9 and solve for R using the derivative equation. Hence, R = sqrt(220000 * 9 / 2) = $1000. Therefore, the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is ​$1,000 is found by substituting the revenue value into derivative equation.

These types of problems demonstrate how rates of change can be evaluated using calculus concepts in real-world applications such as understanding marginal revenue and marginal cost in economics and business studies.

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Answer:

[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]

[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]

[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]

[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]

Step-by-step explanation:

The equation needs to be rearranged in terms of one trigonometric function:

[tex]5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0[/tex]

[tex]5\cdot \tan 2\theta - 9 = 0[/tex]

[tex]5\cdot \tan 2\theta = 9[/tex]

[tex]\tan 2\theta = \frac{9}{5}[/tex]

[tex]\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)[/tex]

The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:

[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]

[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]

[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]

[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]

The probability of not getting a '3' when a fair die is rolled four times, rounded to the nearest thousandth, is approximately 0.482.

In a fair die, the probability of getting any one number, such as a 3, is 1/6 because a die has 6 possible outcomes (1 through 6). So, the probability of not getting a 3 is 5/6. If the die is rolled four times, the probability of not getting a 3 on each roll is (5/6)^4. To find this, multiply 5/6 by itself 4 times. The result is approximately 0.482, or rounded to the nearest thousandth, 0.482. So, "the probability of not getting a 3 on four rolls of a die to the nearest thousandth is 0.482."

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Answer:$4125

Step-by-step explanation:

Using the I = P x R x T formula, we can find the simple interest. Substitute all the values into this equation and you get : I = 10,000 x 13.75 x 3. Once you multiply all the values, $4125 is the answer you get. :)

Answer:

57

Step-by-step explanation:

the angles of a triangle together make 180 degrees.

using this, we can find the unknown angle is 115 degrees.

from here, we subtract 1 from both sides of 2d+1=115, then divide by 2, to get the d alone.

114/2=57

d=57

Answer:

d=57

Step-by-step explanation:

The sum of the interior angles of a triangle is 180 degrees

38 +27 +2d+1=180

Combine like terms

(38+27+1) +2d= 180

66+2d=180

Now, solve for d by isolating it

Subtract 66 from both sides

66-66 +2d=180-66

2d=114

Divide both sides by 2

d=57

Answer:

$3,245

Step-by-step explanation:

For a money saved at Simple Interest,

Amount =Simple Interest+Principal

Principal, P=$2750

Rate, r=3%

Time, T=6 Years

[TeX] Simple \: Interest= \frac{Principal X Rate X Time}{100}[/TeX]

[TeX] = \frac{2750X 3 X 6}{100}[/TeX]=$495

Therefore, Amount in Erin's Account after 6 years =2750+495

=$3,245

Final answer:

The area of the rectangular room with length 2 feet longer than the width can be expressed as w^2 + 2w square feet, where w represents the width of the room.

Explanation:

Barry needs to calculate the area of a rectangular room where the length is 2 feet longer than the width. If we denote the width as w, then the length will be w + 2 feet. The area of a rectangle is found by multiplying the length by the width.

Therefore, the expression for the area in terms of the width will be:

Area = width × length

Area = w × (w + 2 feet)

Area = w² + 2w square feet

This expression will give us the area of the rectangle in square feet.

Answer:

The value of x is 16°

Step-by-step explanation:

Using the formula, angle = 1/2(θ°-x°) :

Let θ = 96°, x = x°, angle = 40°,

1/2×(96°-x°) = 40°

96° - x° = 80°

-x° = 80° - 96°

-x° = -16°

x = 16°

Answer:

5.46 kilograms or 6.6 kilograms  

Step-by-step explanation:

Assume that 2 5 in your question has two possible meaning:

Let divide 9.1 kilograms into 5 equal part

=> 1 equal part =  9.1 / 5 = 1.82 kilograms  

Because 2/5 of this weight is apples, so the weight of apples accounted for 2 equal parts

=> the weight of apples is: 2*1.82 kilograms  = 3.64 kilograms

=>  the weight of pears is: 9.1 kilograms - 3.64 kilograms = 5.46 kilograms

Given the total weight is 9.1 kilograms

=>  the weight of pears is: 9.1 kilograms - 2.5 kilograms = 6.6 kilograms

Final answer:

To find the amount of pears sold, calculate two-fifths of the total weight for the apples and subtract this from the total weight. The farmer sold 5.46 kilograms of pears.

Explanation:

The student has asked a question that requires understanding of basic fractions and weight calculation in a real-life context, specifically within a farmer's market scenario. To solve the problem, we note that the total weight of apples and pears sold is 9.1 kilograms. If two-fifths (2/5) of this weight is apples, then to find the weight of pears, we first calculate the weight of apples and then subtract this from the total weight to get the weight of pears.

Step 1: Calculate the weight of apples by multiplying the total weight by the fraction that represents apples. This is 2/5 of 9.1 kg.

Step 2: Subtract the weight of the apples from the total weight to find the weight of pears.

Here are the calculations:

Weight of apples = (2/5) × 9.1 kg = 3.64 kg

Weight of pears = Total weight - Weight of apples = 9.1 kg - 3.64 kg = 5.46 kg

Therefore, the farmer sold 5.46 kilograms of pears at the farmer's market.

Answer:

x = 50.5°

Step-by-step explanation:

∠ BDC and ∠ BDA are adjacent and supplementary, thus

∠ BDC = 180° - 78° = 102°

Calculate ∠ BCD using the Sine rule in Δ ABC, that is

[tex]\frac{5.6}{sinC}[/tex] = [tex]\frac{9.3}{sin50}[/tex] ( cross- multiply )

9.3 × sinC = 5.6 × sin50° ( divide both sides by 9.3 )

sinC = [tex]\frac{5.6sin50}{9.3}[/tex] ≈ 0.4613, thus

C = [tex]sin^{-1}[/tex] (0.4613 ) ≈ 27.5°

The sum of the 3 angles in Δ BCD = 180°, thus

x = 180° - (102 + 27.5)° = 180° - 129.5° = 50.5°

The angle x is also 52 degrees.

To find the measure of angle x in triangle ABC, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Given that angle A is 78 degrees and angle B is 50 degrees, we can find angle C using the following equation:

Angle C + Angle B + Angle A = 180 degrees

Angle C + 50 degrees + 78 degrees = 180 degrees

Now, subtract the known angles from 180 degrees to find the measure of angle C:

Angle C = 180 degrees - (50 degrees + 78 degrees)

Angle C = 180 degrees - 128 degrees

Angle C = 52 degrees

Now that we know angle C is 52 degrees, we can use the fact that the angles in a triangle add up to 180 degrees to find angle x:

Angle A + Angle B + Angle x = 180 degrees

78 degrees + 50 degrees + Angle x = 180 degrees

Now, subtract the known angles from 180 degrees to find angle x:

Angle x = 180 degrees - (78 degrees + 50 degrees)

Angle x = 180 degrees - 128 degrees

Angle x = 52 degrees

So, angle x is also 52 degrees.

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Answer:

2 Scoring Attempts

Step-by-step explanation:

There are 48 attempts divided by 24 game which equals 2.

Answer:

it is b

Step-by-step explanation:

Answer:

She ran 5 laps

Step-by-step explanation:

Why? Because with each lap stating to be one and a half miles; you first and only step is to divide, seeing how each time you put 1 1/2 into the value of this 7 1/2 miles, you got a lap each time.

you divide 7 1/2 by 1 1/2,

this results in getting, 5

Answer: Erin ran 5 laps.

Step-by-step explanation

if he ran 7 1/2 miles and one lap is 1 1/2 miles then you need to add 1 1/2 miles up until you get the distance he ran which is 7 1/2 miles and when u keep adding 1 1/2 miles to get to 7 1/2 you get 5 laps. hope this helps :)

Answer:

PK represents a radius. Radius only goes half way of the circle.

Answer:

B) chord

Step-by-step explanation:

N and M are two points on the circumference and the segment MN doesn't pass through the centre, so it's a chord

It will take Lin 12 seconds to finish her milkshake. The time it takes Diego to finish his milkshake cannot be determined without the rate at which he drinks.

The problem is about how long it will take for Diego and Lin to finish their milkshakes. Lin is drinking her milkshake at a rate of 1 ounce per second and began with a total of 12 ounces. Therefore, it will take her 12 seconds to finish. For Diego, it doesn't specify how quickly he is drinking his milkshake, which began with 20 ounces, it is impossible to calculate how long it would take him to finish his drink without this information. Hence, to fully solve this problem, you need additional rate information for Diego.

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Answer:

blue marble is the right answer

Answer:

1. Points scored

Step-by-step explanation:

A numerical data is defined as a data that is made up of numbers representing the quantity of a measurement. It is a measurable data such as weight or height, at it can be arranged in ascending or descending order as well as being able to provide an average.

The two types of numeric data are discrete and continuous data

A categorical data is made up of item labels, names or description, that are qualitative in their nature.

Information about a football team that is considered as numeric includes

1. Points scored

Which represents a quantifiable measurement that can be different with different teams and matches

2. Attendance this year.

To eliminate the parameter and find the Cartesian equation of the curve x = 7sin⁡θ,y = cos2⁡θ, we can express x in terms of θ, rearrange the equation, and substitute it into the other equation to eliminate the parameter θ. The resulting equation 2(x/7)² + y - 1 = 0 represents the Cartesian equation of the curve.

To eliminate the parameter and find the Cartesian equation of the curve, we can express x in terms of θ using the given equation x = 7sin⁡θ. Rearranging this equation, we get sin⁡θ = x/7. Similarly, we can express y in terms of θ using the given equation y = cos2⁡θ, which can be rewritten as cos⁡(2θ) = y.

Now we can use the trigonometric identity cos⁡(2θ) = 1 - 2sin²⁡θ to eliminate θ from the equations. Substituting this identity into the second equation, we get 1 - 2(sin⁡θ)² = y.

Simplifying this equation, we have 2(sin⁡θ)² + y - 1 = 0. Finally, we can express sin⁡θ in terms of x using the equation sin⁡θ = x/7, and substitute it into the simplified equation to eliminate θ. This gives us 2(x/7)² + y - 1 = 0, which represents the Cartesian equation of the given curve.

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600 is the total number of pages in the book

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Joshua is reading a book for history class.

He has read 180 pages so far.

This number represents 30% of the total number of pages in the book.

We need to find  total number of pages in the book.

Let x be the number of pages in the book.

30% of x=180

Convert 30% to decimal

30/100x=180

0.3x=180

Divide both sides by 0.3

x=600

Hence, 600 is the total number of pages in the book

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Answer:

B) The misappropriation theory

Step-by-step explanation:

The misappropriation theory states that a person who uses insider information in trading securities has committed securities fraud against the information source.

In this case, Street Bikes Company is the information source because the information rightfully belong to them, Rico trades Street Bikes Stocks because he stole the firm's information which does not belong to him, according to the misappropriation theory, Rico is liable to the offence of insider trading.

Step-by-step explanation:

40° + 90° + 90° + angle ACB = 360°

220° + angle ACB = 360°

angle ACB = 360° - 220°

Therefore angle ACB = 140°

Hope it will help :))

Answer:

If the price before depretiation be P and price after depreciation be Pt..

The eqn would be,

Pt=P(1-12/100)^t

Hope it helps!!

Final answer:

The function to represent the value of a car over time, with an initial value of $9000 and depreciating at 12% per year, is V = 9000(1 - 0.12)^t. This exponential decay function calculates the car's value at any time t years after purchase.

Explanation:

The question asks for a function to represent the value of a car over time, given that the car was purchased for $9000 and depreciates at a rate of 12% per year. To model this, we can use an exponential decay function. The general form of an exponential decay function is V = P(1 - r)^t, where V represents the value of the car at time t, P is the initial purchase price, r is the rate of depreciation, and t is the time in years.

Substituting the given values into the formula, we get V = 9000(1 - 0.12)^t. This function can be used to calculate the value of the car at any given time t years after the purchase. The rate of depreciation (12%) and the initial purchase price ($9000) are the critical factors that determine the car's value over time.

Answer:

3.14 cm squared

Step-by-step explanation:

First, identify the formula necessary to calculate the area of the circle.

Area of a circle = pi x r^2

Remember, the radius is just half of the diameter! Then to square a number, is to multiply it by itself once.

pi x 1^2 =?

pi x 1

Pi

The circumference of your circle is approximately 3.14 cm squared.

Answer:

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

Step-by-step explanation:

sin(2x) + sin(4x) = 0

Use double angle formula.

sin(2x) + 2 sin(2x) cos(2x) = 0

Factor.

sin(2x) (1 + 2 cos(2x)) = 0

Solve.

sin(2x) = 0, cos(2x) = -½

2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

Answer:

30N

Step-by-step explanation:

Normal reaction

The force feel by fist is 30N.

A Force is a push or pull upon an object resulting from the object's interaction with another object.

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

Since you punch a wall with a force of 30N, the fist will feel the same force in the opposite direction as per the Newton's Third Law of Motion.

Hence The force feel by fist is 30N.

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Answer:

11 tshirts would cost £106.15

Step-by-step explanation:

67.55 divided by 7 = 9.65

9.65 x 11 = 106.15

Therefore the total would be £106.15.

Answer: 106.15

Step-by-step explanation:

Answer: -4

Step-by-step explanation:

[tex]3x-7x=x\\-4x=-4x[/tex]

Answer:

The answer is -4x.

Step-by-step explanation:

You can just substract easily by writing 7-3 but remember to add negative to the final value as 3 is smaller than 7 and lastly, you only have to add x to the final answer.

Answer:

40 milimeters

Step-by-step explanation:

8*5=40

Answer:

195¢

Step-by-step explanation:

1 inch of the wire costs

[tex]\frac{85}{17}[/tex] cents

So we just multiply by 39 to get the total cost.

[tex]\frac{85}{17} * 39 = 195[/tex]

Answer: 195 cents

Explanation:

17 inches cost 85 cent

Means 1-inch will cost 85/17 = 5 cents

At the same rate 39 inches will cost 39×5= 195 cents

Answer:

the movie is 2 hours and 10 min long

no it will not be over by 8:45pm

Step-by-step explanation:

if the movie begins at 3:45 pm and the next begins at 6:25pm with a half hour break you need to take 30 min from 6:25 to see what time the movie ended which is 5:55pm then you figure the time between 3:45pm and 5:55pm which is 2hours and 10 min.

since thw movie is starting 20 min late from 6:25pm that is now a start time of 6:45pm if the movie is 2hours and 10 min it will not be over by 8:45pm since that is only 2 hours

About $70.31.

You would take $1968.00 and subtract $421.00 from it. Once you've subtracted, you would have gotten $1547.00. You would divide $1547.00 by the 22 people and get about $70.31 per person. :)