What is the measure of angle x? 1) 10 2) 18 3) 20 4) 25

Answer:

Its c because im quad-RAD-ic... PERIOD LUV

Answer:

Correct answer:  First answer is true

Step-by-step explanation:

Where x is independently variable and refers to the elapsed time and

( i-d )(x) is a function or dependent variable and shows the number of gallons during that time.

f (x) = ( i-d )₍ₓ₎ = 3 x² + 2 - ( 4 x - 1) = 3 x² - 4 x + 3

( i-d )₍ₓ₎ = 3 x² - 4 x + 3

( i-d ) (3) = 3 · 3² - 4 · 3 + 3 = 27 - 12 + 3 = 18

( i-d ) (3) = 18 gallons after 3 hours in the tank

God is with you!!!

There are 18 gallons of liquid in the tank at t = 3 hours

The liquid tank has both an inlet pipe to add liquid and a drain pipe to drain liquid from the tank.

The modeled function of inlet pipe = i(x) = 3[tex]x^{2}[/tex]+2

The modeled function of drain pipe = d(x) = 4x-1 ,

where the rate is measured in gallons per hour in both functions.

(i-d)(x) = 3[tex]x^{2}[/tex]+2-(4x-1)

⇒ (i-d)(x) =  3[tex]x^{2}[/tex]+2-4x+1

⇒ (i-d)(x) =   3[tex]x^{2}[/tex]-4x+3

⇒ (i-d)(3) = 3×[tex]3^{2}[/tex]-4×3+3

⇒ (i-d)(3) = 27-12+3

⇒ (i-d)(3) = 18

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Answer:

Belle's weekly earnings per week in 2008: $245.7

Step-by-step explanation:

The federal minimum wage in the year 2008 was: $6.55

She worked 37.5 hours per week.

She earn each week:

[tex]weekly earnings = 6.55*37.5=245.7[/tex]

Step-by-step explanation:

Below is an attachment containing the solution.

Answer:

16

Step-by-step explanation:

Let x and y be two numbers other than 12.

We have been given that the average (arithmetic mean) of three positive numbers is 10. We can represent this information in an equation as:

[tex]\frac{x+y+12}{3}=10[/tex]

We are also told that the product of the other two numbers is 32. We can represent this information in an equation as:

[tex]x\cdot y=32...(2)[/tex]

[tex]x=\frac{32}{y}[/tex]

Upon substituting this value in above equation, we will get:

[tex]\frac{\frac{32}{y}+y+12}{3}=10[/tex]

[tex]\frac{\frac{32}{y}\cdot y+y\cdot y+12\cdot y}{3}=10\cdot y[/tex]

[tex]\frac{32+y^2+12y}{3}=10y[/tex]

[tex]\frac{32+y^2+12y}{3}\cdot 3=10y\cdot 3[/tex]

[tex]32+y^2+12y=30y[/tex]

[tex]y^2+12y-30y+32=30y-30y[/tex]

[tex]y^2-18y+32=0[/tex]

[tex]y^2-16y+2y+32=0[/tex]

[tex]y(y-16)-2(y-16)=0[/tex]

[tex](y-16)(y-2)=0[/tex]

[tex]y=2, 16[/tex]

Since product of 2 and 16 is 32, therefore, the greatest of the three numbers would be 16.

Answer:

The greatest of the three number is 16.            

Step-by-step explanation:

We are given the following in the question:

Let x and y be the two numbers.

[tex]\text{Mean} = \dfrac{12+x+y}{3} = 10\\\\12 + x + y = 30\\x + y = 18[/tex]

Also

[tex]xy = 32[/tex]

Puting values, we get,

[tex]x(18-x) = 32\\-x^2 + 18x - 32 = 0\\x^2 - 18x + 32 = 0\\(x-16)(x-2) = 0\\x = 16, x = 2[/tex]

When x = 16, y = 2

When x = 2, y = 16

Thus, the greatest of the three number is 16.

Answer: the total cost of this order is $14

Step-by-step explanation:

She sells 3 hot dogs and 2 pretzels for $15.00.

She sells 5 hot dogs and 1 pretzel for $21.50. The system of linear equations used to model the situation is

3h+2p=15 - - - - - - - - - - - -1

5h+p=21.5 - - - - - - - - - - -2

Multiplying equation 1 by 5 and equation 2 by 3, it becomes

15h + 10p = 75

15h + 3p = 64.5

Subtracting, it becomes

7p = 10.5

p = 10.5/7

p = 1.5

Substituting p = 1.5 into equation 1, it becomes

3h + 2 × 1.5 = 15

3h + 3 = 15

3h = 15 - 3 = 12

h = 12/3 = 4

If Tracy sells 2 hot dogs and 4 pretzels, the total cost of this order would be

(4 × 2) + (4 × 1.5)

= 8 + 6 = $14

Answer:

Step-by-step explanation:

X and y =4 so X+y is gonna be 4 X+y+16= and 16 times 4 is 64 so the answer is 64

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes

y = kx

If y = 16 when x = 4, then

16 = 4k

k = 16/4 = 4

Therefore, the direct variation function is

y = 4x

Answer:

[tex]A = 640000\,yd^{2}[/tex]

Step-by-step explanation:

Expression for the rectangular area and perimeter are, respectively:

[tex]A (x,y) = x\cdot y[/tex]

[tex]3200\,yd = 2\cdot (x+y)[/tex]

After some algebraic manipulation, area expression can be reduce to an one-variable form:

[tex]y = 1600 -x[/tex]

[tex]A (x) = x\cdot (1600-x)[/tex]

The first derivative of the previous equation is:

[tex]\frac{dA}{dx}= 1600-2\cdot x[/tex]

Let the expression be equalized to zero:

[tex]1600-2\cdot x=0[/tex]

[tex]x = 800[/tex]

The second derivative is:

[tex]\frac{d^{2}A}{dx^{2}} = -2[/tex]

According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:

[tex]y = 800[/tex]

The maximum area is:

[tex]A = (800\,yd)\cdot (800\,yd)[/tex]

[tex]A = 640000\,yd^{2}[/tex]

Answer:

74/4= 18.5

Step-by-step explanation:

Answer:

c. 3 to 5 observation periods

Step-by-step explanation:

The time that should he spend taking baseline data is 3 to 5 observation periods. The correct option is C).

Data that analyzes conditions before the project begins for subsequent comparison is known as baseline data (or simply baseline). In other words, the baseline serves as the previous point of comparison for the subsequent project monitoring and assessment phases.

For instance, a business can use the number of units sold in the first year as a benchmark against which to compare subsequent annual sales in order to assess the success of a product line. The baseline acts as the benchmark against which all subsequent sales are evaluated.

The performance measurement baseline is the result of combining the three baselines. A baseline is a set timeline that serves as the benchmark against which the project's performance is evaluated.

Therefore, the correct option is C) 3 to 5 observation periods.

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The question is incomplete. Your most probably complete question is given below:

A) 30 minutes

B) 10 observation periods

C) 3 to 5 observation periods !!

D) immediately

Answer:

3, 2, 8, 3, -12

Step-by-step explanation:

d(2x⁴ - 6x²)³/dx

= 3(2x⁴ - 6x²)²(8x³ - 12x)

Answer:  3, 2, 8, 3, -12

Step-by-step explanation:

To find the derivative using the chain rule, multiply by the exponent and the reduce the exponent by 1. Then multiply by the derivative of the inside (of the parenthesis).

 3(2x⁴ - 6x²)² (4·2x³ - 2·6x)

= 3(2x⁴ - 6x²)² (8x³ - 12x)

The blanks from left to right are:

3

2

8

3

-12

Answer:

41

Step-by-step explanation:

There are 3 times as many used bike as new bike.  For the problem to work you have to include the used bikes and the new bikes.  So you divide 164 by 4 instead of three.

So 164/3=41

Number of new bike in showroom is 41 bikes.

Given that;

Total number of bikes in showroom = 164 bikes

3 times Number of new bike = Number of old bikes

Find:

Number of new bikes in showroom

Computation:

Assume;

Number of new bike = a

So,

Number of old bike = 3a

So,

a + 3a = 164

4a = 164

a = 41

So,

Number of new bike = 41

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Answer:

Sample=15 Workers

Population=200 Workers

Step-by-step explanation:

Out of a group of 200 workers, 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the 15 workers selected to participate in the survey.The population consist of 200 workers

SAMPLE: This is a representative part of a population on which a research is about the population is administered

POPULATION: This is the large collection of people or objects that is the focus of a scientific query or research. Often times, the logistics involved in reaching the entire population may be unavailable, so a sample is taken

Final answer:

A group of 200 workers is the population of interest for a survey, and 15 are chosen as a sample to determine the number of miles driven to work each week. The sample represents the subset from which data is collected, while the population encompasses all 200 workers. The effectiveness of the survey depends on the representativeness of the sample.

Explanation:

In the situation described, a group of 200 workers is the overall group of interest for a survey about the number of miles they drive to work each week. Out of these, 15 workers are chosen to participate in the survey. Here, the sample consists of the 15 workers selected to participate in the survey, whereas the population consists of all 200 workers. Sampling is a critical concept in statistics that allows researchers to gather data from a subset of individuals from a larger group to make inferences about the entire group without the need to analyze every individual.

The success of a statistical analysis mainly depends on how well the sample represents the population. In an ideal scenario, a random sample is preferred, where every person in the population has an equal chance of being chosen. This method helps ensure that the sample is representative of the population, allowing findings from the sample to be reasonably generalized to the larger group.

This is a function because each input (x-value) has only one output (y-value). If an input (x-value) has more than one output (y-value) it is not a function. It is still a function if an output has more than one input.

Your answer is A

The probability of no more than 2 successes in 5 trials of a binomial experiment with 18% success rate is the sum of the probabilities of 0, 1, or 2 successes computed individually using the binomial probability formula.

To solve the problem, we use the formula for the probability of x successes in n trials of a binomial experiment, P(x; n, p) = C(n, x) * (p^x) * ((1-p)^(n-x)). 'P' represents the probability of success on a single trial (18% = 0.18 in this case), 'n' is the number of trials (5), 'x' is the number of successes. The symbol C(n, x) stands for the combination of n items taken x at a time.

So, we are looking for the probability of 0, 1, or 2 successes. We then add those three probabilities together:

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Answer:

yˆ=1.225x^2−88x+1697.376 is correct for all future users

Step-by-step explanation:

Quadratic regression equation: [tex]\( y = -0.5235x^2 - 1.9836x + 1931.2 \)[/tex], derived using sums and solving the normal equations.

To find the quadratic regression equation for the given data set, we need to fit a quadratic model of the form:

[tex]\[ y = ax^2 + bx + c \][/tex]

The data set provided is:

[tex]\[ (2, 1526.28), (3, 1444.4), (5, 1288), (6, 1213.48), (8, 1071.78), (10, 939.88), (20, 427.38) \][/tex]

We'll use the least squares method to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. This involves solving the system of equations derived from the normal equations for quadratic regression.

Steps to Calculate Quadratic Regression Coefficients

1. Calculate the necessary sums:

  [tex]\[ \sum x_i, \sum y_i, \sum x_i^2, \sum x_i^3, \sum x_i^4, \sum x_i y_i, \sum x_i^2 y_i \][/tex]

  Given data:

|        [tex]$x$[/tex]     |        [tex]$y$[/tex]      |

|        2     | 1526.28 |

|        3     | 1444.4    |

|        5     |   1288     |

|        6     |   1213.48 |

|        8     | 1071.78   |

|       10     | 939.88   |

|       20    | 427.38   |

  Calculate the following sums:

  [tex]\[ \sum x_i = 2 + 3 + 5 + 6 + 8 + 10 + 20 = 54 \][/tex]

  [tex]\[ \sum y_i = 1526.28 + 1444.4 + 1288 + 1213.48 + 1071.78 + 939.88 + 427.38 = 7911.2 \][/tex]

 [tex]\[ \sum x_i^2 = 2^2 + 3^2 + 5^2 + 6^2 + 8^2 + 10^2 + 20^2 = 4 + 9 + 25 + 36 + 64 + 100 + 400 = 638 \][/tex]

   [tex]\[ \sum x_i^3 = 2^3 + 3^3 + 5^3 + 6^3 + 8^3 + 10^3 + 20^3 = 8 + 27 + 125 + 216 + 512 + 1000 + 8000 = 9888 \][/tex]

  [tex]\[ \sum x_i^4 = 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 10^4 + 20^4 = 16 + 81 + 625 + 1296 + 4096 + 10000 + 160000 = 176114 \][/tex]

  [tex]\[ \sum x_i y_i = 2 \cdot 1526.28 + 3 \cdot 1444.4 + 5 \cdot 1288 + 6 \cdot 1213.48 + 8 \cdot 1071.78 + 10 \cdot 939.88 + 20 \cdot 427.38 = 3052.56 + 4333.2 + 6440 + 7280.88 + 8574.24 + 9398.8 + 8547.6 = 47016.28 \][/tex]

  [tex]\[ \sum x_i^2 y_i = 2^2 \cdot 1526.28 + 3^2 \cdot 1444.4 + 5^2 \cdot 1288 + 6^2 \cdot 1213.48 + 8^2 \cdot 1071.78 + 10^2 \cdot 939.88 + 20^2 \cdot 427.38 = 4 \cdot 1526.28 + 9 \cdot 1444.4 + 25 \cdot 1288 + 36 \cdot 1213.48 + 64 \cdot 1071.78 + 100 \cdot 939.88 + 400 \cdot 427.38 = 6105.12 + 12999.6 + 32200 + 43685.28 + 68593.92 + 93988 + 170952 = 346524.92 \][/tex]

2. Set up the normal equations:

  [tex]\[ \begin{cases} n c + \sum x_i b + \sum x_i^2 a = \sum y_i \\ \sum x_i c + \sum x_i^2 b + \sum x_i^3 a = \sum x_i y_i \\ \sum x_i^2 c + \sum x_i^3 b + \sum x_i^4 a = \sum x_i^2 y_i \\ \end{cases} \][/tex]

  Substituting the calculated sums:

  [tex]\[ \begin{cases} 7c + 54b + 638a = 7911.2 \\ 54c + 638b + 9888a = 47016.28 \\ 638c + 9888b + 176114a = 346524.92 \\ \end{cases} \][/tex]

3. Solve the system of equations:

  Use a method such as Gaussian elimination or matrix operations to solve for [tex]\(a\), \(b\), and \(c\)[/tex].

Using a computational tool to solve this system, we get the coefficients [tex]\(a\), \(b\), and \(c\)[/tex]:

  [tex]\[ a \approx -0.5235, \quad b \approx -1.9836, \quad c \approx 1931.1561 \][/tex]

Quadratic Regression Equation:

  [tex]\[ y = -0.5235x^2 - 1.9836x + 1931.1561 \][/tex]

So, the quadratic regression equation for the given data set is:

[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.2 \][/tex]

The correct question is:

What is the quadratic regression equation for the data set?

[tex]$$\begin{aligned}& x y \\& 21526.28 \\& 31444.4 \\& 51288 \\& 61213.48 \\& 81071.78 \\& 10939.88 \\& 20427.38\end{aligned}$$[/tex]

Answer:

  d = (21√13)/130 ≈ 0.582435

Step-by-step explanation:

First of all, you need to put one of the equations into general form (Ax +By +C = 0), so you can make use of the formula. Multiplying the first equation by 6, we have ...

  6y = -4x -3

Adding the opposite of the right side, we have the general form equation ...

  4x +6y +3 = 0

___

The distance formula will tell you the distance from this line to any point. To find the distance between the two lines, you need to choose the point to be one that is on the other line. It is probably convenient to use the y-intercept, (0, 1/5).

The formula is ...

  d = |4x +6y +3|/√(4²+6²)

The distance from the point (0, 1/5) is ...

  d = |4·0 +6(1/5) +3|/√52 = 4.2/(2√13)

  d = (21/130)√13 . . . . . with denominator rationalized

_____

Alternate solution

Another way to do this is to put the equations of both lines into the same general form, differing only in their constant "C".

Multiplying both equations by 30, we get ...

  30y = -20x -15

  30y = -20x +6

So, the two general form equations are ...

  20x +30y +15 = 0

  20x +30y -6 = 0

The distance between the two lines is a fraction of the difference of the constants in the equations*. It will be ...

  |15 -(-6)|/√(20² +30²) = 21/√1300 = 21/(10√13) = (21√13)/130 . . . . as above

___

* Any (x, y) pair that satisfies the first equation will make 20x+30y = -15. Using the second equation in the distance formula, you then have |-15-6|/√( ) = d. The number in the numerator is the difference of the two constants "C".

Answer:

Step-by-step explanation:

Put the value of x = 2 and the value of y = 5 from the given point to the equations and check the equality.

x + 3 = y

2 + 3 = 5

5 = 5          CORRECT

7 - x = y

7 - 2 = 5

5 = 5           CORRECT

4 + x = y

4 + 2 = 5

6 = 5        FALSE

y = 2x

5 = 2(2)

5 = 4             FALSE

Answer:

y 2x

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

The diameter of the wheel is 29 in.

The circumference of the wheel is 3.14 × 29 in = 91.06 in.

For each revolution, the bike moves forward one circumference.  So the number of revolutions is (200 ft × 12 in/ft) / 91.06 in ≈ 26.

[tex](2x+1)(x-2) = 0[/tex]

Multiplying the factors we obtain:

[tex]2x\cdot x+2x\cdot (-2)+1\cdot x+1\cdot (-2)=0[/tex]

[tex]2x^2-4x+x-2=0[/tex]

[tex]2x^2-3x-2=0[/tex]

The general form of quadratic equation is:

[tex]ax^2+bx+c=0[/tex]

Therefore,

[tex]a=2[/tex]

[tex]b=-3[/tex]

[tex]c=-2[/tex]

The correct answer is the first one.

Answer:

Step-by-step explanation:

a) Profit is the difference between revenue and cost.

  P(y) = R(y) -C(y)

  P(y) = (0.005y² +10y) -(20y +1000000) . . . . use the functions for revenue and cost

  P(y) = 0.005y² -10y -1000000 . . . . . profit as a function of y

___

b) Evaluating this function for y=30,000, we get ...

  P(30000) = 0.005(30000)² -10(30000) -1000000

  = 3,200,000

The company will have a profit of 3,200,000 from the sale of 30,000 cars.

Answer:

9 ft × 7 ft × 1 ft and 21 ft × 3 ft × 1 ft

Step-by-step explanation:

The formula for the volume of a rectangular prism is

V = lwh

The prime factors of 63 are

3, 3, and 7.

Most raised garden beds are 1 ft deep, so two combinations that would work are

(3 × 3) × 7 × 1 =   9 ft × 7 ft × 1 ft = 63 ft³

3 × (3 × 7) × 1 = 21 ft × 3 ft × 1 ft = 63 ft³

Answer:

Step-by-step explanation:

This is a parabola.  The only way you could find the actual rate of change at those x values is by finding the instantaneous rate of change at each of those points which requires calculus.  The average rate of change is found when you find the slope of the line between the 2 points (-20, y) and (-15, y).  To find y in each case, sub in the x values and solve for y:

[tex]f(-20)=(-20)^2+7(-20)+10[/tex] and

f(-20) = 270 and the resulting coordinate is (-20, 270).

Likewise for f(-15):

[tex]f(-15)=(-15)^2+7(-15)+10[/tex] and

f(-15) = 130 and the resulting coordinate is (-15, 130)

Applying the slope formula now will find the average rate of change between those 2 points:

[tex]m=\frac{130-270}{-15-(-20)}[/tex] which simplifies to

[tex]m=\frac{-140}{5}[/tex] so

m = -28

Answer: 275 cm squared

Step-by-step explanation: We need to divide the shapes first into smaller areas, and since all the areas we need are given to us, we just need to break it apart into smaller parts that we can find the area for.

Length x Width = Area

Answer:

¼

Step-by-step explanation:

BBBB

GGGG

BBBG

BBGB

BGBB

GBBB

GGGB

GGBG

GBGG

BGGG

BBGG

GGBB

GBGB

BGBG

GBBG

BGGB

3G and 1B

4/16 = 1/4

Using probability and sample space concepts, it is found that there is a 0.25 = 25% probability of getting three girls and one boy (in any order ).

-------------------------

-------------------------

For 4 children, the sample space is given by:

B - B - B - B

B - B - B - G

B - B - G - B

B - B - G - G

B - G - B - B

B - G - B - G

B - G - G - B

B - G - G - G

G - B - B - B

G - B - B - G

G - B - G - B

G - B - G - G

G - G - B - B

G - G - B - G

G - G - G - B

G - G - G - G

-------------------------

Thus:

[tex]p = \frac{D}{T} = \frac{4}{16} = 0.25[/tex]

0.25 = 25% probability of getting three girls and one boy (in any order ).

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Answer:

1. Carissa must scoop out of the sink 125 cups of water with the first cup to empty it.

2. Carissa must scoop out of the sink 31 cups of water with the second cup to empty it.

Step-by-step explanation:

1. Let's calculate the volume of the first cup, this way:

d = 4 ⇒ r =2

Volume of the first cup = π * r² * h /3

Volume of the first cup = π * 2² * 8 /3

Volume of the first cup = 32/3π in³

2. Let's calculate the volume of the second cup, this way:

d = 8 ⇒ r = 4

Volume of the second cup = π * r² * h /3

Volume of the second cup = π * 4² * 8 /3

Volume of the second cup = 128/3π in³

3. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the first cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the first cup

Number of cups = (4000π/3)/(32π/3)

Number of cups = 4,000π/3 * 3/32π (multiplying by the reciprocal)

We eliminated 3 and π in the numerator and denominator

Number of cups = 4,000/32 = 125

4. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the second cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the second cup

Number of cups = (4000π/3)/(128π/3)

Number of cups = 4,000π/3 * 3/128π (multiplying by the reciprocal)

Number of cups = 4,000/128 = 31.25

We eliminated 3 and π in the numerator and denominator

Number of cups = 31 (rounding to the next whole)

Answer:

a = 1

h = -1

k = 2

Vertex: (-1,2)

It's a V-shaped graph completely above the x-axis.

Vertex at (-1,2) and y-intercept at 3

For the function f(x)=|x+1|+2, a = 1, indicating no vertical stretch or compression and upward direction, h = -1 indicating a shift one unit to the left, and k = 2 indicates a shift two units up. The vertex of the function is at point (-1,2).

The function f(x)=|x+1|+2 is a transformation of the base absolute value function |x|. Here, the 'a' refers to the vertical stretch/compression and reflection, 'h' refers to the horizontal shift, and 'k' refers to the vertical shift. The absolute value function is in the form f(x) = a|x-h|+k. For this specific function, a = 1 since the graph opens upward and is not stretched or compressed, h = -1 because the function is shifted 1 unit to the left, and k = 2 because the function is shifted 2 units up. As the vertex of an absolute value function is the point of its highest or lowest value, the vertex in this case is the point (-1,2).

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Answer:

Step-by-step explanation:

There are total 5 types of sampling.

Since, in the given question the students are chosen randomly, Random sampling is being used here.

Answer: The same trip will require 3.8 hours.

Step-by-step explanation:

Since we have given that

Time = [tex]4\dfrac{1}{2}=\dfrac{9}{2}[/tex]

Speed = 55 mph

So, distance would be

[tex]Speed\times time=55\times 4.5=247.5\ miles[/tex]

If the speed limit = 65 mph

So, time will be

[tex]\dfrac{247.5}{65}=3.8\ hours[/tex]

Hence, the same trip will require 3.8 hours.

Answer: 83 points

Step-by-step explanation:

To find the first game we must divide 747 by 9, because 747 is 9 times the amount of points scored in the first game.

Divide 747 by 9

747/9= 83

They scored 83 points in the first game

Hope this helped!

Answer:

The area of the rectangle is increasing at a rate of  [tex]22\ cm^2/s[/tex].

Step-by-step explanation:

Given : The width of a rectangle is increasing at a rate of 2 cm/ sec. While the length increases at 3 cm/sec.

To find : At what rate is the area increasing when w = 4 cm and I = 5 cm?

Solution :

The area of the rectangle with length 'l' and width 'w' is given by  [tex]A=l w[/tex]

Derivative w.r.t  't',

[tex]\frac{dA}{dt}=w\frac{dl}{dt}+l\frac{dw}{dt}[/tex]

Now, we have given

[tex]\frac{dl}{dt}=3\ cm/s[/tex]

[tex]l=5\ cm[/tex]

[tex]\frac{dw}{dt}=2\ cm/s[/tex]

[tex]w=4\ cm[/tex]

Substitute all the values,

[tex]\frac{dA}{dt}=(4)(3)+(5)(2)[/tex]

[tex]\frac{dA}{dt}=12+10[/tex]

[tex]\frac{dA}{dt}=22\ cm^2/s[/tex]

Therefore, the area of the rectangle is increasing at a rate of  [tex]22\ cm^2/s[/tex].

The area of rectangle is increasing at rate of 22 cm/ second.

Let us consider the length and width of rectangle is L and W respectively.

Given that,  [tex]\frac{dW}{dt}=2cm/s,\frac{dL}{dt}=3cm/s[/tex]

Area of rectangle is,

                                   [tex]A = L *W[/tex]

Differentiate above expression with respect to time t.

     [tex]\frac{dA}{dt} =L\frac{dW}{dt}+W\frac{dL}{dt} \\\\\frac{dA}{dt}=2L+3W[/tex]

substituting w = 4cm and L = 5cm in above expression.

   [tex]\frac{dA}{dt} =2(5)+3(4)=22cm/s[/tex]

Thus, The area of rectangle is increasing at rate of 22 cm/ second.

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Answer: the value of the car will be about $12634

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^ t

Where

A represents the value of the car after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate of decay.

From the information given,

P = $22000

r = 10.5% = 10.5/100 = 0.105

t = 5 years

Therefore

A = 22000(1 - 0.105)^5

A = 22000(0.895)^5

A = $12634