The equation r = 3cos(6θ) represents a rose curve. How many petals does the graph contain

Step-by-step explanation:

Looks as though it has been cropped.....picture is only a PART of the original...it has been 'cut off'  or 'cropped' on both sides .

The product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.

To represent the product of a complex number and a real number on the complex plane:

We multiply the real part and the imaginary part of the complex number by the real number.

The magnitude (or length) of the resulting complex number is multiplied by the absolute value of the real number.

The angle (or argument) of the resulting complex number is the same as the angle of the original complex number.

For the product of 2−4i and 3:

We multiply the real part (2) and the imaginary part (-4i) of the complex number by the real number (3), to get:

3(2) + 3(-4i) = 6 - 12i

The magnitude of the resulting complex number is:

|6 - 12i| = √(6² + (-12)²) = √180 = 6√5

The angle of the resulting complex number is the same as the angle of the original complex number (2-4i), which can be found using the inverse tangent function:

tanθ = (imaginary part) / (real part) = (-4) / 2 = -2

θ = atan(-2) ≈ -1.107 radians or ≈ -63.43 degrees

Therefore, the product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.

To know more about complex number refer here:

https://brainly.com/question/20566728

#SPJ11

the actual perimeter of the living room  in the scale drawing  is 216 inches.

We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.

When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.

When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.

When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.

One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.

You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.

If the length and breadth of the living room in real life are 9/4 inches each, we can use the given scale of the drawing to find the corresponding dimensions of the living room in the drawing:

1/4 inch = 2 feet

So, 9/4 inches in real life is equal to:

(9/4) inches / (1/4 inch per 2 feet) = 18 feet

This means that each side of the living room in the drawing would be 18/2 = 9 inches long.

To find the actual perimeter of the living room, we need to convert the dimensions back to real-life measurements and add up the lengths of all four sides:

Length in real life = 9/4 inches x 2 x 12 inches/foot = 54 inches

Breadth in real life = 9/4 inches x 2 x 12 inches/foot = 54 inches

Perimeter in real life = 2 x (Length + Breadth)

Perimeter in real life = 2 x (54 inches + 54 inches)

Perimeter in real life = 2 x 108 inches

Perimeter in real life = 216 inches

Therefore, the actual perimeter of the living room is 216 inches.

To know more about scale drawing visit :-

brainly.com/question/17388747

#SPJ1

The quantity that gives maximum profit is 1,750 units.

To find the quantity that gives maximum profit, we first need to determine the profit function.

Profit = Total Revenue - Total Cost

Total Revenue is given by the price (p) times the quantity (q):

TR = pq

Since the corporation has monopolistic control, it can set the price to maximize profit. We can use the demand function

to find the price that will maximize profit:

Q = 180,000 - 50p

Solving for p, we get:

p = 3,600 - 0.02Q

Now we can substitute this into the profit equation:

Profit =[tex](3,600 - 0.02Q)Q - (900 + 100Q + Q^2)[/tex]

Simplifying:

Profit = [tex]-Q^2 + 3,500Q - 900[/tex]

To find the quantity that gives maximum profit, we can take the derivative of the profit function with respect to Q and

set it equal to zero:

[tex]d/dQ (-Q^2 + 3,500Q - 900) = 0[/tex]

-2Q + 3,500 = 0

Q = 1,750

for such more question on  maximum profit

https://brainly.com/question/11251879

#SPJ11

Answer:

the answer is D

Step-by-step explanation:

Answer:

C. x = 2 1/3, y = 1 1/3.

Step-by-step explanation:

To solve this question, we need to plot the two equations on the graph and see where they cross. The graph below shows the two lines in different colors:

Answer:

0.16 gallons of paint

the number lies between 0 and 1

Step-by-step explanation:

Chairs and tables used the same amount of paint,

20x + 5x = 4

25x = 4

x = 0.16

So, each piece of furniture will use 0.16 gallons of paint.

The solution to the  Linear equation is x = 1.5.

The math equation for the given problem is 15 - x = 7x + 3.

To solve this equation, first simplify it by combining like terms on one side of the equation.

15 - x - 7x = 3

Next, combine like terms on the left side of the equation.

15 - 8x = 3

Now, isolate the variable by subtracting 15 from both sides of the equation.

-8x = -12

Finally, solve for x by dividing both sides by -8.

x = 1.5

Therefore, the solution to the equation is x = 1.5.

To summarize, the linear equation 15 - x = 7x + 3, we simplify it by combining like terms. Subtracting x and 7x from both sides gives us 15 - 8x = 3. Next, we isolate the variable by subtracting 15 from both sides, resulting in -8x = -12.

Finally, we solve for x by dividing both sides by -8, giving us x = 1.5. This means that when we substitute x with 1.5 in the original equation, both sides will be equal. The solution x = 1.5 satisfies the equation and represents the value at which the equation is true.

To learn more about Linear equation go to :

https://brainly.com/question/11897796#

#SPJ11

Answer:

x=81

Step-by-step explanation:

Rewrite log_3 (x)=4 in exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then log_b(x)=y is equivalent to b^y=x.

Rewrite the equation as x=3^4

Raise 3 to the power of 4 

x=81

The amount of interest Amy will pay over the 3 years is $105.

Simple interest is a method of calculating the interest amount on a loan or investment by multiplying the principal amount, the annual interest rate, and the time in years. In Amy's case, she borrowed $1,000 with an annual interest rate of 3.5% and will take 3 years to pay back the loan.

To calculate the interest Amy will pay, use the formula: Interest = Principal x Rate x Time

Interest = $1,000 x 0.035 (3.5% as a decimal) x 3 years

Interest = $1,000 x 0.035 x 3 = $105

Amy will pay $105 in interest over the 3 years.

Learn more about Simple interest here: https://brainly.com/question/25845758

#SPJ11

a. The cost for a 100-mile radius for 3 weeks is $585, and there are 98 resumes within this radius, so the average cost per resume would be:

$585 / 98 = $5.96 per resume

b. The cost for a 150-mile radius for 3 weeks is $675, and there are 208 resumes within this radius, so the average cost per resume would be:

$675 / 208 = $3.25 per resume

c. If an employer opts for the 150-mile radius option instead of the 100-mile radius option, they would pay an extra $90 ($675 - $585) to see an additional 110 resumes (208 - 98).

The average cost to the employer for looking at each extra resume would be:

$90 / 110 = $0.82 per resume

d. An advantage of opting for the more expensive plan is that the employer would have access to a larger pool of potential candidates, which could increase the likelihood of finding a qualified applicant.

A disadvantage is that the employer would have to pay more money, which could be a significant expense for smaller businesses or those with limited budgets.

To know more about resumes refer here

https://brainly.com/question/862477#

#SPJ11

To apply the pigeonhole principle, we need to determine the number of pigeonholes and the number of pigeons. The pigeonhole principle cannot be applied to this question.

In this case, the"  holes" are the high minidresses and the" lockers" are the ranges of  particular records. Let's assume that the range of  particular records is from 6  bases( 72  elevation) to 7  bases( 84  elevation).   The difference between the upper and lower bounds of the range is

84- 72 =  12  elevation.

We can divide this range into five subintervals of length2.4  elevation( 72,74.4),(74.4,76.8),(76.8,79.2),(79.2,81.6), and(81.6, 84).  

Since there are only five subintervals, but we've three high minidresses, it isn't  inescapably true that two of the  platoon members must have  particular records that are within four  elevation of each other. For  illustration, if the three high minidresses have  particular records of 6  bases 3  elevation( 75  elevation), 6  bases 7  elevation( 79  elevation), and 7  bases( 84  elevation),  also none of them have  particular records within four  elevation of each other.

Learn more about  pigeonhole principle at

https://brainly.com/question/29242775

#SPJ4

The serum be said to be effective can't be concluded, since the test statistic is less than the critical value, we fail to reject the null hypothesis.

Let [tex]n_A[/tex] denotes the number of mice which receiving treatment. Therefore,

[tex]n_A[/tex] = 5,

Let [tex]n_B[/tex] denotes the number of mice which do not receive treatment. Therefore, [tex]n_B[/tex] = 4

Survival times for the mice receiving the treatment are: 2.1; 5.3; 1.4; 4.6; 0.9

Survival times for the mice not receiving the treatment are: 1.9; 0.5; 2.8; 3.1

Let [tex]x_A[/tex] be the mean of survival time for the mice receiving the treatment and [tex]x_B[/tex] be the mean of survival time for the mice not receiving the treatment.

We have: [tex]x_A[/tex] = 2.86

[tex]x_B[/tex] = 2.075

Standard deviation be:

[tex]S_A=\sqrt{\frac{\sum (x_a-x_A)^2}{n_A-1} }[/tex]

[tex]=\sqrt{\frac{[(2.1-2.86)^2+(5.3-2.86)^2+(1.4-2.86)^2+(4.6-2.86)^2+(0.9-2.86)^2]}{4} }[/tex]

= 1.971

[tex]S_B=\sqrt{\frac{\sum (x_b-x_B)^2}{n_B-1} }[/tex]

[tex]=\sqrt{\frac{[(1.9-2.08)^2+(0.5-2.08)^2+(2.8-2.08)^2+(3.1-2.08)^2]}{3} }[/tex]

= 1.167

[tex]\mu_A[/tex] and [tex]\mu_B[/tex]  are population means for the groups receiving the treatment and not receiving the treatment respectively.

Level of significance is α = 0.05

If P-value is less then 0.05, we will reject [tex]H_o[/tex]

The test statistic is,

[tex]t=\frac{(x_A-x_B)-(\mu_A-\mu_B)}{s_p\sqrt{\frac{1}{n1} +\frac{1}{n2} } }[/tex]

[tex]=\frac{2.86-2.07)-(0)}{1.674388\sqrt{\frac{1}{5} +\frac{1}4} } }[/tex]

= 0.79/1.123

t = 0.70

Degrees of freedom is,

[tex]d_f=n_A+n_B-2[/tex]

= 5 + 4 - 2

= 7.

According to the value in the table, the test's critical value is 1.895.

We are unable to reject the null hypothesis since the test statistic is less than the threshold value.

We thus cannot draw the conclusion that the serum is working.

Learn more about the Test statistics:

https://brainly.com/question/15980493

#SPJ4

To build a ramp with a 15-inch rise for rolling gym equipment into your school, following ADA specifications, we should create a ramp with a run of 180 inches to maintain a 1:12 slope.

For building a ramp with a rise of 15 inches for rolling gym equipment into your school, following ADA specifications. Let's use these terms in our step-by-step explanation:

1. ADA specifications: The Americans with Disabilities Act (ADA) specifies that the slope of a ramp should be no more than 1:12, which means that for every 1 inch of rise, there should be 12 inches of run.

2. Ramp rise: In this case, the rise is 15 inches.

3. Calculate ramp run: To find the ramp run, we can use the ADA specification of 1:12. Multiply the rise (15 inches) by 12.

15 inches x 12 = 180 inches

4. Ramp run: Based on the calculation, the run for the ramp should be 180 inches.

5. Ramp length: To ensure a safe and accessible ramp, follow the ADA specifications and use a ramp length of 180 inches to achieve the 15-inch rise.

To know more about ADA specifications refer to

https://brainly.com/question/30286625

#SPJ11

r has negative values when 2 cos θ > 1, and positive values otherwise.

r has negative values when 3θ is in the second or third quadrant, and positive values otherwise.

r has negative values when sin θ > 1/5, and positive values otherwise.

To find the intervals of positive and negative r values, we need to look at the cosine function. Since the cosine function has a maximum value of 1, we have r = 1 - 2 cos θ ≥ -1. Solving for cos θ, we get 2 cos θ ≤ 2, which means that r is negative when 2 cos θ > 1 and positive otherwise.

We can rewrite the polar equation r = 5 sin (3θ) as r = 5(sin θ)(cos^2 θ)(3)^(1/2). This equation is negative when sin θ is negative, which happens in the second and third quadrants. Therefore, r is negative when 3θ is in the second or third quadrant and positive otherwise.

Similarly, we can rewrite the polar equation r = 1 - 5 sin θ as r = 5(cos θ)(sin(π/2 - θ)). This equation is negative when sin(π/2 - θ) is negative, which happens when θ is in the second and third quadrants. Therefore, r is negative when sin θ > 1/5, and positive otherwise.

For more questions like Function click the link below:

https://brainly.com/question/16008229

#SPJ11

When a multiple regression model created incorrectly then leaves out one and more than one important factors are omitted.

Multiple regression is a statistical way that can be used to analyze the relationship between a single dependent variable and several independent variables. Equation is written as y =

We have regressors x₁ and x₂ where both variables are determinants of the dependent variable. you first regressor y on x₁ only and find no relationship. however when regressing y on x₁ and x₂.

For more information about multiple regression model, visit:

https://brainly.com/question/28167705

#SPJ4

Complete question:

consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. you first regress y on x1 only and find no relationship. however when regressing y on x1 and x2, the slope coefficient changes by a large amount. this suggests that your first regression suffers from:

The ladder makes an angle of approximately 82 degrees with the ground when it is extended to a length of 18 feet and the bottom of the ladder is 4.5 feet from the base of the building.

To determine the angle that the ladder makes with the ground, we can use trigonometry. Let x be the height of the ladder when it is leaned against the building. Then, using the Pythagorean theorem, we have: [tex]x^{2}[/tex] + [tex]4.5^{2}[/tex] = [tex]18^{2}[/tex]

Solving for x, we get: x = sqrt([tex]18^{2}[/tex] - [tex]4.5^{2}[/tex]), x ≈ 17.29

Therefore, the ladder makes an angle θ with the ground such that: sin θ = opposite/hypotenuse = x/18, θ = arcsin(x/18)

Substituting x ≈ 17.29, we get: θ ≈ 81.99 degrees

Therefore, the ladder makes an angle of approximately 82 degrees with the ground when it is extended to a length of 18 feet and the bottom of the ladder is 4.5 feet from the base of the building.

To know more about Pythagorean theorem, refer here:

https://brainly.com/question/14930619#

#SPJ11

The length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.

Aspect ratio refers to the proportional relationship between the width and height of an image or screen. In the case of a wide screen TV, the aspect ratio is 2.39:1, which means that for every 2.39 units of width, there is 1 unit of height.

To find the length of the diagonal of a wide screen TV with an area of 150 inches, we need to use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the width and height.

First, we need to find the width and height of the TV screen. We can do this by setting up the equation:

2.39x^2 = 150

where x is the width of the screen. Solving for x, we get:

x = √(150/2.39) = 10.87 inches

Now we can find the height by dividing the width by the aspect ratio:

h = 10.87 / 2.39 = 4.55 inches

Using the Pythagorean theorem, we can find the length of the diagonal:

d^2 = 10.87^2 + 4.55^2 = 126.68

d = √126.68 = 11.25 inches

Therefore, the length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.

To know more about aspect ratio, visit:

https://brainly.com/question/18492629#

#SPJ11

The equation which most accurately represents the word problem,  is (b) 68 = 2L + 2(9).

The word problem states that the perimeter of a rectangle is 68 inches, and the perimeter equals twice the length (L) plus twice the width (9). We can represent this relationship by using the equation as :

We know that, the perimeter of rectangle is : 2(length + width),

Substituting the value,

We get,

⇒ 68 = 2(L + 9);

⇒ 68 = 2L + 2(9); and this statement is represented by Option(b).

Therefore, the correct equation is (b) 68 = 2L + 2(9).

Learn more about Equation here

https://brainly.com/question/1681271

#SPJ1

The given question is incomplete, the complete question is

Select the equation that most accurately depicts the word problem.

"The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches".

(a) 68 = 9(L + 2)

(b) 68 = 2L + 2(9)

(c) 68 = 2(L - 9)

(d) 68 = 9L + 2

(e) 68 = 2/L + 2/9

(f) 68 = L/2 + 2(9)

Under the federal list, the total amount of exemptions that Jerry would be allowed is $27,900.

Under the state list, the total amount of exemptions that Jerry would be allowed is $37,500.

Under the federal list, Jerry's exemptions can only be be:

Equity in home:                     $15,000

Motor vehicle:                        $2,400

Household goods:                  $8,000

Tools (for debtor’s trade):       $1,500

Total exemptions              =   $27,900

Under the state list, Jerry's exemptions can only be be

Equity in home:                               $25,000

Motor vehicle:                                $1,500

Household goods:                          $6,000

Tools:                                               $5,000

Total exemptions =                       $37,500

Based on the above, the state list can be more favorable for Jerry as it will give him  a lot of exemption a higher total value of assets.

Learn more about exemptions  from

https://brainly.com/question/2170674

#SPJ1

See full question below

Computing Exemptions Under Chapter 7 Bankruptcy

Assume the current federal bankruptcy exemptions are listed at the left, and the state exemptions are

listed at the right. The debtor may use the exemption table that best benefits him or her. For the two

circumstances shown below, compute the exemption amounts and decide which will be better for the

debtor—the federal list or the state list.

LIST A. FEDERAL EXEMPTIONS

Equity in home .......................................$15,000

Motor vehicle .............................................2,400

Household goods .......................................8,000

($400 limit for a single item)

Jewelry .......................................................1,000

Other property ..............................................800

Tools (for debtor’s trade) ...........................1,500

LIST B. STATE EXEMPTIONS

Equity in home ....................................... $25,000

Motor vehicle ............................................. 1,500

Household goods ..................................... 10,000

($1,000 limit for a single item)

Jewelry .......................................................... 500

Other property .............................................. 100

Tools ........................................................... 5,000

1. Jerry has the following assets: a house with equity of $15,000, a car with equity of $2,500, and household goods worth $6,000 (no single item over $400). He also has tools worth $5,800 that he needs for his business. What is the total amount of exemptions Jerry would be allowed using the federal list? The state list? Which list will be more favorable for him? SHOW YOUR WORK!

When all 967 tickets are purchased, the probability of not winning is 0 (or 0%).

The probability of an event occurring is defined by probability. There are numerous real-life scenarios in which we must forecast the outcome of an occurrence.

To find the probability of not winning the TV with a given number of tickets, we need to calculate the ratio of the number of losing tickets to the total number of tickets. The completed table is as follows:

Number of Tickets | Number of Losing Tickets | Probability of Not Winning

-----------------|-------------------------|----------------------------

      0         |           967           |           1.000        

      1         |           966           |           0.999        

      10        |           957           |           0.990        

      50        |           917           |           0.948        

      100       |           867           |           0.897        

      200       |           767           |           0.793        

      300       |           667           |           0.690        

      400       |           567           |           0.587        

      500       |           467           |           0.483        

      600       |           367           |           0.380        

      700       |           267           |           0.277        

      800       |           167           |           0.173        

      900       |            67           |           0.069        

      967       |             0           |           0.000        

As the number of tickets purchased increases, the probability of not winning the TV decreases. When no tickets are purchased, the probability of not winning is 1 (or 100%). When all 967 tickets are purchased, the probability of not winning is 0 (or 0%).

Learn more about probability on:

https://brainly.com/question/13604758

#SPJ4

The numerical value of the two-sample t-statistic for this test is 0.414 . So, the correct option is A).

To determine if there is a significant difference in the mean bacterial concentration in air between carpeted and uncarpeted rooms, the two-sample t-test can be used.

First, we need to calculate the sample means and standard deviations for each group. The sample mean for the carpeted rooms is 22.0 with a standard deviation of 184, while the sample mean for the uncarpeted rooms is 16.9 with a standard deviation of 175.

Next, we can calculate the t-statistic using the formula

t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^0.5

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values, we get

t = (22.0 - 16.9) / ((184^2/7 + 175^2/7)^0.5) = 0.414

Comparing the calculated t-value with the critical t-value for a two-tailed test with 12 degrees of freedom at a 0.05 significance level, we find that the critical t-value is 2.179. Since the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis and conclude that there is no significant difference in the mean bacterial concentration in air between carpeted and uncarpeted rooms.

So, the correct answer is A).

To know more about t-statistic:

https://brainly.com/question/15236063

#SPJ4

A graph that shows a line on the scatter plot that fits the data include the following: B. scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 2 and 8 comma 4.

In Mathematics and Geometry, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:

By critically observing the scatter plot using the aforementioned characteristics, we can reasonably and logically deduce that line B represents the line of best fit because the data points are in a linear pattern.

Read more on line of best fit here: brainly.com/question/12284501

#SPJ1

Interpretation:

The regression coefficient b = 16.6 represents the change in the predicted ozone level (in parts per million) for each additional million people in the population.

Specifically, for each additional million people, the predicted ozone level is expected to increase by 16.6 parts per million.

For Rascoville, a city with a population of 3 million people, we can use the estimated regression equation to predict the average ozone level:

ozone⌢ = 8.89 + 16.6 × 3 = 8.89 + 49.8 = 58.69

Therefore, the predicted average ozone level for Rascoville is 58.69 parts per million.

If the ozone level is approximately 142 ppm, we can use the estimated regression equation to estimate the population:

142 = 8.89 + 16.6 × population

Solving for population, we get:

133.11 = 16.6 × population

population ≈ 8.02 million

Therefore, the approximate population of the city is 8 million people (rounded to the nearest million).

To know more about ozone level refer here

https://brainly.com/question/29672449#

#SPJ11

The maximum height of the fireworks using the equation h=-4.6t^2+27.6t+33.6 is 75 meters.

Identifying the coefficients a, b, and c from the given quadratic equation.
a = -4.6, b = 27.6, and c = 33.6

Calculating the t-value of the vertex using the formula t = -b / (2 × a)
t = -27.6 / (2 × (-4.6)) = 27.6 / 9.2 = 3

Now, plugging in the t-value back into the equation to find the maximum height.
h = -4.6(3)^2 + 27.6(3) + 33.6

  = -4.6(9) + 82.8 + 33.6

  = -41.4 + 82.8 + 33.6

  = 75

The maximum height of the fireworks is 75 meters.

To learn more about height: https://brainly.com/question/12446886

#SPJ11

The volume of the solid is given by V = 9r/2 - 3.

To calculate the volume of this solid, we will use a triple integral, which involves integrating a function of three variables over a three-dimensional region. The triple integral is denoted by ∭f(x, y, z) dV, where f(x, y, z) is the function we are integrating, and dV is the volume element.

In our problem, the function f(x, y, z) is equal to 1, which means we are integrating a constant function. Therefore, we can simplify the triple integral to V = ∭dV, where V represents the volume of the solid.

To evaluate the triple integral, we need to determine the limits of integration for each variable. We are given the limits for x, y, and z, so we can set up the triple integral as follows:

V =  ∫₂⁰ ∫₃⁰ r2-2y 1 dz dy dx

We integrate first with respect to z, then y, and finally x.

Integrating with respect to z, we get:

V = ∫₂⁰ ∫₃⁰[r2-2y - 1] dy dx

Simplifying the integral, we get:

V =  ∫₂⁰ [r2y - y2]dy dx

Integrating with respect to y, we get:

V = ∫₂⁰ [(r2/2)y2 - (1/3)y3]dy

Simplifying the integral, we get:

V = [(r/2)(3)2 - (1/3)(3)3] - [(r2/2)(0)2 - (1/3)(0)3]

V = 9r/2 - 3

To know more about volume here

https://brainly.com/question/11168779

#SPJ4

To find the projection of b onto the subspace W spanned by vi and v2, we need to first find the orthogonal projection of b onto W.

We can use the formula for orthogonal projection:

projW b = ((b ⋅ vi)/(vi ⋅ vi))vi + ((b ⋅ v2)/(v2 ⋅ v2))v2

where ⋅ denotes the dot product.

Plugging in the given values:

projW b = ((1*3 + 2*1 - 1*0 - 5*(-1))/(3*3 + 1*1 + 0*0 + (-1)*(-1)))vi + ((1*0 + 2*1 - 1*3 - 5*1)/(0*0 + 1*1 + 3*3 + 1*1))v2

Simplifying:

projW b = (22/11)vi + (-6/11)v2

Therefore, the projection of b onto the subspace W is given by (22/11, -6/11, 0, 0).
To find the projection of vector b onto the subspace W spanned by vectors v1 and v2, we will use the following formula:

proj_W(b) = (b · v1 / v1 · v1) * v1 + (b · v2 / v2 · v2) * v2

First, calculate the dot products:

b · v1 = (1 * 3) + (2 * 1) + (-1 * 0) + (-5 * -1) = 3 + 2 + 0 + 5 = 10
b · v2 = (1 * 0) + (2 * 1) + (-1 * 3) + (-5 * 1) = 0 + 2 - 3 - 5 = -6
v1 · v1 = (3 * 3) + (1 * 1) + (0 * 0) + (-1 * -1) = 9 + 1 + 0 + 1 = 11
v2 · v2 = (0 * 0) + (1 * 1) + (3 * 3) + (1 * 1) = 0 + 1 + 9 + 1 = 11

Now plug the dot products into the formula:

proj_W(b) = (10 / 11) * v1 + (-6 / 11) * v2
proj_W(b) = (10/11) * (3, 1, 0, -1) + (-6/11) * (0, 1, 3, 1)

Perform scalar multiplication:

proj_W(b) = (30/11, 10/11, 0, -10/11) + (0, -6/11, -18/11, -6/11)

Finally, add the two vectors:

proj_W(b) = (30/11, 4/11, -18/11, -16/11)

So the projection of b onto subspace W is:

proj_W(b) = (30/11, 4/11, -18/11, -16/11)

Learn more about orthogonal projection here: brainly.com/question/30834408

#SPJ11

Answer: 26/100   OR     0.26  (I would put the answer as a fraction)

Step-by-step explanation:

We need both fractions to have the same denominator before we add them. The denominator of 6/100 is 100. The denominator of 2/10 is 10. We need to turn 10 into 100. To do that, we can do 10*10. This gives us 100. However what we do to the bottom must be done to the top therefore we have 20/100 + 6/100

Now the two fractions can be added together. 20/100 + 6/100 = 26/100.

Normally we would simplify this down to 13/50 but if you want it unsimplified 26/100 would be your answer.

This situation represents exponential decay because the depth of the lake decreases over time.

Exponential decay is a mathematical term used to describe the process of decreasing over time at a constant rate where the amount decreases by a constant percentage at regular intervals. It is a type of exponential function where the base is less than 1.

In other words, the quantity is decreasing by a fixed percentage at regular intervals.

The rate of decay, r, is equal to 0.98 because the depth decreases by 2% per year.

So the depth of the lake each year is 0.98 times the depth in the previous year. It will take between 5 and 6 years for the depth of the lake to reach 26.7 meters.

To know more about exponential decay refer here:

https://brainly.com/question/17161065?referrer=searchResults

#SPJ11