Tamara was asked to write an example of a linear functional relationship. She wrote this example: My babysitting service charges an initial $5.00 fee plus an additional $6.50 per hour. Complete the table below to show the babysitting rate for different numbers of total hours. Then write a linear equation in the form y=mx+b that represents this relationship where m is the slope and b is the y-intercept. Use the on-screen keyboard to type your answers in the boxes below. Total Hours 1 $
2 $
3 $
4 $

Answers

Answer 1

Answer:

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Step-by-step explanation:

In an equation y=mx+b, we can interpret the intercept b as the value of the initial charge and the slope m as the additional charge per hour. So, we can formulate the following equation:

y = 6.5x + 5

Where x is the hours and y are the charges for the babysitting, so, we can fill the table as:

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Answer 2

The answer should be like

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Calculation of the number of hours:

Since we know that the equation should be in the form of

y = mx + b

So, here

y = 6.5x + 5

Here  x is the hours and y are the charges for the babysitting.

So, the table be like

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

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Related Questions

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 36 − x2 , y = 0, x = 2, x = 4; about the x-axis

Answers

Answer: V = 193.25π

Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:

V =  [tex]\pi\int\limits^a_b {[f(x)]^{2}} \, dx[/tex]

f(x) is the area is the function that rotated forms the solid.

For f(x)=y= [tex]\frac{5}{36}-x^{2}[/tex] and solid delimited by x = 2 and x = 4:

V = [tex]\pi\int\limits^4_2 {(\frac{5}{36}-x^{2} )^{2}} \, dx[/tex]

V = [tex]\pi\int\limits^4_2 {(\frac{25}{1296}-\frac{10x^{2}}{36}+x^{4}) } \, dx[/tex]

V = [tex]\pi(\frac{25.4}{1296}-\frac{10.4^{3}}{108}+\frac{4^{5}}{5}-\frac{25.2}{1296}+\frac{10.2^{3}}{108}-\frac{2^{5}}{5} )[/tex]

V = [tex]\pi(\frac{50}{1296}-\frac{560}{1296}+\frac{992}{1296} )[/tex]

V = 193.25π

The volume of a solid formed by y = [tex]\frac{5}{36} - x^{2}[/tex] and delimited by x = 2 and x = 4

is 193.25π cubic units.

20 points! Brainliest will be given!

Answers

Answer:

I always factor out the -1 so my leading coefficient is 1

Step-by-step explanation:

-x^2 + 10x -24

I always factor out the -1 so my leading coefficient is 1

-1 ( x^2 -10x +24)

Then what 2 terms multiply to 24 and add to -10

-6*-4 = 24

-6+-4 = -10

-1( x-6)(x-4)

The floor of a rectangular room is to be covered with square floor tiles with
1
-foot sides. The floor of the room is
18
feet long and
12
feet wide. If the square tiles cost
$
4
each, how much would it cost to completely cover the floor with these tiles?

Answers

Answer:

Total cost = $864

Step-by-step explanation:

The area of the rectangular room

= 18*12

= 216 ft²

The sides of the square is 1ft

The area of the square= 1ft²

To know how many square tiles it will take= 216/1 = 216 square tiles.

The total cost to completely cover the room with tiles if each tiles cost $4

= 216*4

= $864

Total cost=$864

Help please and thank you

Answers

Answer:

1

Cans              4cans                  8 cans                   12 cans

Cost                $2.25                   $4.5                      $6.75

2

Ice Cream   180 q       360 q      540 q       720q        900q           1080 q

Hours       2 hours     4 hours    6 hours    8 hours   10 hours      12 hours

***q = quarts

3

Distance        650 miles           1300 miles           1950 miles

Hours              3 hours                 6 hours                9 hours

Answer:

Question 1 - 8 cans = $4.50, 12 cans = $10.13

Question 2 - 4 hours = 360 quarts, 6 hours = 540 quarts, 8 hours = 720 quarts, 12 hours = 1,170

Question 3 - 1,950 miles in 9 hours

Hope this helps :)

Find the length of BC

Answers

Answer:

The answer is option A

Step-by-step explanation:

To find the length of BC we use tan

tan ∅ = opposite / adjacent

From the question

AC is the opposite

BC is the adjacent

So we have

tan 61 = AC / BC

tan 61 = 47/BC

BC = 47/tan 61

BC = 26.05

Hope this helps you

A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured.

Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6

Required:
a. Estimate the model: Height = β0 + β1Fertilizer + ε.
b. Does the y-intercept make practical sense?
c. Use the estimated model to predict, after four months, the height of a tomato plant which received 3.0 ounces of fertilizer.

Answers

Answer: hello your table is incomplete here is the complete table

Fertilizer Amount (ounces) Tomato Plant Height (inches)

1.9 20.4

5.0 49.2

4.2 56.1

1.3 24.3

4.9 29.2

5.4 60.8

3.1 24.6

0.0 25.3

2.3 26.2

2.5 25.7

0.9 26.5

1.0 28.6

4.5 62.9

3.8 30.8

5.3 43.2

2.3 33.4

4.0 35.1

1.4 22.1

3.9 40.6

4.0 44.5

3.6 29.7

0.6 21.1

1.6 25.4

2.5 29.6

4.5 27.6

3.6 32.6

2.0 33.5

0.0 22.5

2.5 27.6

3.1 46.4

Answer : a)Height = 18.639 + 5.208  * fertilizer

b) The Y intercept make practical sense because without fertilizer there will still be an  increase in plant height ( y intercept )  

c) 34.263

Step-by-step explanation:

A) Estimating  the model

Height = β0 + β1 FERTILIZER + ∈

β0 = 18.639

β1 = 5.208

hence

Height = 18.639 + 5.208  * fertilizer  ( using excel )

B) The y- intercept

The Y intercept make practical sense because without fertilizer there will still be an  increase in plant height ( y intercept )  

C ) using the estimated model to predict  after four months

the model = 18.639 + 5.208 * fertilizer

fertilizer ounce given = 3

therefore height of tomato plant after 4 months that received 3 ounces of fertilizer = 18.639 + 5.208 * 3 = 34.263

PLEASE HELP!!! The side lengths of a square are each 5q. By adding 3 to the length and subtracting 3 from the width, a rectangle is made. What is the area of the rectangle? a. 10q^2-6 b. 9q^2+25 c. 25q^2-9 d. 25q^2-30q-9

Answers

The area of the rectangle is [tex]25q^2-9[/tex].

Area of the rectangle

The area of the rectangle is the product of length and width.

How to determine the area of the rectangle?

The length of the sides of the square is 5q.

3 is added and 3 is subtracted to the length and the width of the square so, the dimensions of the new quadrilateral is (5q+3) and (5q-3).

So, the area of the rectangle is-

[tex]A=(5q+3)\times (5q-3)\\=25q^2-9[/tex]

Thus, the area of the rectangle is [tex]25q^2-9[/tex].

Learn more about the area of the rectangle here- https://brainly.com/question/20693059

#SPJ2

Answer:25q^2-9

Step-by-step explanation:

your welcomeeeeeeee

The population of a city can be modeled with a linear equation Y equals -80 X +3450 where X is the number of years after 2000 and why is the cities population by the description of the cities population based on equation

Answers

Answer:

retype that im not understanding .

Step-by-step explanation:

If the sampled population is finite and at least _____ times larger than the sample size, we treat the population as infinite.

Answers

Answer:

The answer is "20".

Step-by-step explanation:

It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.  

Its sampling distribution of the "x bar" should also be naturally independent of the random sample, that is usually distributed. We consider the population as endless if the sampling size is at least 20 times greater than the sample size.

Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month

Answers

Answer:

D.

m = 2 = figures/month

b = 20 = # of action figures

N
5. Use AABC to find the value of sin B.
A 7
B
25
B 24
C
24
А
C7
25
D 24​

Answers

*see the attachment below for the missing figure

Answer:

[tex] sin B = \frac{24}{25} [/tex]

Step-by-step explanation:

Given a right angled triangle, ∆ABC

AB = 25

BC = 7

AC = 24

<ACB = 90°

Required:

Value of Sin B

Solution:

Using trigonometric ratio formula,

[tex] sin B = \frac{opposite}{hypotenuse} [/tex]

Opposite = AC = 24 (the side opposite to <B)

Hypotenuse = AB = 25 (the longest side facing the right angle)

[tex] sin B = \frac{24}{25} [/tex]

What is the value of x?

Answers

Answer:

13=x

Step-by-step explanation:

Since BE is a bisector

ABE = EBC

2x+20 = 4x-6

Subtract 2x from each side

2x+20-2x =4x-6-2x

20 = 2x-6

Add 6 from each side

20+6 = 2x-6+6

26 = 2x

Divide each side by 2

26/2 = 2x/2

13=x

Answer:

x = 13

Step-by-step explanation:

The angle bisector theorem means that m<ABE = m<EBC. Now that we know they are equal, we can set the equations to each other and solve for x.

2x + 20 = 4x - 6

26 = 2x

13 = x

So the value of x is 13.

Cheers.

.19 OF JOE'S SALARY GOES FOR TAXES. WHAT PERCENT OF HIS SALARY DOES THIS REPRESENT?

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

19%

▹ Step-by-Step Explanation

0.19 → hundreth's place.

19/100 (since the denominator is 100, that represents 100% while 19 represents 19%)

Final Answer - 19%

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

This represent 19% of his salary.

Given, Joe's salary goes for tax is 0.19.

We have to represent the value in percent.

Here 0.19 can be written in fraction form as,

[tex]\dfrac{19}{100}[/tex]

It means 19 part from 100 part goes for taxes, means 19% of the Joe's salary goes for taxes.

Hence this represent 19% of his salary.

For more details follow the link:

https://brainly.com/question/8011401

Evaluate the expression 23^0-15^1+18^0+(43-12)

Answers

Answer:

18

Step-by-step explanation:

23^0 - 15^1 + 18^0 + (43 - 12) =

= 1 - 15 + 1 + 31

= -14 + 1 + 31

= -13 + 31

= 18

Please answer please please thank

Daniels freezer is set to 0degrees Fahrenheit he places a load of bread that was at a temperature of 78 degrees Fahrenheit in the freezer the bread cooled at a rate of 11 degrees Fahrenheit per hour write and graph an equation that models the temperature t of the bread

Answers

Answer:

it took 7 hours for the bread to drop at a constent rate

Step-by-step explanation:

A pyramid shaped building is 311 feet tall and has a square base with sides of 619 ft. The sides of the building are made from reflective glass. what is the surface area of the reflective glass

Answers

Answer:

Surface area of the reflective glass is 543234.4 square feet.

Step-by-step explanation:

Given that: height = 311 feet, sides of square base = 619 feet.

To determine the slant height, we have;

[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]

   = 96721 + 95790.25

   = 192511.25

⇒ l = [tex]\sqrt{192511.25}[/tex]

      = 438.761

The slant height, l is 438.8 feet.

Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height

  area =  [tex]\frac{1}{2}[/tex] × 619 × 438.8

          = 135808.6

          = 135808.6 square feet

Since the pyramid has four reflective surfaces,

surface area of the reflective glass = 4 × 135808.6

                                                          = 543234.4 square feet

Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 66 times and record the outcomes. They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level. (a) The null and alternative hypotheses are: H0: The die has the uniform distribution. Ha: The die does not have the uniform distribution. (b) χ20=15.091. (c) χ20.05=11.070. (d) What conclusions can be made? Select all that apply. Select all that apply: We should reject H0. We should not reject H0. At the 5% significance level, there is sufficient evidence to conclude that the die is not fair. At the 5% significance level, there is not enough evidence to conclude that the die is not fair.

Answers

Answer:

We should reject H0

At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.

Step-by-step explanation:

Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The critical value is 15.091 and  test statistic is 11.070. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.

Graph the equation y = 1/2x + 5 on the coordinate plans provided below.

Answers

Answer:

Well, of course, i can not graph it in the coordinate plane in the image, but i can try to teach you how to do it.

We have the function y = (1/2)*x + 5

The first step is to generate pairs (x, y)

You can do it by evaluating the function in different values of x.

For example;

if x = 0

y = (1/2)*0 + 5 = 5

then we have the point (0,5)

if x = 2

y = (1/2)*2 + 5 = 6

Then we have the point (1, 6)

Now, with only two points you can graph the line.

First find the points in the coordinate plane, and mark them.

Now, with a ruler, draw a line that connects the two points.

That line is the graph of the function.

An example of the graph is:

pls help me with all 3 questions! correct answer will get brainliest and a kiss...

Answers

Answer:

1.union = {20 21 22 23 25 27 29}

2. intersection = {5 14 22}

3.1/3

Step-by-step explanation:

1. union U of sets a nd b ={20 21 22 23 25 27 29}

2. intersection n of sets a nd b = {5 14 22}

3. probability = one item / total

= 1/3

1.

A. {22, 25, 27, 29}

B. {20, 21, 22, 23}

Answer: A∪B = {22, 25, 27, 29, 20, 21, 23}

2.

A. {1, 5, 10, 14, 22}

B. {5, 14, 20, 22, 27}

Answer: A∩B = {5, 14, 22}

3.

A. {1, 5, 10, 14, 22}

B. {5, 14, 20, 22, 27}

Answer: The three items that are intersecting each have a 1/3 chance of being chosen.

Change Y = 3X to the standard form of the equation of a line.

Answers

Answer:

-3x+y=0

Step-by-step explanation:

Standard form= Ax+Bx=C

Add -3x both sides, answer -3x+1y=0

In the given diagram, find the values of x, y, and z.

a. x = 36°, y = 36°, z = 34°
b. x = 44º, y = 44°, z = 44°
c. x = 34º, y = 34°, z = 34°
d. x = 36°, y = 34°, z = 34°

Answers

Answer:

a. x = 36°, y = 36°, z = 34°

Step-by-step explanation:

X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°

The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°

Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
u = -4 A = 1 0 3
-5 -2 -1 -4
3 3 -3 0
1 -1 3 6
A) In Col A, not in Nul A
B) Not in Col A, not in Nul A
C) In Col A and in NulA
D) Not in Col in Nul A

Answers

Answer: d) Not in Col in Nul A

Step-by-step explanation: The definition of Column Space of an m x n matrix A is the set of all possible combinations of the columns of A. It is denoted by col A. To determine if a vector is a column space, solve the matrix equation:

A.x = b or, in this case, [tex]A.x=u[/tex].

To solve, first write the augmented matrix of the system:

[tex]\left[\begin{array}{cccc}1&0&3&-4\\-2&-1&-4&-5\\3&-3&0&3\\-1&3&6&1\end{array}\right][/tex]

Now, find the row-echelon form of matrix A:

1) Multiply 1st row by 2 and add 2nd row;

2) Multiply 1st row by -3 and add 3rd row;

3) MUltiply 1st row by 1 and add 4th row;

4) MUltiply 2nd row by -1;

5) Multiply 2nd row by 3 and add 3rd row;

6) Multiply 2nd row by -3 and add 4th row;

7) Divide 3rd row by -15;

8) Multiply 3rd row by -15 and add 4th row;

The echelon form matrix will be:

[tex]\left[\begin{array}{cccc}1&0&3&-4\\0&1&-2&13\\0&0&1&-\frac{51}{15}\\0&0&0&-13 \end{array}\right][/tex]

Which gives a system with impossible solutions.

But if [tex]A.x=0[/tex], there would be a solution.

Null Space of an m x n matrix is a set of all solutions to [tex]A.x=0[/tex], so vector u is a null space of A, denoted by null (A)

Maricopa's Success scholarship fund receives a gift of $ 230000. The money is invested in stocks, bonds, and CDs. CDs pay 2.5 % interest, bonds pay 2.2 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 12095 , how much was invested in each account?

Answers

Maricopa's Success scholarship fund receives a gift of $ 170000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25 % interest, bonds pay 4.4 % interest, and stocks pay 11.4 % interest. Maricopa Success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 10055 , how much was invested in each account?

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

Equations:

s + b + C = 170000

11.4s + 4.4b + 3.25C = 1005500

b = C + 25000

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

Rearrange::

s + b + C = 170000

1140s + 440b + 325C = 100550000

0 + b - C = 25000

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

Use any method you know to solve the system to get:

 

stocks = 45000

bonds = 75000

CD's = 50000

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

Cheers,

Stan H.

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

Maricopa Success invested $

in stocks.

Maricopa Success invested $

in bonds.

Maricopa Success invested $

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

Hope this helps!

Brainliest would be great!

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

With all care,

07x12!

The prices for a loaf of bread and a gallon of milk for two supermarkets are shown below. Sue needs to buy bread and milk for her church picnic. At Supermarket A, she would pay $137.24. At Supermarket B, she would pay $140.04. Which of the following system of equations represents this situation?

Answers

Answer:

B. 3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Step-by-step explanation:

A B

Bread $3.19 $3.49

Milk $4.59 $4.39

Sue paid $137.24 in supermarket A

Sue paid $140.04 in supermarket B

Let

Price of bread A=$3.19

Price of bread B=$3.49

Price of milk A=$4.59

Price of milk B=$4.39

Quantity of Bread=b

Quantity of Milk=m

Pb=price of bread

Pm=price of milk

Qb=Quantity of bread

Qm=Quantity of milk

For each supermarket

Supermarket A Equation

PbQb + PmQm =$137.24

3.19b+ 4.59m = 137.24

Supermarket B Equation

PbQb + PmQm=$140.04

3.49b + 4.39m = $140.04

Combining both equations

3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?

Answers

Answer:

The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.

Step-by-step explanation:

Convert to a mixed number:

209/8

Divide 209 by 8:

8 | 2 | 0 | 9

8 goes into 20 at most 2 times:

| | 2 | |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

8 goes into 49 at most 6 times:

| | 2 | 6 |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 |  

Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:

| | 2 | 6 | (quotient)

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 | (remainder)

The quotient of 209/8 is 26 with remainder 1, so:

Answer: 26 1/8° C

Suppose we want to test the claim that the majority of adults are in favor of raising the vote age to 21. Is the hypothesis test left tailed, right tailed or two tailed

Answers

Answer:

The hypothesis test is right-tailed.

Step-by-step explanation:

We are given that we want to test the claim that the majority of adults are in favor of raising the voting age to 21.

Let p = proportion of adults who are in favor of raising the voting age to 21

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%

As we know that the majority is there when we have more 50% chance of happening of that event.

Here, the null hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is less or equal to 50%.

On the other hand, the alternate hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is more than 50%.

This shows that our hypothesis test is right-tailed because in the alternate hypothesis, the greater than sign is included.

For each of the following determine a unit rate using the information given. Show the division that leads to your answer. Use appropriate units. All rates will be whole numbers. At a theatre, Mia paid $35 for five tickets

Answers

Answer:

Step-by-step explanation:

cool

Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.
A. yp(x)=Ax2+Bx+C,
B. yp(x)=Ae2x,
C.yp(x)=Acos2x+Bsin2x,
D. yp(x)=(Ax+B)cos2x+(Cx+D)sin2x
E. yp(x)=Axe2x,
F.yp(x)=e3x(Acos2x+Bsin2x)
1. d2ydx2+4y=x−x220
2. d2ydx2+6dydx+8y=e2x
3. y′′+4y′+20y=−3sin2x
4. y′′−2y′−15y=3xcos2x

Answers

Answer and Step-by-step explanation:

1. Data provided

[tex]\frac{d^2y}{dx^2} + 4y = x - x^2 + 20\\\\ \frac{d^2y}{dx^2} + 4y = - x^2 + x + 20[/tex]

Now as a non homogeneous part which is

[tex]- x^2 + x + 20[/tex] let us assume the computation is

[tex]y_p(x) = Ax^2 + Bx + C[/tex]

2. Data provided

[tex]\frac{ d^2y}{dx^2} + \frac{6dy}{dx} + 8y = e^{2x}[/tex]

As a non homogeneous part is [tex]e^2x[/tex] , let us assume the computation is

[tex]y_p(x) = Ae^{2x}[/tex]

3. Data provided

[tex]y'' + 4y' + 20y = -3sin2x[/tex]

As a non homogeneous part −3sin(2x), let us assume the computation is

[tex]y_p(x) = Acos(2x) + Bsin(2x)[/tex]

4. Data provided

[tex]y'' - 2y' - 15y = 3xcos(2x)[/tex]

As a non homogeneous part  3xcos(2x), let us assume the computation is

[tex]y_p(x) = (Ax+B)cos2x+(Cx+D)sin2x[/tex]

A submarine is moving parallel to the surface of the ocean at a depth of 626 m. It begins a
constant ascent so that it will reach the surface after travelling a distance of 4420 m.
a) What angle of ascent, to the nearest tenth of a degree, did the submarine make? (3
marks)
b) How far did the submarine travel horizontally, to the nearest metre, during its ascent to
the surface? (3 marks)

Answers

Answer:

a) the angle of ascent is 8.2°

b) the horizontal distance traveled is 4375 m

Step-by-step explanation:

depth of ocean = 626 m

distance traveled in the ascent = 4420 m

This is an angle of elevation problem with

opposite side to the angle = 626 m

hypotenuse side = 4420 m

a) angle of ascent ∅ is gotten from

sin ∅ = opp/hyp = 626/4420

sin ∅ = 0.142

∅ = [tex]sin^{-1}[/tex] 0.142

∅ = 8.2°  this is the angle of ascent of the submarine.

b) The horizontal distance traveled will be gotten from Pythagoras theorem

[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]

The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances

[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]

adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]

adj = 4375 m  this is the horizontal distance traveled.


If y ∝ 1∕x and y = –2 when x = 14, find the equation that connects x and y.
Question 11 options:

A)

y = –28x

B)

y = –7∕x

C)

y = –28∕x

D)

y = –7x

Answers

C. y= -28/x

y=k/x

cross multiply

k= y×x

k = -2×14

k = -28

y = -28/x [ equation connecting x and y]

The equation that connects x and y si y = –28∕x.

The correct option is (C)

What is proportionality constant?

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant. The proportionality constant's value is determined by the proportion between the two specified quantities.

For example,  The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

We have given that

y ∝ 1∕x

To remove proportional sign we use proportionality constant

y=k/x

Now, cross multiply

k= y×x

k = -2×14

k = -28

y = -28/x

Hence, the equation is y = -28/x .

Learn more about proportionality here:

https://brainly.com/question/8598338

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