Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
mi/h

Answers

Answer 1

The rate at which the distance between the two cars increased four hours later is 30 mi/h.

How to determine the rate?

First of all, we would determine the distances travelled by each of the cars. The distance travelled by the first car after four (4) hours is given by:

Distance, x = speed/time

Distance, x = 24/4

Distance, x = 6 miles.

For the second car, we have:

Distance, y = speed/time

Distance, y = 18/4

Distance, y = 4.5 miles.

After four (4) hours, the total distance travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):

z² = x² + y²

Substituting the parameters into the mathematical expression, we have;

z² = 6² + 4.5²

z² = 36 + 20.25

z² = 56.25

z = 7.5 miles.

Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to time, we have:

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)

Therefore, the rate of change of speed (dz/dt) between the two (2) cars is given by:

dz/dt = [x(dx/dt) + y(dy/dt)]/z

dz/dt = [6(24) + 4.5(18)]/7.5

dz/dt = [144 + 81]/7.5

dz/dt = 225/7.5

dz/dt = 30 mi/h.

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Answer 2

Answer:

30 mi / hr

Step-by-step explanation:

First find out how far the cars are apart after 4 hours

24 * 4 = 96 mi = y

18 * 4 = 72 mi = x

Now use the pythagorean theorem

   s^2 =  ( x^2 + y^2 )                shows s = 120 miles apart at 4 hours

Now s^2 = x^2 + y^2     Differentiate with respect to time ( d  / dt )

       2 s ds/dt    =  2x dx/ dt  + 2y dy / dt

             ds/dt    =   (x dx/dt + y dy/dt)/s

                           =  (72(18)  + 96(24)) / 120

               ds/dt   = 30 mi/hr


Related Questions

I need help with the question above. I took a picture of it.

Answers

The answer is: It will be a line.

1. A piece of power transmission equipment is being designed. The design includesa set of three different meshed gears with a total of 107 teeth between them. If thesecond gear has 13 more teeth than the first gear. The third gear has 15 more teeththan the second gear.How many teeth does the second gear have?

Answers

[tex]x+y+z=107[/tex]

where x is the first, y the second and z the third

the second gear has 13 more teeth than the first gear

[tex]x+13=y[/tex]

The third gear has 15 more teeth than the second gear

[tex]y+15=z[/tex]

we need solve z form the third equation and solve x from the second equation an replace on the first

[tex]\begin{gathered} z=y+15 \\ x=y-13 \end{gathered}[/tex]

replacing

[tex]\begin{gathered} (y-13)+y+(y+15)=107 \\ y-13+y+y+15=107 \\ 3y+2=107 \\ 3y=105 \\ y=35 \end{gathered}[/tex]

so, the second gear have 35 teeth

Determine the odds against rolling a 4 on one roll
of a die.
Solution
P(4)=1
6
5
P (fails to roll a 4)=-
6

Answers

Answer:

1/6

Step-by-step explanation:

SIX possible rolls    1,2,3,4,5,6

   4 is 1 out of 6      or 1/6

A native wolf species has been reintroduced into a national forest. Originally 200 wolves were transplanted. After 3 years, the population had grown to 270 wolves. If the population grows exponentially, then at what annual rate is the population growing? Round the answer to the nearest tenth of a percent.

Answers

The population is growing at an annual rate of 16.2%

Here, we want to calculate the exponential growth rate

Mathematically, we can write the exponential equation of growth as follows;

[tex]\begin{gathered} P=I(1+r)^t \\ \\ \end{gathered}[/tex]

Where P is the population after a certain number of years ( 270 after 3 years

I is the initial popultaion which is 200

r is the percentage we want to calculate

t is the number of yeats to reach P which is 3 in this case

[tex]\begin{gathered} 270=200(1+r)^3 \\ (1+r)^{3\text{ }}\text{ = }\frac{270}{200} \\ \\ (1+r)^3\text{ = 1.35} \\ \\ 1\text{ + r = }\sqrt[3]{1.35} \\ \\ 1\text{ + r = 1.162} \\ \\ r\text{ = 1.162 - 1} \\ \\ r\text{ = 0.162} \end{gathered}[/tex]

To the nearest tenth of a percentage, this is 16.2%

The table shows a proportional relationship.


x 12 8 24
y 3 2 6


Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).

Answers

A graph of which best describes what the proportional relationship would look like is: D. A line passes through the point (0, 0) and continues through the point (12, 3).

What is a graph?

In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Additionally, a graph that represents a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).

Since the graph represents a proportional relationship we have:

Constant of proportionality, k = 12/3 = 8/2 = 24/6 = 4

Ratio = 24:6 = 12:3.

Therefore, (0, 0) and (12, 3) are points on this graph that represents a proportional relationship.

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Answer:d

Step-by-step explanation:trust

Find the percentage decrease and round to the nearest tenth

Answers

Answer:

16.6%

Step-by-step explanation:

First, find the difference between the prices:

$3.95 - $3.45 = $0.50

Then, divide the difference by yesterday's price.

$0.50 ÷ $3.95

≈ 0.166

≈ 16.6%

Answer:

12.7%

Step-by-step explanation:

$3.95 - $3.45 = $.50

$.50 / $3.95 = .127 = 12.7%

please help and could u give all the steps if there’s more after this thank you so much

Answers

Angle IJL is 54 because congruent angles have equal measure.

What are congruent angles?

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.

According to question, angle m IKL = 54

And AB// CD and EF// GH

Angle IKL is alternate interior angle to angle HLK

m angle HLK= m angle IKL (congruent angles have equal measure)

m angle HLK= 54

Similarly, m angle IJL = m angle HLK

Hence, angle IJL= 54

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The formula for the area of a triangle is A = -bh, in which b represents the length of the base and h2represents the height. If a triangle has an area of 115 mm2 and the height is 10 mm, what is the measureof the base?The measure of the base ismm.

Answers

The formula for the area of a triangle is A is;

given the preimage coordinates complete the translation provide and give the image Coordinates

Answers

The coordinates are made up of an x-​​coordinate and a y-coordinate, written in the form (x, y), the translation given is (x + 1, y - 1), which means adding +1 to all x-coordinates and subtracting -1 to all y-coordinate.

Then, the pair B(0, -4) will be transformed into B'(0 + 1, -4 - 1) → B'( 1, -5)

C( -1, 1) → C' (-1 + 1, 1 - 1) → C'( 0, 0)

D( 1, 3) → D' ( 1 + 1, 3 - 1) → D'( 2, 2)

E( 4, -1) → E' ( 4 + 1, -1 - 1) → E'( 5, -2)

Emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. After 2​ weeks, she will owe​ $456, and after 5​ weeks, she will owe​ $228.
a. What was the original amount Emery​ borrowed?
b. How much does she pay each​ week?
c. How useful are equations in​ point-slope and​ slope-intercept forms for answering each​ question?

Answers

The $456 and $228 Emery owed from the amount she borrowed to buy a new phone after 2 weeks and 5 weeks gives;

a. The original amount owed is $608

b. Emery pays $76 each week

c. The point and slope and slope and intercept both gives the amount Emery pays each week as the slope, while the slope and intercept form further gives the original amount borrowed as the y–intercept, c

What is a straight line equation?

A straight line equation is one which expresses a linear relationship between variables

Let y represent the original amount of money Emery borrowed from her brother, and let m represent the amount she pays each week to settle the loan, we have;

The given parameters are;

The amount Emery owes after 2 weeks = $456

The amount Emery will owe after 5 weeks = $228

a. The above information can be expressed by writing the following equations;

456 = y - 2•m...(1)

228 = y - 5•m...(2)

Subtracting equation (2) from equation (1) gives;

y - 2•m - (y - 5•m) = 456 - 228 = 228

3•m = 228

Therefore;

m = 228 ÷ 3 = 76

m = 76

The original amount Emery borrowed, y, from equation (1) is therefore;

y = 456 + 2•m

y = 456 + 2 × 76 = 608

The original amount Emery borrowed, y, is $608

b. The amount Emery pays each week, m = $76

c. The straight line equation in point and slope form is presented as follows;

[tex] y_2 - y_1 = m•(x_2 - x_1) [/tex]

From the above equation, the two points (456, 2) and (228, 5) given in the question can be used to find the slope, m, which is the amount paid each month

The slope and intercept form of a straight line equation is y = m•x + c

From the slope and intercept form, we have;

The slope, m = The amount Emery pays per month

The intercept, c = The original amount Emery borrowed

Therefore, both forms of the straight line equation gives the amount Emery pays each week, while the slope and intercept form also gives the original amount Emery borrowed

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Mrs. Ojo is 5 times older than her son. 3 years ago the product of their ages was 185. How old are they now?​
need it now please.

Answers

A= 5B •••> (1)
(A – 3)(B – 3)= 185
AB – 3A – 3B + 9= 185
AB – 3(A + B)= 185 – 9= 176
AB – 3(A + B)= 176 •••> (2)

Put (1) in (2),
5B(B) – 3(5B + B)= 176
5B² – 3(6B)= 176
5B² – 18B – 176= 0
(B – 8)(B + 22/5)= 0
B= 8 and B= –22/5

When B= 8, from (1),
A= 5(8)= 40.

Thus, Mrs Ojo is 40 while her son is 8.

what is the shape of a cross section that is perpendicular to the basis

Answers

If we get the cross section perpendicular to the base of this image, we would get the same shape as the image.

Through the diagram, we can see that if we cut the image to get the cross section perpendicular to its base, we would get the same shape as the image, which is a pentagon.

Z divided 12 equal 9

Answers

Answer:

108

Step-by-step explanation:

12×9=108

just for the extra characters

Answer:

108

Step-by-step explanation:

z/12 = 9

z = 9 × 12

z = 108

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if the sum of the first three terms of a GP is half it's sum to infinity. find it's positive common ratio.​

Answers

Answer:

See below

Step-by-step explanation:

Sum of n = inf    =     a / ( 1-r)       one half of this = 1/2 ( a/(1-r) )

Sum of first 3 terms =   a ( 1- r^n) / ( 1-r)   = a (1-r^3) / (1-r)

The underlined value are equal ( given in the Q)

1/2  a / (1-r)    = a ( 1-r^3) / (1-r)           Multiply both side by ( (1-r) )

1/2 a = a ( 1-r^3)           divide both sides by  a

1/2 = 1- r^3      subtract 1 from both sides

-1/2 = - r^3

1/2 = r ^3

r = cuberoot ( 1/2)  =  1/2 ^(1/3)  =   .793700526

The half life of iron-59 is 44.5 days. How much of
a 50g sample would remain after 178 days?

Answers

Answer:

If the half-life of a nuclide is 44.5 days, then 178 days is four half-lives.

explanation:

After four half-lives, 0.0625 (0.54) of the original nuclides remains. If 50g is the original mass, then the mass after 4 half-lives is 3.125g.

AT = A0 2(-T/H)

A178 = (50) 2(-44.5/178)

A178 = 3.125

4 thousands +12 hundreds =

Answers

Answer:

that's too easy

4 thousands=4000

12 hundreds=120

4000+120=4120

4 thousands and 12 hundreds

4000
4000+
4000+120
4000+120=
Answer is 4,120

(4,000+120=4,120)

I have to send you the question

Answers

The given expression fro the sum of n terms:

[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ \text{ Where: }a_1\text{ is the firm term \& }a_n\text{ is the last term} \end{gathered}[/tex]

From the given question we have:

[tex]a_1=8,a_n=79,\text{ n =6}[/tex]

Substitute these value in the expression of sum of n terms

[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ S_6=\frac{6}{2}(8+79) \\ S_6=3(87) \\ S_6=3\times87 \\ S_6=261 \end{gathered}[/tex]

So, sum of 6 terms is 261

help me pleaseeeeeeeeeeeeeeeeeeeeeeeee !!!

Answers

Answer:

[tex]f(x)=\frac{5}{6}x+21[/tex]

Step-by-step explanation:

Slope = 5/6

Point = (-18,6)

Using Point-Slope form

y-6=5/6(x+18)

y-6=5/6x+15

y=5/6x+21

:]

question shown in picture below!!(i only need the 2nd one)

Answers

Given the following sequence:

[tex]\mleft\lbrace17,14,11,8,\ldots\mright\rbrace[/tex]

notice that the common difference between each term is -3, therefore, we can use the explicit formula for a sequence:

[tex]\begin{gathered} a_n=a_1+(n-1)\cdot d \\ d=-3 \\ a_1=17 \\ \Rightarrow a_n=17+(n-1)(-3) \\ \Rightarrow a_n=17-3n+3=20-3n \\ a_n=20-3n \end{gathered}[/tex]

we have that the explicit formula is a_n=20-3n, while the recursive formula is:

[tex]\begin{gathered} a_n=a_{n-1}+d \\ d=-3 \\ \Rightarrow a_n=a_{n-1}-3 \end{gathered}[/tex]

S is the midpoint of segment OU. OS= 7x-9 and SU=4x+3. Determine the length of segment OU.

Answers

Answer:

The equation for the value of OU is;

[tex]OU=11x-6[/tex]

Explanation:

Given that S is the midpoint of segment OU.

Then;

[tex]OU=OS+SU[/tex]

Given in the question;

[tex]\begin{gathered} OS=7x-9 \\ SU=4x+3 \end{gathered}[/tex]

Substituting the values of OS and SU to get OU;

[tex]\begin{gathered} OU=OS+SU \\ OU=7x-9+4x+3 \\ OU=7x+4x-9+3 \\ OU=11x-6 \end{gathered}[/tex]

Therefore, the equation for the value of OU is;

[tex]OU=11x-6[/tex]

Which of the following lists of data has the largest standard deviation? Hint: you should not need to compute the standard deviation for each list.Select the correct answer below:22, 25, 25, 22, 25, 23, 24, 23, 26, 2413, 11, 11, 11, 10, 14, 14, 10, 11, 1116, 14, 15, 15, 16, 16, 15, 16, 18, 1425, 23, 25, 22, 21, 25, 22, 21, 25, 237, 14, 19, 18, 4, 16, 5, 11, 11, 12

Answers

Answer:

7, 14, 19, 18, 4, 16, 5, 11, 11, 12

Explanation:

The standard deviation is a statistic that measures the spread of a dataset relative to its mean.

From the given options, find the range in each of them:

[tex]Range=Highest\;Value-Lowest\;Value[/tex]

• Option 1: Range = 26-22=4

,

• Option 2: Range=14-10=4

,

• Option 3: Range=18-14=4

,

• Option 4: Range = 25-21=4

,

• Option 5: Range = 19-4=15

We see that the dataset in Option 5 has a far greater range and thus the dataset will have the biggest spread relative to its mean.

Option 5 has the largest standard deviation.

1. Fiber-Brite could clean 48 rugs in 12 hours. At that rate, how many rugs could Fiber-Brite
clean in 20 hours?

Answers

80 rugs cleaned in 20 hours

Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the around it to two decimal places if necessary.8i4 + 5i

Answers

SOLUTION

The given complex expression is:

[tex]\frac{-8i}{4+5i}[/tex]

Rationalize the denominator

This gives

[tex]\begin{gathered} \frac{-8i}{4+5i}\times\frac{4-5i}{4-5i} \\ =\frac{-32i-40}{16+25} \\ =-\frac{40}{41}-\frac{32i}{41} \end{gathered}[/tex]

Roseanne makes 1 1/2 of strawberry lemonade. She pours 1/4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2/5 of the remaining lemonade. How much lemonade does Roseanne's brother drink? Which expression can be used to determine the amount of lemonade Roseanne's brother drank? A. 1 1/2 - (1/4 x 2/5) B. (1 1/2 + 1/4) x 2/5 C. (1 1/2 - 1/4) x 2/5 D. (1 1/2 - 1/4) ÷ 2/5

Answers

we know that

the total lemonade is 1 1/2 liter

She pours 1/4 of a liter of lemonade into a thermos

Her brother drinks 2/5 of the remaining lemonade

the remaining lemonade is equal to

1 1/2-1/4=3/2-1/4=5/4 liters

Multiply by 2/5

(5/4)(2/5)=10/20=1/2 liter

therefore

answer is option

C. (1 1/2 - 1/4) x 2/5

in a 30 16 90° triangle given the short leg equals five find the long leg of the triangle

Answers

In a 30-60-90 triangle:

[tex]\begin{gathered} Hypotenuse_{\text{ }}=_{\text{ }}2\cdot short_{\text{ }}length \\ Long_{\text{ }}length=\sqrt[]{3}\cdot short_{\text{ }}length \\ \end{gathered}[/tex]

so:

[tex]\begin{gathered} Long_{\text{ }}length=\sqrt[]{3}\cdot5 \\ Long_{\text{ }}length=5\cdot\sqrt[]{3}\approx8.66 \end{gathered}[/tex]

2 5 4 Q Find the area of the shaded region above.

Answers

As you can see in the given figure, there are two different shapes.

One is a rectangle and the other is a triangle.

Recall that the area of a rectangle is given by

[tex]A_R=L\cdot W[/tex]

Where L is the length and W is the width.

As you can see from the figure,

W = 4

L = 5

So the area of the rectangle is

[tex]A_R=L\cdot W=5\cdot4=20[/tex]

Recall that the area of a triangle is given by

[tex]A_T=\frac{1}{2}\cdot b\cdot h[/tex]

Where b is the base of the triangle and h is the height of the triangle.

As you can see from the figure,

b = 4

h = 2

So the area of the triangle is

[tex]A_T=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot4\cdot2=\frac{1}{2}\cdot8=\frac{8}{2}=4[/tex]

Now the total area of the shaded region is the sum of the area of the rectangle and the area of the triangle.

[tex]A=A_R+A_T=20+4=24[/tex]

Therefore, the area of the shaded region is 24

If you don’t need further explanation on this question, we can end the session. I’d really appreciate you letting me know how I did by rating our session after you exit.

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Ainsley had 3 yards of string. She used 1/4 yard for a project. She wants to divide the rest into pieces 5/6 yard long. How many pieces can she make?

Answers

She can make 3.3 pieces from the remaining length

How to determine the number of pieces to make?

From the question, the given parameters are:

Length of string = 3 yardsAmount used for project = 1/4 yardLength of each piece = 5/6 yard

We start by calculating the length of the remaining pieces as a whole

This is calculated as

Length of remaining piece + length used for project = Length of string

Substitute the known values in the above equation

So, we have

Length of remaining piece + 1/4 yard = 3 yards

Subtract 1/4 from both sides

Length of remaining piece = 2.75 yards

The number of pieces is then calculated as

Pieces = Length of remaining pieces/Length of each piece

This gives

Pieces = 2.75 yards/(5/6 yards)

Evaluate the quotient

Pieces = 3.3

Hence, the number of pieces she can make is 3.3

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Evaluate: base 6 exponent 0

Answers

Answer:

1

Explanation:

Given:

[tex]6^0[/tex]

To evaluate the expression above, apply the law of indices below.

[tex]a^0=1,a\neq0[/tex]

That is, whenever a number (except 0) is raised to the power of 0, the result is always 1.

Therefore:

[tex]6^0=1[/tex]

how do I find the given z score

Answers

The formula for calculating a z-score is

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Where:

*x is the raw score

*μ is the population mean

*σ is the population standard deviation

A bag of cookies weighs 19.1 ounces. The bag contains 50 cookies. How much does each cookie weigh?
O2.6 ounces
O 0.3 ounces
O 0.382 ounces
O 3.82 ounces

Answers

Answer: 0.382 ounces

Step-by-step explanation:

To find the unit rate of the weight of a single cookie, we will use division.

        19.1 ounces per bag / 50 cookies in the bag = 0.382 ounces per cookie

To check our work, we will multiply 0.382 ounces per cookie by 50. Since the bag, with 50 cookies, weighs 19.1 ounces, 0.382 times 50 should equal about 19.1 ounces.

        0.382 ounces * 50 cookies = 19.1 ounces ✓

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