Suppose a blue car is 1/2 mile south of an intersection, driving north towards the intersection at 40 mph (miles per hour). At the same time, a red car is 1/2 mile east of the intersection, driving east (away from the intersection) at an unknown speed. The the straight-line distance between the blue and red car is increasing at a rate of 15 mph. What is the speed of the red car?

Answers

Answer 1

Answer:

dx/dt  = - 18,79 mph

Step-by-step explanation:

The two cars with the intersection point and the straight-line distance between the cars make up a right triangle. In that right triangle, the legs are the distance between each car and the intersection point, and the distance between cars is the hypothenuse

If we call  x  and  y  distances between blue car and red car respectively  and L the hypothenuse by Pythagoras theorem we have:

L²  =  x²  + y²      (1)

Tacking derivatives on both sides of the equation

2*L*dL/dt  = 2*x*dx/dt + 2*y*dy/dt

And from equation (1)

L²  = (0,5)² + (0,5)²    ⇒  L = √(0,5)²  + (0,5)²   ⇒ L = 0,5*√2

By subtitution in equation (2)

2*(0,5*√2)*15 = 2*0,5*dx/dt + 2*0,5*40

(15*√2 - 40 ) / 1  = dx/dt  [mph]

dx/dt  = - 18,79 mph

Note the( - ) sign is equivalent to say that the car is driving away from the intersection point


Related Questions

Would the space in between 2 transversals be an interior angle?

Answers

Answer:

When the two lines being crossed are Parallel Lines the Consecutive Interior Angles add up to 180°. so yes

Step-by-step explanation:

Given: FG is an median. What can you conclude?

Answers

Answer:

The last option line DG is congruent to line GE

Step-by-step explanation:

Median: a segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side

So basically G is the midpoint of DE because FG is the median.

The last option, we can conclude that line DG is congruent to line GE

What is median?

Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong same number of observations.

Median is a line segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.

We are given that FG is an median.

Thus, basically G becomes the midpoint of DE because FG is the median.

So, DG = GE

Hence,

The last option, we can conclude that line DG is congruent to line GE

Learn more about median;

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1. Let U the set of students of the university of Cambridge. Let the subsets of U:
A: over 20 years, B: women, C: with social stratum of 1, 2 and 3.
Describe in words the next sets:
a)A
0
∩ C b)A ∪ B c)B
0
∪ C
0

d)(A ∩ C)
0

e)A
0
∪ C
0

f)(A ∪ C)
0

g)A
0
∩ C
0

h)A ∩ B ∩ C
i)A − B j)(A − B) ∩ C k)B 4 C l)A 4 B.
Compare the given description in c) and d) and the given in f) and g), can you conclude something?.

Answers

Answer:

A) A ∩ C means in both sets, in this case A and C, and in this question all students both over 20 years and with social stratum of 1, 2 and 3.

B) A ∪ B means in either set or both, both will do, in this case meaning all students in A or B or any in between, and in this question all students over 20 years and/or are women.

C) As is already explained above, B  ∪ C means in this question all students that are women and/or have social stratum of 1, 2, and 3.

D) This is the same as A). Refer to A).

E) A ∪ C is already explained above, and in this question means all students over 20 years and/or have social stratum of 1, 2, and 3.

F) Same as E). Refer to E).

G) Same as A). Refer to A).

H) A ∩ B ∩ C means in students in all three sets simultaneously, and in this question all students that are over 20 years, women, and with social stratum of 1, 2 and 3.

I) A - B, in set theory would mean all students in A but not in B, in other words the difference. In this question, it would mean all students over 20 years that are not women.

J) (A - B) ∩ C would mean, as already explained above, all students over 20 years that are not women and with social stratum of 1, 2 and 3. Usually, it's easier to treat all unions or intersections or whatnot inside brackets as one whole thing, kind of like how you do algebra.

K) B 4 C is nonsensical, there is nothing in set theory like this.

L) Same as K).

The given description between C) and D) would be that they are the same, and comparing F) and G), it seems that the question is trying to make the point that they are almost the same but defined differently.

Step-by-step explanation:

Hope this helped!

An automobile assembly line operation has a scheduled mean completion time, , of minutes. The standard deviation of completion times is minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of completion times under new management was taken. The sample had a mean of minutes. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean completion time has decreased under new management

Answers

Answer:

Step-by-step explanation:

Here are the missing values;

Mean μ = 15.5 minutes

Standard deviation = 1.7 minutes

A Random sample of 90 completion

The sample mean = 15.4 minutes

Level of significance = 0.1

Then the following analysis can be made on the above study.

Firstly, the null hypothesis is [tex]\mathbf{H_o : \mu = 15.5}[/tex]

the alternative hypothesis is [tex]\mathbf{H_a: \mu < 15.5}[/tex]  

Since, the value is less than, then this is a one-tailed test.

The Z test statistics can be computed as:

[tex]Z = \dfrac{ \overline x - \mu }{\dfrac{\sigma}{\sqrt{n}} } \ \ \sim \ \ N(0.1)[/tex]

[tex]Z = \dfrac{ 15.4-15.5 }{\dfrac{1.7}{\sqrt{90}} }[/tex]

[tex]Z = \dfrac{ -0.1 }{\dfrac{1.7}{ 9.4868} }[/tex]

Z = −0.560

The critical value of Z at 0.1  level  of significance is:

[tex]Z_{0.1} = -1.28[/tex]

Decision Rule: We fail to reject the null hypothesis sInce -0.560 > -1.28

Conclusion: NO, there is no evidence to support the claim that the mean completion time has decreased. We conclude that the mean completion time remains at 15.5 minutes.

A parabola has the focus at (4, 6) and the directrix y = –6. Which equation represents this parabola?

(x – 4)2 = 24y
(x – 4)2 = StartFraction 1 Over 24 EndFractiony
(x – 4)2 = –24y
(x – 4)2 = Negative StartFraction 1 Over 24 EndFractiony

Answers

Answer:

Step-by-step explanation:

If you graph both the focus and the directrix you will see that the directrix is below the focus...12 units below to be exact. The focus is on the vertical line x = 4, so the vertex also has an x coordinate (which is actually h since h and k represent the vertex) of 4. The vertex is exactly halfway between the focus and the directrix, so that means that the vertex is at (4, 0). h = 4, k = 0. The standard form for this parabola (we know it opens upwards since the parabola ALWAYS wraps itself around the focus and is directed away from the directrix) is:

[tex](x-h)^2=4p(y-k)[/tex]

p is the number of units between the focus and the vertex, or the vertex and the directrix (which is the same number of units since the vertex is smack dab in the middle of them!). That means that p = 6. Filling in 6 for p, 4 for h, and 0 for k we have:

[tex](x-4)^2=4(6)(y-0)[/tex] and simplify to

[tex](x-4)^2=24y[/tex] which is the first choice you're given.

The equation that shows the parabola when parabola has the focus at (4, 6) and the directrix y = –6 should be considered as the (x – 4)2 = 24y.

What is a parabola?

In terms of mathematics, a parabola represent the plane curve  in which there is the mirror-symmetrical and should be made of U-shaped.

Since there has the focus at (4, 6) and the directrix y = –6

So the first equation should be considered.

Learn more about parabola here: https://brainly.com/question/8063993

The forces exerted on an object are shown.

A box has an arrow pointing right labeled 6 N and an arrow pointing left labeled F.

If the object moves right, which of the following is a possible value of F?

Answers

Answer:

The possible value of F must be 5N.

Step-by-step explanation:

A vector quantity is a quantity that comprises of both magnitude and direction. And an example of a vector quantity is force.

In the given question, the pointing arrows are two forces in action, pushing the box in opposite directions.

If the values of both forces pointing left and right are equal, the box would not move. This implies that the two forces are balanced, so the box would be at a state of dynamic equilibrium.

If the box moves to the right, it implies that the force F is less than that pointing right i.e 6N > F.

Therefore, the possible value of F is less than 6N. Thus, F = 5N.

Please help me with this problem will give branlyiest.

Mr. Thompson, a retiree, looks at his check register. What is Mr. Thompson's yearly rent (using 12 months)? $______ What was the average grocery expense in this time period? $_________ Knowing that he buys groceries weekly, Mr. Thompson estimates his yearly expense for groceries to be (4*12* $______ or $_____ Then, Mr. Thompson realizes there are more than 48 weeks in a year. He revises his estimate using (52 x $______ to get $_______ for his estimate. Based on the calculations above, how much money should Mr. Thompson budget annually for food and rent? $______ If Mr. Thompson receives $1,006.28 twelve (12) times a year, what is his yearly income? $_______ Expressed as a percent of income, enter an estimate for rent (to the nearest tenth) and food expenses. Rent: ______%; Food: _____%​

Answers

Answer:

$2459.04

$32.31

$33.45 or $34.92

$32.31

$1680.12

$4139.16

$12075.36

20.4% and 3.2%

Step-by-step explanation:

Monthly rent is 204.92, so yearly rent is 204.92 * 12 = 2459.04

His average grocery expenses is the sum of all the grocery expenses, divided by the number of times he did them

33.45 + 34.92 + 28.56 = 96.93

96.93 / 3 = 32.31

33.45 or 34.92

Since he's revising the calculation, and he does groceries once a week, we will multiply the average he spent on grocery by the 52 weeks he's using in calculations. So, 32.31

The estimate for grocery in a year is,

52 * 32.31 = 1680.12

His annual budget for food and rent would be adding the estimated amount he's to spend on grocery together with the estimated amount he's to spend on rent

2459.04 + 1680.12 = 4139.16

If he receives 1006.28 in a month, multiplying by 12 would give us the estimate he's to receive in a year.

1006.28 * 12 = 12075.36

Percentage

Rent = 204.92 / 1006.28 * 100%

Rent = 20.4%

Food = 32.31 / 1006.28 * 100%

Food = 3.2%

Don't forget the brainliest :)

The value of y varies directly with x, and y =-10 when x=40, identify the value of y when x =-5​

Answers

Answer:

I think that answer is 5 or 35

what's 2+2-2-4+77 and what is the square root of the sum

Answers

Answer:

simplified it is 75 the square root of 75 is 8.66025403784

Step-by-step explanation:

3 1/3 x 5? Tell me exactly how you got this answer like divide or multiply.

Answers

1. covert 3 1/3 to an improper fraction --> 10/3 --> 10/3 x 5
2. just multiply :) --> 10/3 x 5/1 --> 50/3
--> 16 2/3

Answer:

50/3

Step-by-step explanation:

3 1/3 MULTIPLY 3 times 3 plus 1 to to get the anwser in a fraction

get 10/3 and MULTIPLY by 5/1

multiply and get 50/3

That is it. Hope this helps.

:)

What is the relationship between the length of one leg and the length of the hypotenuse of an isosceles right triangles?
A) Leg = Hypotenuse ∙ √2
B) Hypotenuse = Leg ∙ √2
C) Leg ∙ Hypotenuse = √2

Answers

Answer:

B) Hypotenuse = Leg ∙ √2

Step-by-step explanation:

This is a well-known ratio in the 45-45-90 right triangle, but we can derive it.

An isosceles right triangle has two congruent legs forming the right angle and the hypotenuse opposite the right angle. The Pythagorean theorem works since it is a right angle.

Normally, the legs are a and b, and the hypotenuse is c, and we have

a^2 + b^2 = c^2

Here the legs are congruent, so we have a = b.

Substituting a for b, we have

a^2 + a^2 = c^2

2a^2 = c^2

c^2 = 2a^2

c = a√2

Answer: B) Hypotenuse = Leg ∙ √2

Answer:

progably B) Hypotenuse = Leg ∙ √2

Step-by-step explanation:

Solve the system of equations given below.
y - 15 = 3
-2.1 + 5y = -3

Answers

Answer:

1) y=18

2)y=-0.18

Step-by-step explanation:

1) y-15=3. Add 15 on both sides.

y=18

2)-2.1+5y=-3. Add 2.1 on both sides

5y=-0.9. Divide 5 on both sides

y=-0.18

Which expressions are equivalent to -6(6 + 2) + 8?
Choose all answers that apply:
A
-66 + 2 +8
B
- 66 - 4
None of the above

Answers

Answer:

None of the above

Step-by-step explanation: -6(6+2) + 8 = -40 so -66 + 2 +8 = 56 and -66 - 4 = 70

The answer is. None of the above

What is 820 milliliters equal to in liters?

Answers

Answer:

0.82 L

Step-by-step explanation:

Answer: 0.82 liters

Step-by-step explanation:

Vuu try further gridiron

Answers

Answer:

A. M and P

Step-by-step explanation:

To be perpendicular, they only need to have opposite reciprocal slope. For example, the lines, y=3x+8 and y= -(1/3)x-3 would be perpendicular because -1/3 is the opposite reciprocal of 3.

A grocery store sells a bag of 7 oranges for $3.08. What is the cost of oranges, in dollars per orange

Answers

Answer:

$0.44 each

Step-by-step explanation:

3.08/7 = 0.44

The required cost in dollars per orange is $0.44.

Given that,
A grocery store sells a bag of 7 oranges for $3.08. What is the cost of oranges, in dollars per orange is to be determined.

What is the Ratio?

The ratio can be described as the proportion of the fraction of one amount towards others. e.g.- water in milk.

What is arithmetic?

In mathematics, it deals with a number of functions according to the statements.

here,
Let the cost of 1 orange = $x
The grocery store sells a bag of 7 oranges for $3.08.
So for 1 orange,
x = 3.08 / 7
x = $ 0.44

Thus, the required cost in dollars per orange is $0.44.

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The Student Council sold the following items at the home football game. A B C D E F 1 Item Number Price Income Cost Per Sold Item 2 lollipops 85 $0.25 $21.25 $0.12 3 Gummies 48 $0.35 $16.80 $0.18 4 Bubble Gum 79 $0.45 $35.55 $0.22 5 Combos 46 $0.55 $25.30 $0.26 $ $ $ 16! DHE $ 6. TOTAL $50.72

If n stands for number sold and c stands for cost per item, in which column would you use the formula: n x c?

A; Column D
B: Column E
C: Column F
D: Column G​

Answers

Answer: D: Column G​

Step-by-step explanation:

If n is the number of items sold and c is the cost per item, multiplying n and c would give the total expenses for selling that item.

As expenses are in column G, this is therefore the right column to use n * c.

This is can be proven by using the Lollipops as an example.

n = 85

c = $0.12

n * c = 85 * 0.12 = $10.20

$10.20 is the amount of expenses for lollipops in Column G so Column G must be right.

I need G PLZZZZZZZZZZZZZZZ

Answers

I can’t even read it

The lay in Burlington collected $3 930 in overdue fees last year. This year, the library
collectieted 3144 What is the percent of decrease in the amount collected?

Answers

Answer:

We conclude that the percent of decrease = 20%

Step-by-step explanation:

Given

Original amount = $3930Amount of decrease = $3930 - $3144 = $786

Using the formula

Percent of decrease = ( amount of decrease / orignal amount × 100 ) %

                                   = ( 786 / 3930 × 100 ) %

                                    = ( 0.2 × 100 ) %

                                    = 20%

Therefore, we conclude that the percent of decrease = 20%

Consider the figure below. If ∆ABC is translated using the vector (x, y)→(x−3, y+3), then rotated 180° about the origin, what will be the x-coordinate of C’ ?

Answers

Answer: -7

Step-by-step explanation:

I’m doing the test

You can spend up to $35 on a shopping trip. You want to buy a shirt that cost $14. Write and solve an inequality that represents the amount of money you will have left if you buy the shirt

Answers

Answer:

Step-by-step explanation:

a. 35 greater than or equal to 14 + x

   35 - 14 = 21

   x = $21

b. If the shirt is 30% off it would cost $9.80

   14 x 0.3 = 4.2

   14 - 4.2 = 9.8

   35 is greater than or equal to 9.80 + x

   35 - 9.8 = 25.2

   x = $25.20

   This changes the inequality by making x greater than it was in part a

c. Yes, you do have enough money to buy the shirt that is on sale and a pair of pants. x is the amount that you have left to spend after you buy the shirt that is on sale. 25.20 is greater than the cost of the pants.

2. Which of the following vectors is equal to vector with initial point (3, 7) and
terminal point (-5, -3)?
f. u= <2,-10>
g. u = <-2,-4>
h, u =<-8,4>
j. u = <-8,-10>

Answers

Answer:

j

Step-by-step explanation:

We can subtract 3 in the x-coordinate and 7 in the y-coordinate for both points.

(3-3,7-7) = (0,0)

(-5-3,-3-7) = <-8,-10>

Hope this helps!

26+5 i am in kinder pls help

Answers

31 you kinder ok bud
Answer:
31
you could just use a calculator yk

Carla currently has $300 in her bank account. Each time she goes to the ATM,
she withdraws $20. Write an equation representing this situation:

Answers

Answer:

y = -20x + 300

Step-by-step explanation:

y is total amount of money left (because this is the answer we are trying to find.)

x is the amount of times she goes to the ATM (because this is our unknown variable.)

-20 multiplies by x because she loses $20 every time she goes to the ATM. The equation has + 300 because she already has $300 in her bank account.

Find f(2) If f(x) = (x + 1)2.​

Answers

Answer:

f(2)=9

Step-by-step explanation:

Kendal bought x boxes of cookies to bring to a party. Each box contains 12 2 points
cookies. Someone else brought 24 cookies. Let 'y' represent the total
number of cookies at the party. Show an equation in SLOPE-INTERCEPT
FORM that models this situation. Kendal brings 60 boxes to the party. How
many cookies in total were at the party?

Answers

Answer:

744 cookies

Step-by-step explanation:

PLZ MARK BRAINLIEST ON THE TOP RIGHT CLICK THE CROWN.

Nine children on the swim team dont like ice cream if this represents 18% of children on the swim team how many children are on the swim team

Answers

Answer:

Um.. Im not sure about this one.. you're in college?

Step-by-step explanation:

Answer:

50 children in total

Step-by-step explanation:

question is really asking this:  9 is 18% of what number

9 = .18x

9/.18 = 50

A group of eight people are attending the movies together.

a. Two of the eight insist on sitting side by side. In how many ways can the eight be seated together in a row?
b. Two of the people do not like each other and do not want to sit side-by-side. Now how many ways can the eight be seated together in a row?

Answers

Answer:

I think A

Step-by-step explanation:

I need help i dont understand any of this

Answers

Step-by-step explanation:

multiply all the fractions together in your calculator :)

solve the following equation for y

x+y=3​

Answers

9514 1404 393

Answer:

  y = 3 -x

Step-by-step explanation:

Subtract x from both sides of the equation.

  x -x +y = 3 -x

  y = 3 - x

Answer:

y=3-x

explanation

its that

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Troy runs marathons, which are about 26 miles long. He usually runs 4 marathons a year, and he has been doing this for 11 years. Troy estimates he has run a little over 100 miles during all these marathons. Is that a good estimate?Yes No it is much high No it is much low WHICH DEFINTIOION GOES TO EACH LETTER/WORD. FILL IN THE BLANK-The place inside Earth where the energy is an earthquake is centered is the ________.-The instrument used to record earthquake activity is a/an __________.-The __________ of an earthquake is the point on the surface of Earth directly above the focus.-The __________ of an earthquake is based on the amplitude of the seismic waves.-An undersea earthquake may produce a/an _________.-Buildings constructed to withstand most earthquakes are said to be _________ ________.-_______ is magma that has flowed onto Earth's surface.-The __________ is divided into about 13 major plates.-________ are long cracks produced at divergent plate boundaries.-The __________ scale measures the magnitude of an earthquake.-The seismic waves that do the most damage to structures and property during an earthquake are _________ _________.-An avalanche of glowing rocks flowing on a cushion of hot gases is called a/an ___________ __________.-A large, broad volcano with gently sloping sides that is formed by the build-up of basaltic layers is a ________ volcano.-A relatively small volcano formed by moderate to explosive eruptions of tephra is a _________________ volcano.-A steep-sided volcano formed from alternating layers of violent eruptions of tephra and quieter eruptions of lava is a ___________ volcano.-The movement of the ground that occurs when rocks inside Earth pass their elastic limit, break suddenly, and experience elastic rebound is called a/an ______________.-A fracture that occurs when rocks break and that results in relative movement of opposing sides is called a ________.A. lavaB. faultC. seismic safeE. shieldF. cinder-coneG. focusH. tsunamiI. riftsJ. seismographK. hot spotL. surface wavesM. epicenterN. 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Find the slope of the line (0,1) and (4,2)6. Find the slope of the line (-1,6) and (4,2) 1. Is an arithmetic sequence a function?Sometimes, it depends on the arithmetic sequence.Yes, always.Not enough information is given.No, never Solve the system of equation by elimination. Amit solved the equation StartFraction 5 over 12 EndFraction = Negative StartFraction x over 420 EndFraction for x using the steps shown below. What was Amits error? StartFraction 5 over 12 EndFraction = Negative StartFraction x over 420 EndFraction. StartFraction 5 over 12 EndFraction (420) = Negative StartFraction x over 420 EndFraction (420). X = 175. Amit should have multiplied both sides of the equation by StartFraction 5 over 12 EndFraction. Amit should have multiplied both sides of the equation by StartFraction 12 over 5 EndFraction. The product of StartFraction 5 over 12 EndFraction and 420 is not equal to 175. 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Need help plz need to solve for x.1) 2x-7= -2x+12) 2(x-7)=6-2x Need help pleaseeee. It is most important for the media in a multimedia presentation to beformal and academic.relevant and engaging.exciting and dramatic.humorous and relatable. If an object has a weight of 4050 N near the surface of the Earth, what is its mass? Write an equation that represents the tile pattern in the table below