Doug is a dog, and his friend Bert is a bird. They live in Salt Lake City, where the streets are 1/16 miles apart and arranged in a
square grid (see map). They are both standing at the corner of 6th avenue and L street. Doug can run at an average speed of 30
mi/hr through the streets of Salt Lake, and Bert can fly at an average speed of 20 mi/hr. They are about to race to the corner of
10th avenue and Estreet. who would win and why?

Answers

Answer 1

No map given but it shouldn't matter.

E is the 5th letter, L the 12th.

Start at S(6,12).  End at E(10,5)

The vector between them, E-S=(4,-7)

Each unit is 1/16 of a mile, though that probably doesn't matter that much.

Doug has to stay on the grid, so has to run |4|+|7|=11 units.  At 30 mi/hr that takes (11/16)/30 =  0.022916 hours.

Bert can go diagonally, so flies √(4²+7²)=√65 ≈ 8.06 units.  At 20 mi/hr that takes (8.06/16)/20 = 0.025194 hours.

Answer:  Doug wins

Why? Because it's quicker to cover 4+7 at 30 mph than it is to cover √(4²+7²) at 20 mph.  That is, Doug is 1.5 times faster and the 1.5 times the diagonal distance is more than the grid distance.

Answer 2

Answer:

Doug wins. He finishes in 1.38 minutes. Bert takes 1.51 minutes.

Step-by-step explanation:

Each city block is a square 1/16 mile by 1/16 mile.

From 6th Av and L Street to 10th Av and E Street, they need to go 4 avenues and 7 streets over. These two distances along blocks are the legs of a right triangle. The right triangle has legs of length 4 * 1/16 mile and 7 * 1/16 mile.

leg1 = 4 * 1/16 mile = 0.25 mile

leg2 = 7 * 1.16 mile = 0.4375 mile

The hypotenuse of the right triangle can be calculated by the Pythagorean theorem.

a^2 + b^2 = c^2

(0.25 mile)^2 + (0.4375 mile)^2 = c^2

c = 0.50389

The direct distance from one corner to the other is 0.50389 miles.

The bird travels this distance since the bird can fly above the streets.

The dog has to travel along the legs of right triangle by running in the streets and avenues. The dog travels 0.25 mile + 0.4375 mile = 0.6875 miles

Now we need to see what takes less time:

Bird: distance of 0.50389 miles at 20 mph, or

Dog: distance of 0.6875 miles at 30 mph

We start with the formula for speed:

speed = distance/time

s = dt

Now we solve it for time:

st = d

t = d/s

Time equals distance divided by speed.

Now we find the times for the bird and for the dog.

Bird:

t = d/s = (0.50389 mi)/(20 mi/h) = 0.02519 hours = 1.51 minutes

Dog:

t = d/s = (0.6875 mi)/(30 mi/h) = 0.0229 hours = 1.38 minutes

The bird takes 1.51 minutes, and the dog takes 1.38 minutes.

The dog takes less time to get there, so the dog wins.


Related Questions

A stack of 12 bricks is 27 inches high. How high is each brick?

Answers

Answer: 2.25 inches

Step-by-step explanation:

27/12= 2.25

What does the word ‘Denotation’ mean?

Answers

Answer: Depends on what your talking about so I'll give all 3 definitions.

Step-by-step explanation:

1.)The literal or primary meaning of a word, in contrast to the feelings or ideas that the word suggests.

-Used in a sentence- Beyond their immediate denotation, the words have a connotative power.

2.) When used in philosophy it means, the object or concept to which a term refers, or the set of objects of which a predicate is true.

3.) And, the last definition is, the action or process of indicating or referring to something by means of a word, symbol, etc.

PLEASE HELP AGAIN, SORRY I SUCK AT MATH.

Answers

Answer:

C. 24 degrees

Step-by-step explanation:

All triangle must be 180 degrees in total. So you have to add all the known degrees together to find the missing degree.

120+36=156

Then subtract the sum of the known angles from 180 to find the degree of the unknown angle

180-156=24

Answer: C

Step-by-step explanation:

I'll explain why.

The sum of the angles in a triangle must be equal to 180º. We already know 2 of the 3 angles, therefore, we can make an equation to find x.

The sum of the angles (x+36+120) must be equal to 180 (=180)

x+36+120=180

Combine like terms

x+156=180

Subtract 156 to isolate x

x=180-156

x=24

The price of a gallon of milk, in dollars, is measured in the

Answers

What is that the question

Answer:ones

Step-by-step explanation:

math question down below screen shot

Answers

Answer:

the screen shoy isnt showing up

Step-by-step explanation:

Finding Distances from the Mean
The mean of the data is 44.7. Complete the chart to find the distances from the mean.
Of
Temp (°F)
2938
45
31
50
58
62
Distance
from the
Mean
15.7
6.7
13.7
y
13.3

Answers

Answer:

x = 0.3, y = 5.3, z = 17.3

Step-by-step explanation:

Since given question is incomplete, so here is the complete table for the distance from the mean.

Temp (°F)                              29      38       45    31      50     58     62    

Distance from the mean    15.7    6.7       x    13.7      y     13.3       z

It's given that the mean of the data is 44.7

Since distance from the mean of a data is the absolute value of the difference of data and mean,

Therefore, distance from the mean of the data will be,

x = |44.7 - 45| = 0.3 (absolute value of the difference)

y = |44.7 - 50| = 5.3

z = |44.7 - 62| = 17.3

Answer:

x =   0.3

y =   5.3

z =   17.3

Step-by-step explanation:

6 customers entered a store over the course of 18 minutes. At what rate were the customers entering the store in customers per minute?

Answers

Answer:

3 minutes

Step-by-step explanation:

18 divided by 6 = 3 minutes

Hope this helps :)

In July 2008, a wildfire near Yosemite
National Park burned about 53 square
miles of forest. If one square mile equals
640 acres, about how many acres of
forest were burned?

Answers

I’m not positive but do 53 times 640 and you should get the answer

PLEASE HELP FAST

Which transformation preserves size and shape. Choose ALL correct answers

A) Dilations
B) Rotations
C) Translations
D) Reflections

Question 2

Which transformations preserve orientation?

A) Translations
B) Rotations
C) Reflections
D) Dilations

Answers

Answer:

A) Dilation  C)Reflections or B) Rotations

Step-by-step explanation:

Need help please owo with all of them

Answers

First one d second c and third one a

Answer:

d, c and a

Step-by-step explanation:

O///O

Solve: 5/9 + (-4/5)

Answers

Answer:

-11/45

Step-by-step explanation:

5/9 + (-4/5)

25/45 + (-36/45)

(Multiplied each side by opposite denom.)

25/45 -36/45

Simplify

25-36=-11

-11/45

Cannot simpfily

Answer:

Step-by-step explanation:

5/9 + (-4/5)

-11/45 or − 0.244444444 and on and on forever

Please help with this

Answers

Answer:

A

Step-by-step explanation:

Draw the shape described below and find its total surface area.
A cylinder 25 ft tall with a diameter of 12 f

Answers

Answer:

hope this helps :)

Step-by-step explanation:

8:07

Cylinder volume & surface area (video)

30 students apply for a scholarship,
10 have college degrees
18 have school certificates
8 have both qualifications.
(a) Draw a Venn diagram to show thi
information.
(b) How many students have no
qualification?​

Answers

Answer:

A - school certificates

B - college degrees

So 30 - (10 + 8 + 2) = 10 have no qualification

find the output, y, when the input, x, is -5.​

Answers

Answer:

y = -2

Step-by-step explanation:

When x = -5

Go to the blue line

y = -2

Answer:

There are 2 questions with the same question but with a different graph.

This graphs answer is -2.

But the other graph that people are confused about is 7.

Step-by-step explanation:

Hope this helps! :)

what is the difference between - 21 and -8 on a number line?

Answers

the difference is 13

Answer:

They are 13 units apart. -8 is closer to zero while -21 is farther ways from zero.

A survey will ask people if they want
more stop signs near a school. Which
group would be probably be biased
against this idea?
A students
B teachers
C driver

Answers

driver because it slows them down

Answer:

I believe the answer is C. Driver.

Step-by-step explanation:

The driver is the person who has to pass by the school everyday. This means they would have to take out extra time because of the stop signs, so they would be against this.

There are 30 marbles in a bag. You randomly choose 20 marbles from the bag. The results are shown in the table. Predict the total number of red marbles.

Color
Blue 6
Red 12
Yellow 2
There are about how many red marbles?

Answers

Answer:

12 because if you add 6 and 12

Step-by-step explanation:

hope it helps uou !!

Answer:

It's 12

Step-by-step explanation:

hope it helps you !!

You are wakeboarding on a river. You travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a dock. The boat travels x miles per hour during the entire trip, and the river current is 3 miles per hour.

How long will the trip take when then speed of the boat is 18 miles per hour? Round to the nearest tenth minute.

Answers

Answer:

17.3

Step-by-step explanation:

(2+18)=(20mph*2miles)=6 minute

(18-2)=16mph*3miles=11.25

17.25

Point L was plotted at (-4, 1), then L was transformed creating point L’ at (-1, -4).Which transformation rule could have been used to plot L’?
Reflection across the x-axis
a 180 degree rotation about the origin
A 270 degree rotation counterclockwise rotations about the origin
A translation using the rule (x,y) -->(x+3, y -5)

Answers

Answer:

you would go down 2 from the point

Step-by-step explanation:

add or subtract (7x^2-x-2)-(-6x^3+3)

Answers

Answer:

[tex] \tt{}6x ^{3} + {7x}^{2} - x - 5[/tex]

Step-by-step explanation:

[tex] \tt{}(7 {x}^{2} - x - 2) - ( - 6 {x}^{3} + 3)[/tex]

[tex] \tt{}7 {x}^{2} - x - 2 + 6x^{3} - 3[/tex]

[tex] \tt{} {7x}^{2} - x - 5 + 6x ^{3} [/tex]

[tex] \tt{}6x ^{3} + {7x}^{2} - x - 5[/tex]

Answer:

[tex]6 {x}^{3} + 7 {x}^{2} - x - 5[/tex]

Step-by-step explanation:

[tex](7 {x}^{2} - x - 2) - ( - 6 {x}^{3} + 3)[/tex]

➡️ [tex]7 {x}^{2} - 2 - ( - {6}^{3} + 3)[/tex]

➡️ [tex]7 {x}^{2} - x - 2 + 6 {x}^{3} - 3[/tex]

-2 - 3-(2 + 3)-5

➡️ [tex]7 {x}^{2} - x - 5 + 6 {x}^{3} [/tex]

➡️ [tex]6 {x}^{3} + 7 {x}^{2} - x - 5[/tex] ✅

Complete the equation of the line whose slope is -2 and y-intercept is (0,-8)

y=

Answers

Answer:

y = -2x - 8

Step-by-step explanation:

We want to find the slope-intercept form of this equation. Slope-intercept form is denoted by: y = mx + b, where m is the slope and b is the y-intercept.

We already know that the slope is -2, so that means m = -2.

We also know the y-intercept (or the point where the line crosses the y-axis) is (0, -8), which means b = -8.

Thus, our equation is: y = -2x - 8.

~ an aesthetics lover

y=-2x-8 this should be right i had this same problem before :)

There are 90 chickens on the farm. If 60% of the animals on the farm are chickens, how many animals are on the farm? Pls help asap!

Answers

Answer:

150

Step-by-step explanation:

You need to add 60 to the 90 and then check it by doing 60% of 150.

Hope this helps.

Answer: 150 is the answer

Step-by-step explanation:

Can someone help with this

Answers

Answer:

the answered is -3 like in the picture

Step-by-step explanation:

Help please will give brainly! Clara’s friend Brian decides to find his median as well. Find the median and type it in the answer box. What does the median show us?

Answers

Answer:

The median is 88. The median shows that Brian gets on average 88% on his tests.

Step-by-step explanation:

If you put the numbers in order and get the average of the two middle number, it is 88.

Fond the equation of the line shown

Answers

Answer:

y+-1/2x-1

Step-by-step explanation:

The line is negative

It rises one digit and runs 2

and it crosses though -1 on the y axis

233 is equal to r more than 48?

Answers

I think it’s equal to .hope that helps

Answer:

R = 152

Step-by-step explanation:

what i did was if it is talking about more than 48 something plus 48 is 200 so

200 - 48 = 152

r = 152

so 200 is 152 more than 48

Hope this helpsBrainliest plzAsk any more math questions if you want

In a right triangle, sin (40 – x)° = cos (3x).What is the value of x?

Answers

Answer:

Value of x = 25

Step-by-Step Explanation:

~ Knowing that, in a right triangle ~

sin(40-x)=cos(3x) ⇒

sin(40-x)=sin(90-3x) ⇒

40 - x = 90 - 3x ⇒

40 - x  +3x=90 - 3x  +3x =>

40+2x=90 =>

2x=50 =>

x = 25

Now it is proven to be that,

x = 25

Ade has two similar scale models of the same pyramid. The first model has a
height of 5 inches and a surface area of 80.9 square inches. The linear dimensions
of the second model are each increased by a common factor so that the height of
the second model is 15 inches. To the nearest tenth of a square inch, what is the
surface area of the second model?

Please help!

Answers

Answer: 242.7 square inches

Step-by-step explanation:

Hi, to answer this question we have to apply proportions:

The first model has a height of 5 inches and a surface area of 80.9 square inches:

The proportion is : height/ surface area= 5 in / 80.9 in2

For a height of 15 inches

15 in/ x in2

So:

5/80.9 = 15/x

x= 15/ (5/80.9 )

x= 242.7 square inches

Feel free to ask for more if needed or if you did not understand something.  

If you have a cube with a side length of ¼, how many cubes can fit into your rectangular prism? Explain.

Answers

Answer:

Step-by-step explanation:

No of cubes that can fit into rectangular prism =   Volume of rectangular prism

                                                                                   Volume of cube

Find the volume of rectangular prism and divide that by the volume of cube

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