Mathematics, 13.12.2019 04:31 eguzmandpandoracom

Avery can run at 10 uph. the bank of a river is represented by the line 4x + 3y = 12, and avery is at (7, 5). how much time does avery need to reach the river?

Answers: 3

Show answers

Answers

The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)

4x+3y=12

3y=-4x+12

y=-4x/3+12/3

So a line perpendicular to the bank will be:

y=3x/4+b, and we need it to pass through (7,5) so

5=3(7)/4+b

5=21/4+b

20/4-21/4=b

-1/4=b so the perpendicular line is:

y=3x/4-1/4

So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:

(3x-1)/4=(-4x+12)/3 cross multiply

3(3x-1)=4(-4x+12)

9x-3=-16x+48

25x=51

x=51/25

x=2.04

y=(3x-1)/4

y=(3*2.04-1)/4

y=1.28

So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2.04)^2+(5-1.28)^2

d^2=38.44

d=√38.44

d=6.2 units

Since he can run at 10 uph...

t=d/v

t=6.2/10

t=0.62 hours (37 min 12 sec)

So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.

Answer from: Quest

i need a picure

step-by-step explanation:

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Another question on Mathematics

Mathematics, 21.06.2019 15:10

If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system? a. there are infinitely many solutions. b. there is no solution. c. there is exactly one solution. d. the lines in a system cannot be parallel.

Answers: 2

Answer

Mathematics, 21.06.2019 17:00

If the wwight of a package is multiplied by 7/10 the result is 65.8 find the weight of the package

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Interest begins accruing the date of the transaction except for auto loans mortgages credit card cash advances credit card purchases

Answers: 1

Answer

Mathematics, 21.06.2019 23:20

This graph shows which inequality? a ≤ –3 a > –3 a ≥ –3 a < –3