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Slav-nsk [51]
4 years ago
10

Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

Mathematics
1 answer:
jolli1 [7]4 years ago
4 0
1/2y^2=1/2x^2+8. The curve's slope at (x,y) is x/y, so dy/dx=x/y. To solve this differential equation, rearrange it to: y*dy=x*dx, and by integrating both sides, we get 1/2y^2=1/2x^2+C (some constant). Plug in (0,4) into this equation, 8=0+C, so C=8. The curve's equation is 1/2y^2=1/2x^2+8.
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Two buses leave a station at the same time and travel in opposite directions. One bus travels 15 /kmh faster than the other. If
Nat2105 [25]
Since the buses travel in opposite directions, the speed at which they distance themselves is the sum of their speeds.
One bus travels at speed s.
The other bus travels at speed s + 15.
The sum of the speeds is s + s + 15 = 2s + 15

speed = distance/time

distance = speed * time

366 = (2s + 15) * 2

183 = 2s + 15

168 = 2s

s = 84

The slower bus travels at 84 km/h.

s + 15 = 84 + 15 = 99

The faster bus travels at 99 km/h.

Check:
In 2 hours, the slower bus travels 2 * 84 km = 168 km
In 2 hours, the faster bus travels 2 * 99 km = 198 km
In 2 hours, the buses are 198 km + 168 km = 366 km apart.
Our answer is correct.
6 0
3 years ago
Which equation can be used to calculate the area of the shaded triangle in the figure below?
GrogVix [38]

Answer:

It is \frac{1}{2} (12 × 4) = 24

Step-by-step explanation:

\frac{1}{2} (base × height) = area of triangle

\frac{1}{2} (12 × 4) = area

area = 24

3 0
2 years ago
The average human heart beats 75 times every minute. The average horse has a heartbeat of 40 times every minute. How many times
Effectus [21]

Answer:

4500

Step-by-step explanation:

multiply the amount of times the heart beats every minute and multiply it by how many minutes which is 60 so 75 times 60 is 4500

6 0
3 years ago
Reduce 4/36 to simplest terms
Alona [7]

Answer: its 1/9

All you do is divide them by 4

4 divided by 4=1

36 divided by 4=9

Also can I get brainly thing?

5 0
3 years ago
Read 2 more answers
Reasoning A store sells packages of comic books with a poster. A poster and 5 comics cost ​$13.99. A poster and 12 comics cost ​
aliya0001 [1]

Answer:

Step-by-step explanation:

Reasoning A store sells packages of comic books with a poster. A poster and 5 comics cost ​$13.99. A poster and 12 comics cost ​$20.99. Write a linear function rule that models the cost y of a package containing any number x of comic books. Suppose another store sells a similar​ package, modeled by a linear function rule with initial value ​$. Use pencil and paper. Explain which store has the better deal. The linear function rule is y nothing.

8 0
3 years ago
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