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.

Step-by-step explanation:

When x = -1
Substitute x = -1 into y = 2x
y = 2(-1)
y = -2
( -1, -2)
When x = 3
Substitute x = 3 into y = 2x
y = 2(3)
y = 6
( 3, 6)
Answer: The greatest number of playlist Katherine can make =8
Each of playlist will have 4 pop songs and 9 rock songs.
Step-by-step explanation:
Given: The number of pop songs Katherine has= 32
The number of rock songs Katherine has= 72
If she want to make playlist such that in each playlist there is equal number of pop and rock songs, we need to find the GCF(greatest common factor) of 32 and 72.
We know that 
We can see the GCF(32,72)=
Hence, the greatest number of playlist Katherine can make =8
The number of pop songs= 
the number of rock songs=
Each of playlist will have 4 pop songs and 9 rock songs.
Change in altitude:
42,000 - 18,000 = 24,000 feet
Rate of change = 24,000 feet / 12 minutes = 2,000 feet per minute
Because the plane was going down, the rate of change would be negative.
The rate would be -2,000 feet per minute.
The score(s) that will be obtained respectively in an independent-measures design and repeated-measures design are; 1 and 2
<h3>How to interpret Experiments?</h3>
There are different ways to carry out an experiment in mathematics. This is because there are various means of research and also ways to interpret the results.
Now, when comparing two treatment conditions, an independent-measures design would always obtain 1 score for each subject. However, when a repeated-measures design is carried out on the same sample, it will obtain 2 scores.
Read more about Experiments at; brainly.com/question/25677592
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