Answer:
The answer is below
Step-by-step explanation:
The standard form of the equation of an ellipse with major axis on the y axis is given as:
Where (h, k) is the center of the ellipse, (h, k ± a) is the major axis, (h ± b, k) is the minor axis, (h, k ± c) is the foci and c² = a² - b²
Since the minor axis is at (37,0) and (-37,0), hence k = 0, h = 0 and b = 37
Also, the foci is at (0,5) and (0, -5), therefore c = 5
Using c² = a² - b²:
5² = a² - 37²
a² = 37² + 5² = 1369 + 25
a² = 1394
Therefore the equation of the ellipse is:
The solution is where the red line crosses the blue line, which on the X axis is between the 1 and the 2, so about 1.5.
Convert the fractions to decimal and see which one is close to 1.5:
13/8 = 1.625
25/16 = 1.5625
7/4 = 1.75
27/16 = 1.6875
The closest one to 1.5 is 25/16
Hello there! How are you today?
4x + 5 -2 = 3x + 7x - 15
First, we need to get the variable (x) on one side. To do that, we must simplify the right side of the equation, and then decide what to do from there, so let's proceed to do so.
3x + 7x = 10x
4x + 5 - 2= 10x - 15
Now we have x simplified on both sides of the equation. However, we need x to be on one side of the equation in order to solve for it.
Subtract 4x from both sides.
4x - 4x = 0
10x - 4x = 6x
We are now left with:
6x - 15 = 5 - 2
Simplify the right side of the equation.
5 - 2 = 3
6x - 15 = 3
Now we need to isolate x. To isolate x, we need to add 15 to both sides, as x is being subtracted by 15, and adding 15 will cancel it out.
-15 + 15 = 0
3 + 15 = 18
We now are left with:
6x = 18
Now we only have one step left, and that is to solve for x. Since x is being multiplied by 6, we need to perform the opposite order of operations to cancel it out. To do that, we must divide both sides by 6 to solve for x.
6x = 18
Divide both sides by 6.
6x / 6 = x
18 / 6 = 3
We are now left with the solution:
x = 3
I hope this helps!
Answer: Length: 24
Step-by-step explanation:
Joe runs one lap around a track in 80 seconds. Joe and Jim meet after 30 seconds.We know how long does it take for Joe to run one lap, so we can calculate what distance he runs in 30 seconds:
He runs half lap for 40 seconds. He runs quarter lap for 20 minutes and he runs 1/8 lap for ten minutes. So for 30 seconds he runs 3 * 1/8 lap=3/8 lap.
Because Jim runs in opposite direction this means that he will meat with Joe at 1-3/8=5/8 lap. So, Jim runs 5/8 lap for 30 seconds.
1/8 lap Jim runs for 30/5=6 seconds, so Jim needs 8*6=48 seconds to run the lap.
After 30 seconds Joe has run e runs
