Answer:
x^2 + y^2 = r^2
Step-by-step explanation:
See image. "An angle in standard position" means the vertex (point part) of the angle is at the origin (0,0). And one side of the angle is glued onto the x-axis. The other side of the angle is free to rotate around the axis. That's the terminal side. Then there's a point P (x,y) on that side. See image. And r is labelled there. This set up makes a right triangle. So I put Pythagorean theorem as the answer here, but honestly if you are learning any right triangle theorems or trigonometry, you could use this set up. The leg that lays along the x-axis is x units long and the other leg is y units long. The hypotenuse is r units long.
Answer:
Step-by-step explanation:
We have to take the derivatives for both functions and replace in the differential equation. Hence
for y=e^{-5x}:

for y=e^{6x}:

Now we replace in the differential equation y'' − y' − 30y = 0
for y=e^{-5x}:

for y=e^{6x}:

Now, to know if both function are linearly independent we calculate the Wronskian


I hope this is useful for you
Best regard
Answer: £225
Step-by-step explanation:
Let Sarah's amount be represented by x.
Since Caroline gets three times as much as Sarah, Caroline will get: 3x
Bridget gets twice as much as Caroline, therefore Bridget will get: 2 × 3x = 6x
Sarah = x
Caroline = 3x
Bridget = 6x
Total = x + 3x + 6x = 10x
Caroline's faction is 3/10. We then multiply the fraction by £750. This will be:
= 3/10 × £750
= 0.3 × £750
= £225
Caroline will get £225
Answer:
56-15=41is a required answer