Answer:
it will take her 40 years to reach her goal.
Step-by-step explanation:
Answer:
B = (3, 5)
Step-by-step explanation:
Point A is at (-7,5) and point C is at (5,-1). Find the coordinates of point B on AC such that AB is 5 times longer than BC. Then, B split AC in a 5:1 ratio.
rise = yC - yA = -1 - 5 = -6
run = xC - xA = 5 - (-7) = 12
c = 5/(5+1) = 5/6
B = (xA + c*run, yA + c*rise)
B = (-7 + 5/6*12, 5 + 5/6*-6)
B = (3, 5)
Given
2x³ + (x³ - 3) sin(2πy) - 3y = 0
we first notice that when x = ³√3, we get
2 (³√3)³ + ((³√3)³ - 3) sin(2πy) - 3y = 0
2•3 + (3 - 3) sin(2πy) - 3y = 0
6 - 3y = 0
3y = 6
y = 2
Differentiating both sides with respect to x gives
6x² + 3x³ sin(2πy) + 2π (x³ - 3) cos(2πy) y' - 3y' = 0
Then when x = ³√3, we find
6(³√3)² + 3(³√3)³ sin(2π•2) + 2π ((³√3)³ - 3) cos(2π•2) y' - 3y' = 0
6•³√9 + 3•3 sin(4π) + 2π (3- 3) cos(4π) y' - 3y' = 0
6•³√9 + 0 + 0 - 3y' = 0
3y' = 6•³√9
y' = 2•³√9
(that is, 2 times the cube root of 9)
It’s easiest to think about it this way:
If the pond is 15 feet wide, then adding 3 feet to each side would increase the side length to the square by six feet (3 feet on each side). This makes the area within the square equal to 18x18 feet, or 324 square feet. But, this isn’t the area of the sidewalk, it’s the area of the sidewalk plus the area of the pool.
The pool is fifteen feet wide, which means that it has an area of 225 square feet. So, to find the area of the side walk, we can subtract the area of the pool from the area of the pool and sidewalk, which will give us the area of the sidewalk by itself.
324-225=99 square feet.
The pool has an area of 225 square feet, and the sidewalk has an area of 99 feet.
Answer: 1/12 of the cake.
Step-by-step explanation:
First, find the LCM (Least Common Multiple) of 3 and 4. The easiest way to do this is to multiply the two together. 3*4 = 12.
Now, convert each fraction to be out of twelfths. Do this by setting up a proportion. 2/3 = x/12. Cross multiply and divide. 2*12 = 24. 24/3 = 8. Therefore, 2/3 = 8/12.
Do the same for 1/4. 1/4 = x/12. Cross multiply and divide. 12*1 = 12. 12/4 = 3. Therefore, 1/4 = 3/12.
Now add these two fractions by adding the numerators and keeping the denominators the same. 8/12 + 3/12 = 11/12.
Subtract this answer from 1 (12/12). 12/12 - 11/12 = 1/12
