Answer:
The Field's length is 93ft
Step-by-step explanation:
P=2L+2w
360=2(w+6)+2w
360=2w+12+2w
360=4w+12
348=4w
348/4=w
87=w
L=w+6
L=87+6
L=93
OK, so this is assuming we are considering that the first three kids to solve ARE NOT in the first day.
So we have 3 kids and it doubles
Day 1 : 6
Day 2 : 12
Day 3 : 24
Day 4 : 48
Day 5 : 96
Day 6 : 192
Day 7: 384
So it should take 7 days or a week to solve all the problems.
The equation:
(3 * 2)^x = 384
Eric need 5 batches of paving stones to created his patio.
Answer:
Year in which the entrepreneur break even is 4
Step-by-step explanation:
We are given:
p(x) = x^3-4x^2+5x-20
We would find the value of x
Solving:
x^3-4x^2+5x-20 = 0
(x^3-4x^2)+(5x-20) = 0
x^2(x-4)+5(x-4) = 0
(x-4)(x^2+5)=0
=> x-4 = 0 and x^2+5 =0
x = 4 and x^2 = -5
x = 4 and x = ±√-5 or ±√5 i (not real solutions)
So, x = 4
So, year in which the entrepreneur break even is 4
Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
