Answer:
about 29.7 minutes
Step-by-step explanation:
If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:
1/c + 1/(c+16) = 1/18
Multiplying by 18c(c+16), we get ...
18(c +16) + 18(c) = c(c+16)/18
36c +288 = c^2 +16c
c^2 -20c = 288 . . . . . subtract 36c
c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square
(c -10)^2 = 388
c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root
It takes Charles about 29.7 minutes to mow the lawn by himself.
Answer:
x=-0.625
Step-by-step explanation:
24x+15=0
-15 -15
24x=-15
x=-0.625
<span> y = 2/7 x - 1/7
slope = 2/7
</span><span>perpendicular lines, slope is opposite and reciprocal
</span>so slope of new line = -7/2
<span>passes through the point (9,-32)
</span><span>slope-intercept form: y = mx + b
so
b = y - mx
b = -32 - (-7/2)(9)
b = -32 + 63/2
b = -1/2
equation in </span>slope-intercept form:
y = -7/2 x - 1/2
Answer:
First some theory we need to solve this problem.
For a circle of radius R, the perimeter is:
P = 2*pi*R
where pi = 3.14
If we have a section of this circle, defined by an angle θ, the length of this arc will be:
A = (θ/360°)*2*pi*R
In the case of the problem, the total distance that the child travels is equal to the length of an arc of 310° in a circle of radius r = 6ft.
Using the above formula, we know that the length of this arc is:
A = (310°/360°)*2*3.14*(6ft) = 32.4 ft
