198 is the answer ok ok ok
Answer:
C. Ari and Matthew collide at 4.8 seconds.
Explanation:
Ari and Matthew will collide when they have the same x and y position. Since Ari's path is given by
x(t) = 36 + (1/6)t
y(t) = 24 + (1/8)t
And Matthew's path is given by
x(t) = 32 + (1/4)t
y(t) = 18 + (1/4)t
We need to make x(t) equal for both, so we need to solve the following equation
Ari's x(t) = Matthew's x(t)
36 + (1/6)t = 32 + (1/4)t
Solving for t, we get
36 + (1/6)t - (1/6)t = 32 + (1/4)t - (1/6)t
36 = 32 + (1/12)t
36 - 32 = 32 + (1/12)t - 32
4 = (1/12)t
12(4) = 12(1/12)t
48 = t
It means that after 48 tenths of seconds, Ari and Mattew have the same x-position. To know if they have the same y-position, we need to replace t = 48 on both equations for y(t)
Ari's y position
y(t) = 24 + (1/8)t
y(t) = 24 + (1/8)(48)
y(t) = 24 + 6
y(t) = 30
Matthew's y position
y(t) = 18 + (1/4)t
y(t) = 18 + (1/4)(48)
y(t) = 18 + 12
y(t) = 30
Therefore, at 48 tenths of a second, Ari and Mattew have the same x and y position. So, the answer is
C. Ari and Matthew collide at 4.8 seconds.
Answer: The value of q is exactly 7
------------------------------------
Explanation:
L = 16 is the length
W = 3 is the width
H = q is the unknown height
S = 362 is the surface area
We'll use the formula
S = 2*(L*W+W*H+L*H)
which is the surface area formula for any rectangular block
So plug in the given info and solve for q
S = 2*(L*W+W*H+L*H)
362 = 2*(16*3+3*q+16*q)
362 = 2*(48+3q+16q)
362 = 2*(48+19q)
362/2 = 2*(48+19q)/2 ... divide both sides by 2
181 = 48+19q
48+19q = 181
19q+48 = 181
19q+48-48 = 181-48 .... subtract 48 from both sides
19q = 133
19q/19 = 133/19 .... divide both sides by 19
q = 7
For this case, the first thing we are going to do is define variables.
We have then:
x: number of hours it takes Homer to finish work alone.
They worked together for 3 hours until Homer had to go home:
Mike finished the job working by himself in an additional 5 hours:
From here, we must clear the value of x.
We then have to multiply both sides by x (x-1):
Rewriting we have:
The solutions to the equation are:
Answer:
it has taken Homer to fix the deck himself about:
x2 = 11.75 hours
That is true, I don,t quite know how to explain it but I just did this problem yesterday.