Question 1 (1 point)
1 answer:
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Answer:
The tip of the man shadow moves at the rate of
Step-by-step explanation:
Let's draw a figure that describes the given situation.
Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.
Here it forms two similar triangles.
Let's find the distance "y" using proportion.
From the figure, we can form a proportion.
Cross multiplying, we get
15(y -x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
y =
We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).
----(1)
We are given . Plug in the equation (1), we get
Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.
Xy=10
x+y=29
subtract x from both sides for second equation
y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x=
so
x^2+29x+10=0
a=1
b=29
c=10
x=
x=
x=
x=
x=
or 
those are the 2 numbers
aprox=-28.65 and -0.349
x+y=29
subtract x from both sides for second equation
y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x=
so
x^2+29x+10=0
a=1
b=29
c=10
x=
x=
x=
x=
x=
those are the 2 numbers
aprox=-28.65 and -0.349