Answer:
t = 4 seconds
Step-by-step explanation:
The height of the projectile after it is launched is given by the function :
t is time in seconds
We need to find after how many seconds will the projectile land back on the ground. When it land, h(t)=0
So,
The above is a quadratic equation. It can be solved by the formula as follows :
Here, a = -16, b = 32 and c = 128
Neglecting negative value, the projectile will land after 4 seconds.
<span>If f(x) = 2x + 3 and g(x) = (x - 3)/2,
what is the value of f[g(-5)]?
f[g(-5)] means substitute -5 for x in the right side of g(x),
simplify, then substitute what you get for x in the right
side of f(x), then simplify.
It's a "double substitution".
To find f[g(-5)], work it from the inside out.
In f[g(-5)], do only the inside part first.
In this case the inside part if the red part g(-5)
g(-5) means to substitute -5 for x in
g(x) = (x - 3)/2
So we take out the x's and we have
g( ) = ( - 3)/2
Now we put -5's where we took out the x's, and we now
have
g(-5) = (-5 - 3)/2
Then we simplify:
g(-5) = (-8)/2
g(-5) = -4
Now we have the g(-5)]
f[g(-5)]
means to substitute g(-5) for x in
f[x] = 2x + 3
So we take out the x's and we have
f[ ] = 2[ ] + 3
Now we put g(-5)'s where we took out the x's, and we
now have
f[g(-5)] = 2[g(-5)] + 3
But we have now found that g(-5) = -4, we can put
that in place of the g(-5)'s and we get
f[g(-5)] = f[-4]
But then
f(-4) means to substitute -4 for x in
f(x) = 2x + 3
so
f(-4) = 2(-4) + 3
then we simplify
f(-4) = -8 + 3
f(-4) = -5
So
f[g(-5)] = f(-4) = -5</span>
Answer:
(c) Pi/4
Step-by-step explanation:
3pi/4 = (3 x 180) / 4 = 135 degrees
135 degrees is equivalent to (180 degrees - 135 degrees) 45 degrees
45 degrees = Pi/4
Therefore, the reference angle of 3pi/4 is Pi/4
Thus, the correct option is (c) Pi/4
Answer:
Step-by-step explanation:
The formula of a slope:
Substitute the coordinates of the given points (-1, -1) and (2, -2):
