Answer:
The slope of the line would be 0.00910 in a logarithm graphic.
Step-by-step explanation:
Statement is incomplete. The correct sentences are:<em> The increase in the number of humans living on Earth (N, as measured in billions) with time t (as measured in years since 1800) is modeld by the following function: N = 0.892e^0.00910t. If you were to graph in ln (N) versus t, what would be the slope of the line?</em>
Let be , where is the number of humans living on Earth, measured in billions, and is the time, measured in years since 1800. As we notice, this is an exponential function and its slope is not constant and such expression have to be linearized by using a logartihm graphic. We add logarithms on each side of the formula and simplify the resulting expression by means of logarithmic properties:
In a nutshell, the slope of the line would be 0.00910 in a logarithm graphic.
Hey there!
Apply fraction cross multiply: if a/b = c/d , then a *d = b*c
2 ( 5x - 2 ) = ( 2x + 4 ) * 4
expand : 2 (5x-2 ) => 2*5x - 2*2 => 10x - 4
expand : ( 2x +4 ) * 4 => 2x * 4 + 4*4 => 8x + 16
10x - 4 = 8x+16
add 4 to both sides:
10x-4+4 = 8x+16+4
simplify :
10x = 8x + 20
subtract 8x from both sides:
10x -8x = 8x+20-8x
simplify:
2x = 20
Therefore:
x = 20 / 2
x = 10
Hope that helps!
Answer:
S = (-4, -34)
Step-by-step explanation:
T=(10, 18) is one end of the segment
the midpoint is located at (5, -8)
therefore, using the formula for midpoint, we can find the other end of the segment (point S)
Midpoint x-value = xa + (xb - xa)/2
in our case;
5 = 10 + (xb-10)/2
3 - 10 = (xb-10)/2
-7 = (xb-10)/2
-14 = xb-10
xb = -14 + 10 = - 4
Now for the y value of the midpoint:
Midpoint y-value = ya + (yb - ya)/2
in our case:
-8 = 18 + (yb - 18)/2
- 26 = (yb - 18)/2
- 52 = yb - 18
yb = -52 + 18 = -34
Then. point S is located at: S = (-4, -34)
Answer:
40 ft
Step-by-step explanation:
The maximum height of the ball is the y- coordinate of the vertex
Given a parabola in standard form then the x- coordinate of the vertex is
= -
h(t) = - 16t² + 48t + 4 ← is in standard form
with a = - 16, b = 48 , thus
= - = 1.5
Substitute t = 1.5 into h(t) for max. height
h(1.5) = - 16(1.5)² + 48(1.5) + 4
= - 36 + 72 + 4
= 40