to find the hypotenuse (or the ramp in question 4) you can use the equation
with a and b being the 3 feet and 9 feet and c being the unknown (ramp).
So if you plug 3 and 9 into the equation, it looks like this.
then square them.
simplify.
take the square root of both sides.
is approx. 9.5 so the answer would be H.
Answer: look at pic
Step-by-step explanation:
y=mx+b
m:slope
b:y-intercept
m=-1 (slope) given in the question
y=-1x+b
Plug in the given point (-1,-4) then solve for b
-4=-1(-1)+b
b=-5
y=-x-5
then using the x-intercept and y-intercept you could graph the line
y-intercept = b = -5 (0,-5)
x-intercept (plug in y=0)
0=-x-5
x=-5 (-5,0)
Answer:
69.92°F
Step-by-step explanation:
Given:
Initial temperature ( i.e at time, t = 0) = 40°F
Temperature of the room = 70°F
Temperature after 10 minutes ( i.e at time t = 10 ) = 48°F
Now, from Newton's law of cooling
T'(t) = k(A - T(t))
T(t) temperature after time t
T'(t) =
here, A is the room temperature
thus,
= k(70 - T)
or
= kdt
on solving the differential equation, we get
T = ............(1)
Now from the boundary conditions,
i.e at time, t = 0; T = 40°F
we get,
40 =
or
C = 30
and,
at time, t = 10; T = 48°F
thus,
48 =
or
k =
or
k = 0.03
Therefore,
for t = 25
from 1 we have
T =
or
T = 70 - 0.0780
or
T = 69.92°F