If you're studying differential equations, you can find the solution to the given equation using the boundary conditions given.
Some of us would rather cut to the chase. We recognize that this is an exponential decay problem in which the initial temperature difference from the 75 °F room temperature is decaying to zero.
In 10 minutes, the temperature difference has decayed from 180-75 = 105 to 100-75 = 25, so we can write the temperature function of time as
.. T(t) = 75 +105*(25/105)^(t/10)
We can solve this for
.. T(t) = 80
using logarithms, but it may be easier to do it graphically.
To the nearest minute, it will take 21 minutes for the coffee to cool to 80 °F.
Note what i actually represents.
i is the very basis of a whole new level of counting. When finding discriminants, we often say that a quadratic has no
real roots if the discriminant is 0. Needless to say, there are roots, they are just imaginary.
, in real terms, is non-existent. That is, there are no numbers in the real number system that when multiplied by itself produces a result of -1. This is what i unit represents.
Let's tackle this problem in smaller steps.
Let's first expand our brackets.
(i - 7i)² = (-6i)² = 36i²
Now, let's distribute the xi.
xi(i - 7i)² = xi(36i²) = 36xi³ =
= -36xi
Answer:
x = 16
angle K = 77
angle L = 87
angle M = 16
Step-by-step explanation:
Mathematically, the sum of interior angles of a triangle is 180 degrees
Thus:
(5x-3) + (6x-9) + x =180
12x -12 = 180
12x = 180+12
12x = 192
x = 192/12
x = 16
Angle K = 5x-3 = 5(16)-3 = 80-3 = 77
Angle L = 6(16)-9 = 96-9 = 87
Lastly;
angle M = 16 degrees
The answer is the first one
Using 3.14 for PI.
The radius of a ball and the can is half the diameter = 1.25
The height of the can is the height of 3 diameters = 7.5
Volume of one tennis ball:
4/3 x PI x 1.25^3 = 8.18 cubic inches.
Volume of 3 tennis balls: 3 x 8.18 = 24.54 cubic inches.
Volume of can:
PI x 1.25^2 x 7.5 = 36.80 cubic inches.
Space = 36.80 - 24.54 = 12.26 cubic inches.