Answer:
Step-by-step explanation:
First, subtract by 7 both sides of equation.
Solve.
Then, divide by 12 both sides of equation.
Solve to find the answer.
, which is our answer.
Newton's Law of Cooling
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes
Answer: $900
Step-by-step explanation:
The simple interest is calculated using the formula:
(P × R × T)/100
where,
P = Principal = $3000
R = Rate = 6%
T = Time = 5 years
Simple Interest = (P × R × T)/100
= ($3000 × 6 × 5)/100
= 90000/100
= $900
Therefore, the simple interest is $900
Have you learned matrices yet? I'm going to use that to solve these, please refer to the photos.
I solved the system by using a matrix calculation. The work always needs to be shown and you do that by setting up the matrix like in the first photo and also writing out all your equations. In a TI calculator, to do this you press 2ND-X^-1,GO TO EDIT - [A] - 3×4- now enter the coefficient of the system of equations variables. NOW 2ND MODE- 2ND-X^-1 -GO TO MATH- ALPHA APPS
Now, if you don't know this you may be confuse so after rref([A]) was enter a matrix came up with [1 0 0 -21] in the top row this means x equal -21. So, the next row is y and it came out as [0 1 0 46] so y equals 46 and I'm going to let you figure out what z is by looking at the matrix.
SO... X=-21 Y=46 and Z=-10
Let's Test it
Answer:
Step-by-step explanation:
<u>Given Second-Order Homogenous Differential Equation</u>
<u>Use Auxiliary Equation</u>
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<u>General Solution</u>
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Note that the DE has two distinct complex solutions where and are arbitrary constants.