Answer:
204
Step-by-step explanation:
i took the test
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Answer: Choice D)
S(x) = 6x^2 - 20x
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Explanation:
x = side length of base
x*x = x^2 = area of base
The top also has an area of x^2 since the base and top are both congruent squares. The total base area is x^2+x^2 = 2x^2
The height h is 5 inches shorter than the base, so
h = (base length) - 5
h = x-5
Each lateral side is of area h*x = (x-5)*x = x^2-5x
There are 4 lateral sides
Total lateral area = 4*(area of one lateral side)
Total lateral area = 4*(x^2-5x)
Total lateral area = 4*x^2-4*5x
Total lateral area = 4*x^2-20x
Add the total lateral area (4x^2-20x) to the total base area (2x^2)
Doing so gets us
S(x) = Total Surface Area
S(x) = (Area of bases) + (area of lateral sides)
S(x) = (2x^2) + (4x^2-20x)
S(x) = (2x^2+4x^2) - 20x
S(x) = 6x^2 - 20x
which is why the answer is choice D
Answer:
Step-by-step explanation:
The coefficient of a polynomial expression is the coefficient of the term with the highest exponent. We can see that the term with the highest exponent is 
. So, the leading coefficient is its coefficient which is .
Note that any number can be written as the product of that number and as multiplying by does not fundamentally change that number. In our given example, is equivalent to 
.
The answer is 19. This is very easy just to say.
