12^2 - 6^2 * 3^4 + 5^3
(144) - (36) * (81) + (125)
144 - (36 * 81) + 125
144 - 2916 + 125
-2,772 + 125
-2,647
Answer:
x=-1, y=-3. (-1, -3).
Step-by-step explanation:
x+y=-4
3x-6y=15
---------------
x=-4-y
3(-4-y)-6y=15
-12-3y-6y=15
-12-9y=15
9y=-12-15
9y=-27
y=-27/9
y=-3
x+(-3)=-4
x-3=-4
x=-4+3
x=-1
We are given with the equation y"+ 9 y = t^2 * e^3 t + 6 and asked to determine the general solution to this equation. we convert the equation into r^2 + 9 = 0. The solution to this equation is r = +/- 3i. This solution converted to trigonometric function is equivalent to <span>y</span>= <span>C1 </span>cos3t + <span>C2 </span>sin<span>3t. </span>
The area of the rectangular part = 14 x 20 = 280 sq. cm
The area of the half circle = 1/2 (3.14 x 7^2) = 76.9 sq. cm.
Total area = 280 + 76.93 = 356.9 cm^2
Answer:
y = x³ + 10.5x² + 31x + 13
Step-by-step explanation:
Complex roots (roots that have imaginary terms) always come in conjugate pairs. So if one root is -5 + i, there's another root that's -5 − i.
So the polynomial is:
y = (x + 1/2) (x − (-5 + i)) (x − (-5 − i))
Distributing:
y = (x + 1/2) (x² − (-5 + i)x − (-5 − i)x + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 5x − ix + 5x + ix + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 10x + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 10x + 25 + 5i − 5i − i²)
y = (x + 1/2) (x² + 10x + 25 + 1)
y = (x + 1/2) (x² + 10x + 26)
y = x(x² + 10x + 26) + 1/2(x² + 10x + 26)
y = x³ + 10x² + 26x + 1/2x² + 5x + 13
y = x³ + 10.5x² + 31x + 13
