The answer is B. 97
3 x 27 + 2 x 8
Answer:
a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)
Step-by-step explanation:
Let's solve by separating variables:

a) x’=t–sin(t), x(0)=1

Apply integral both sides:

where k is a constant due to integration. With x(0)=1, substitute:

Finally:

b) x’+2x=4; x(0)=5

Completing the integral:

Solving the operator:

Using algebra, it becomes explicit:

With x(0)=5, substitute:

Finally:

c) x’’+4x=0; x(0)=0; x’(0)=1
Let
be the solution for the equation, then:

Substituting these equations in <em>c)</em>

This becomes the solution <em>m=α±βi</em> where <em>α=0</em> and <em>β=2</em>
![x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)](https://tex.z-dn.net/?f=x%3De%5E%7B%5Calpha%20t%7D%5BAsin%5Cbeta%20t%2BBcos%5Cbeta%20t%5D%5C%5C%5C%5Cx%3De%5E%7B0%7D%5BAsin%28%282%29t%29%2BBcos%28%282%29t%29%5D%5C%5C%5C%5Cx%3DAsin%28%282%29t%29%2BBcos%28%282%29t%29)
Where <em>A</em> and <em>B</em> are constants. With x(0)=0; x’(0)=1:

Finally:

Answer:
answer is c. x=-4
Step-by-step explanation:
7x+6=-22 =》 7x=-28 =》 x=-24/7=-4
Answer:

Step-by-step explanation:
Here we will be using long division method to find the quotient . Here we need to divide (x³+2x²-22x-45) and (x+5) . So lets divide .
x+5) x³+2x²-22x-45 ( x² -3x -7
x³ + 5x²
- -
______________
- 3x²-22x -45
-3x² -15x
+ +
______________
-7x -45
-7x -35
______________
-10
<u>Quotient</u><u> </u>= x² -3x -7
<u>Remainder </u>= (-10)
<h3>
<u>★</u><u>Hence </u><u>the</u><u> </u><u>quotient</u><u> </u><u>is </u><u>x²</u><u> </u><u>-3x </u><u>-</u><u>7</u><u> </u><u>and </u><u>the</u><u> </u><u>remainder</u><u> </u><u>is </u><u>(</u><u>-</u><u>1</u><u>0</u><u>)</u><u> </u><u>.</u></h3>
Answer:
1 + x meters.
Step-by-step explanation:
A square has 4 equal sides so each side will have a length equal to the square root of the area.
Side length = √(1 + 2x + x^2)
= √(1 + x)(1 + x)
= 1 + x.