74tens=how many hundreds

Find the missing term in the following sequence <br><br> -115.2, -109.9, -104.6, -99.3, -94

ohaa [14]

The next term is -88.7

7 0

3 years ago

x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco

igomit [66]

Answer:

$x=-cos(t)+2sin(t)$

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

$a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

$r_1_,_2=\lambda \pm \mu i$

Let's find the solution for $x''+x=0$ using the previous information:

The characteristic equation is:

$r^{2} +1=0$

So, the roots are given by:

$r_1_,_2=0\pm \sqrt{-1} =\pm i$

Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

And

$x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2$

Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

3 0

3 years ago

Draw the graph of R = {(1,1), (2,2), (3,3), (4,4), (5,5), (1,4), (2,5), (4,1), (5,2)}

tresset_1 [31]

Answer:

Step-by-step explanation:

3 0

1 year ago

Deep's property tax is $690.65 and is due April 15. He does not pay until July 6. The county adds a penalty of 7.3% simple int

bazaltina [42]

$\bf \qquad \textit{Simple Interest Earned}\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$690.65\\
r=rate\to 7.3\%\to \frac{7.3}{100}\to &0.073\\
t=years\to &\frac{15+31+30+6}{365}
\end{cases}$

the penalty he'll incurred into, since July 6 is after the deadline of April 15, is I = Prt

now "t" is in years, how many days after April 15 to July 6? well, 15 + 31 + 30 +6, to convert to years, divide by 365

3 0

2 years ago

If p represents the original price, which of the following expressions could be used to calculate the sale price of a shirt that

dezoksy [38]

Answer:

C & D

Step-by-step explanation:

You can do these two ways. You can multiply the cost of the the shirt by 15% (.15 as a decimal.) and then subtract that answer from the original price of the shirt to get the sales price of the shirt.

You can also multiply the price of the shirt by 85% (.85 as a decimal) and that will give you the sales price without having to subtract. 15% + 85% = 100%, so 85% represents the sales price of the shirt.

Anyway, since you multiply, you can eliminate choice A & B.

Since the direction in the question says to select all that apply, I would check both C & D.

C is the equation of the first way I talked about- Price - 15% * price

C p - 0.15p

D is the equation of the second way I talked about. Price times 85%

D 0.85p

7 0

3 years ago