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2 years ago

Given: (x + 5)^2 + (y - 3)^2 = 144, where is the center of the circle? *

Mathematics

1 answer:

Degger [83]2 years ago

6 0

Answer:

8,5 that should be correct if it's not let me know

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Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

4 0

3 years ago

Which graph shows a proportional relationship between the number of hours of renting a bike and the total amount spent to rent t

lions [1.4K]

Answer:

A, the graph is shown

Step-by-step explanation:

4 0

2 years ago

What ever link you send me i will open and mark brainlest

nordsb [41]

Answer:

Princess_Anyla/nka8iza0q6lm8dm1

Step-by-step explanation:

7 0

2 years ago

Someonepleasehelp me asap <br>evaluate (8)-2(15-8)

AnnZ [28]

Answer:

-6

Step-by-step explanation:

You have to multiple -2 by 15 and -8 separately

8 - 2(15-8)

8 -30 + 16

24-30 = -6

4 0

2 years ago

The population of a certain species of bacteria doubles every hour. Use the following

elena55 [62]

Answer:

The bacteria will grow from 1 to 1024 in 10 hours

Step-by-step explanation:

Given

P_0 = 1

P = 1024

We have to find time

Putting values in the formula

$P = P_0(2)^t\\1024=(1)(2)^t$

Anything multiplied with 1 remains the same

$1024=2^t\\2^{10} = 2^t$

Using the property "when bases are same, the exponents can be put equivalent"

t = 10 hours

Therefore, the bacteria will grow from 1 to 1024 in 10 hours ..

7 0

2 years ago