Which graph has a steeper negative slope and a y-intercept that is closer to the origin than y = - 1/2x

Find the area of a circle with radius of the 5.58 give your answer rounded to 2DP?? pls help

marta [7]

Answer:

Area is 97.82.

Step-by-step explanation:

<u>Area of Circle</u>

$A = \pi r^2$

A ... area of circle

r ... radius

<u>Given</u>

r = 5.58

Now insert radius in formula and use a calculator.

$A = \pi r^2$

$A = \pi (5.58)^2$

$A = \pi (31.1364)$

$A \approx 97.8178855$

Rounded to two decimal places:

$A = 97.82$

3 0

2 years ago

Will mark brainliest if question is correct ♡ Answer ASAP please.

ioda

B. p ^m + n

When the base is the same and you're multiplying, you can add the exponents. For example:

p^2 * p^3 = p^5

6 0

3 years ago

Read 2 more answers

3. Solve the differential equations a) y'' + 12y' + 32y = 0 b) y'' + 14y' + 49y = 0 c) y'' + 10y' + 34y = 0, y(0) = 1, y'(0) = 4

alina1380 [7]

Answer:

$y(x)=3e^{-4x}-2e^{-8x}$

Step-by-step explanation:

I will do the first one thoroughly so you won't have any problems following to complete the rest of them.

This is a linear homogeneous second order differential, so to solve it we will use:

$y(x)=C_{1}e^{r_{1}x}+C_{2}e^{r_{2}x}$ which is a theorem that says that if r1x and r2x are both solutions off a linear homogeneous equation, and C1 and C2 are any constants, then the function above is also a solution of the equation.

We need to solve for r1 and r2 using the differential equation:

y'' + 12y' + 32y = 0

Solve the differential equation for r1 and r2 by first replacing the y'' with r^2 and the y' with r:

$r^2+12r+32=0$

W will factor that now to solve for the 2 values of r:

(r + 4)(r + 8) = 0

By the Zero Product Property, either one of those binomials has to equal 0 for the product to equal 0, so

r + 4 = 0 and r = -4

r + 8 = 0 and r = -8

Those are the values for r1 and r2 and we can sub them back in to the y(x) equation:

$y(x)=C_{1}e^{-4x}+C_{2}e^{-8x}$

This we will call Equation 1.

Now we find the derivative of that equation, using the rules for finding derivatives of e's:

$y'(x)=-4C_{1}e^{-4x}-8C_{2}e^{-8x}$

This we will call Equation 2.

Now we will use our first initial condition in Equation 1, where y(0) = 1:

$y(0)=C_{1}e^{(-4)(0)}+C_{2}e^{(-8)(0)}=1$

Simplifying gives you:

$y(0)=C_{1}e^0+C_{2}e^0=1$ so

$C_{1}+C_{2}=1$

Now we will use the second initial condition in Equation 2, where y'(0) = 4:

$y'(0)=-4C_{1}e^{(-4)(0)}-8C_{2}e^{(-8)(0)}=4$

Simplifying gives you:

$y'(0)=-4C_{1}e^0-8C_{2}e^0=4$ so

$-4C_{1}-8C_{2}=4$

We will now go back to the first bold equation and solve it for C1:

$C_{1}=1-C_{2}$ and sub that value in to the second bold equation to solve for C2:

$-4(1-C_{2})-8C_{2}=4$ and

$-4+4C_{2}-8C_{2}=4$ and

$-4C_{2}=8$ so

$C_{2}=-2$

Now sub that back in to the first bold equation to solve for C1:

$C_{1}-2=1$ so

$C_{1}=3$

Finally we go back to the y(x) equation and fill everything in:

$y(x)=3e^{-4x}-2e^{-8x}$

And that's your original equation! Follow this to the "t" and you'll have no problems with the other 2. They are identical in execution.

4 0

3 years ago

Can anyone please solve this question

Arturiano [62]

Answer:

<acb=90°

inscribed angle from the diameter is 90°

4 0

3 years ago

Help plz I’ll give brainliest

Bumek [7]

Answer:

it will be 49 because u will add four because 37+4=41 41+4=45. 45+4= 49

4 0

3 years ago

Read 2 more answers

Which graph has a steeper negative slope and a y-intercept that is closer to the origin than y = - 1/2x - 6