What is the sum of the first 28 terms of this arithmetic sequence? 69,75,81,87,93,99

One sphere has a radius of 3 inches and another sphere has a radius of 6 inches. The volume of the larger sphere is about how ma

NikAS [45]

Answer:

8

Step-by-step explanation:

First off, we need to recognize that the formula for the volume of a sphere is $\frac{4}{3} \pi r^3$ .

Then, we can plug in our r values one at a time.

The volume for the sphere with a 6-inch radius is about 904.779.

The volume for the sphere with a 3-inch radius is about 113.097.

To find how much greater the larger sphere is, we simply create a ratio between the two numbers: $\frac{904.779}{113.097}$

Do the division to find that the volume of the larger sphere is about 8 times the volume of the smaller sphere.

8 0

1 year ago

A fountain is made up of two semicircles and a quarter circle. Find the perimeter of the fountain. Round answers to nearest tent

AlexFokin [52]

Answer:

39.275

Step-by-step explanation:

the diameter of the semicircle is 10

A semicircle is half a circle, and a quarter circle is 1/4 of a circle.

Perimeter of a semicircle is ¶d/2

= 3.142 x 10/2 = 3.142 x 5 = 15.71

For 2 semicircles that will be 15.71 x 2 = 31.42

For the quarter circle, perimeter is ¶d/4 = 3.142 x 10/4 = 3.142 x 2.5 = 7.855

Total perimeter = 31.42 + 7.855 = 39.275

5 0

2 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

2 years ago

The seventh grade class at a Christian school had 24 students enrolled at the beginning of the school year. At the end of the sc

Darya [45]

Answer:

12.5%

Step-by-step explanation:

27-24=3

3/24=1/8

1/8=0.125

0.125 in percent is 12.5%

7 0

1 year ago

Please this is overdue

andre [41]

P=12

A=15

brainiest plizz?

3 0

2 years ago

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