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3 years ago

What is the volume of this sphere?

Mathematics

1 answer:

photoshop1234 [79]3 years ago

6 0

Answer:

3052.08

Step-by-step explanation:

We use the volume formula for spheres

$\frac{4}{3}$ πr³

Plug in 9cm for radius and evaluate

$\frac{4}{3}$ π(9)³

$\frac{4}{3}$ π*729

3052.08

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If y=e5t is a solution to the differential equation

a_sh-v [17]

Answer:

k = 30, $y(t) = C_1e^{5t}+C_2e^{6t}$

Step-by-step explanation:

Since $y=e^{5t}$ is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

$\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}$

Then, replacing the derivatives in the equation we have:

$25e^{5t}-11(5)e^{5t}+ke^{5t}=0 e^{5t}(25-55+k) =0$

Since $e^{5t}$ is a positive function, we have that

$25-55+k = 0 \rightarrow k = 30$ .

Now, consider a general solution $y(t) = Ae^{rt}, A \in \mathbb{R}$ , then, by calculating the derivatives and replacing them in the equation, we get

$Ae^{rt}(r^2-11r+30)=0$

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

$y(t) = C_1e^{5t}+C_2e^{6t}$

8 0

3 years ago

The London theater offers child tickets at 10$each and adult tickets at 20$ each.Mrs burham buys 34 tickets at a total cost of 5

kirill115 [55]

Answer:

A+C=34

10C+20A=570

4 0

3 years ago

A college student took 4 courses last semester. His final grades, along with the credits each class is worth, are as follow: A (

NikAS [45]

Answer:

A college student took 4 courses last semester. His final grades, along with the credits each class is worth, are as follow: A (3), B (4), C (2), and D (3). The grading system assigns quality points as follows: A: 4; B: 3; C: 2; D: 1; and F: 0. Find the student’s GPA for this semester. Round your answer to the nearest thousandth.

another way is

This is a weighted average question. You are going to "weight" each course by the number of credits it is worth and then divide by the total number of credits. In other words, you are going to multiply each grade (A=4, B=3) by the number of credits attached to that grade. This will ensure that the courses that have more credits count more in the overall average. Then you are going to divide by the total number of credits to get the overall GPA.

So,

(3*4 + 4*3 + 2 *2 + 3*1)/(3+4+2+3) = GPA

Step-by-step explanation:

bran-list please

6 0

3 years ago

What is the relationship between Za and Zb? D А E a 6 С B Choose 1 answer: A Vertical angles ® Complementary angles B C Suppleme

Free_Kalibri [48]

Answer:

D. none of the above.

Step-by-step explanation:

7 0

3 years ago

How do I do this -9 - 16m = 7? What are the steps?

nordsb [41]

m = -1

Step-by-step explanation:

-16m = 7 + 9

-16m = 16

m = 16 ÷ -16

m = -1

4 0

3 years ago