The line plot shows the amount of time (in hours) that Jodi practiced the flute over 8 days.

What is the center of the circle? Please show steps!

Vika [28.1K]

Answer:

Step-by-step explanation:

The equation of a circle:

$(x-h)^2+(y-k)^2=r^2$

(h, k) - center

r - radius

We have the equation:

$x^2+(y-4)^2=25\\\\(x-0)^2+(y-4)^2=5^2$

h = 0, k = 4, r = 5

7 0

3 years ago

Suppose a tub has the shape of an elliptical paraboloid given by z = ax2+by2 (where a, b are some positive constants). If a marb

Umnica [9.8K]

Answer:

It would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

Step-by-step explanation:

It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.

Since

$z = ax^2 + by^2$

For this case, the gradient of your function would be

$\nabla z = (2ax , 2by)$

And -1 times the gradient of your function would be

$-\nabla z = (-2ax , -2by)\\$

Then, at

$(1,1,a+b),\\x = 1 \\y = 1$

So it would go towards

$v = (-2a,-2b)$

The magnitud of that vector is

$|v| = 2\sqrt{a^2+b^2}$

and to conclude it would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

6 0

2 years ago

1. Michael invests $2000 in an annuity that offers an interest rate of 4% compounded quarterly for 5 years. What is the value of

Amanda [17]

1. The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n)ⁿˣ

Where:

A = the future value = ?
P = the principal investment amount = $2000
r = interest rate = 4%
n = the number of times that interest is compounded per year = 4
x = the number of years = 5

Calculations:

A = 2000 (1 + 0.04/4)²⁰

A = 2000 (1 + 0.01)²⁰

A = 2000 (1.01)²⁰

A = 2000 ₓ 1.22

A = $2440.38

2. The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n)ⁿˣ

Where:

A = the future value = ?
P = the principal investment amount = $50
r = interest rate = 48%
n = the number of times that interest is compounded per year = 12
x = the number of years = 2

Calculations:

A = 50 (1 + 0.48/12)²⁴

A = 50 (1 + 0.04)²⁴

A = 50 (1.04)²⁴

A = 50 ₓ 2.56

A = $128.16

3. The formula for annual compound interest, including principal sum, is:

A = P (1 + r/n)ⁿˣ

Where:

A = the future value = ?
P = the principal investment amount = $50
r = interest rate = 4%
n = the number of times that interest is compounded per year = 12
x = the number of years = 3

Calculations:

A = 50 (1 + 0.04/12)³⁶

A = 50 (1 + 0.003)³⁶

A = 50 (1.003)³⁶

A = 50 ₓ 1.12

A = $56.36

8 0

3 years ago

Read 2 more answers

Which of these numbers is in the solution set of X+4> 9? Check all that<br> apply

Anuta_ua [19.1K]

Answer:

are there answer choices

Step-by-step explanation:

sorry i did not answer

7 0

3 years ago

Check whether (0, -2) is solution of the equation x - 2y = 4 or not

kaheart [24]

Answer:

Step-by-step explanation:

Plugin x = 0 & y = -2 in the LHS of the equation. After substituting, if you get the RHS, then this point is the solution of the equation.

x - 2y = 0 - 2*(-2)

= 0 + 4

= 4 = RHS.

(0,-2) is solution of the equation.

8 0

2 years ago