Which formula is used to find the explicit equation for geometric sequences?

What is the volume of the rectangular prism? <br> 94.5 yd3 <br> 58.0 yd3 <br> 25.5 yd3 <br> 20.5 yd3

aliina [53]

Answer:

94.5yd³

Step-by-step explanation:

volume = length × width × height

length = 7 yd , width = 4.5 yd and height = 3 yd

so volume = 7 × 4.5 × 3 = 94.5yd³

7 0

2 years ago

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago

Is -1.2 a rational number

Taya2010 [7]

Answer:

I don't think so

Step-by-step explanation:

5 0

3 years ago

Leah ran 5/7 of a lap and Ryan ran 2/3 of a lap. Who ran farther and by how much?

Goryan [66]

Leah, she ran farther by 1/21

How you get the answer:

5/7
Multiply 7x3 to get the denominator and do the same to the numerator 5x3! Which is 15/21
To get 21 from 2/3 is to multiply 3x7 (denominator) and 2x7 (numerator) to get 14/21

15/21 > 14/21 so Leah ran farther by 1/21

7 0

3 years ago

A ferritin test is a popular test to measure a person’s current iron stores. in women, ferritin is normally distributed with a m

MArishka [77]

Given:
μ = 89 ng/ml, population mean
σ = 23 ng/ml, population standard deviation

Random variable, x = 100
To test P(x < 100), calculate the z-score.
z = (x-μ)/σ = (100 - 89)/23 = 0.4783

From standard tables, obtain
P(x < 100) = 0.6838 = 68.4%

Answer: 68.4%

7 0

3 years ago