!!!!I REALLY NEED HELP!!!!!

Find the volume of a hexagonal prism whose base area is 15 yd² and whose height is 10 yd.

stiks02 [169]

Answer:

Volume = 150 cubic yards

Step-by-step explanation:

The basic formula for volume is:

Volume = area of base * height

The image of hexagonal prism is shown attached.

If the base is in different shape, we can use different formula (for that shape the base is in) and find area of base.

But, this problem explicitly gives

Area of Base = 15

Height = 10

We simply substitute in volume formula to find the volume. Shown below:

Volume = Area of Base * Height

Volume = 15 * 10

<u>Volume = 150 cubic yards</u>

3 0

4 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

3 years ago

What is the answer to 2x+4-3x=0

GalinKa [24]

2x+4-3x=0
-4 -4
2x-3x=-4
-1x=-4
_ _
-1 -1
x=4
so the answer is x=4

5 0

3 years ago

Read 2 more answers

Determine the amplitude of the following:

nadya68 [22]

QUESTION 1

The first function is
$y = \sin(4x)$
A function of the form
$y = A \sin(Bx)$

has amplitude equal to

$|A|$

The amplitude of
$y = \sin(4x)$

is

$1$

QUESTION 2

The given function is

$y = 4 \cos(x)$

A trigonometric function of the form
$y = A \cos(Bx)$

also has an amplitude of
$|A|$

The amplitude of
$y = 4 \cos(x)$

is

$4$

QUESTION 3

The given trigonometric function is

$y = 3 \sin( \frac{2}{3} x)$

The amplitude of this trigonometric function is

$3$

QUESTION 4.

The given trigonometric function is

$y = 3 \cos(x)$

The amplitude of this cosine function is
$3$

8 0

3 years ago

A fifth grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics hom

kherson [118]

Answer:

0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Math homework:

$\mu_M = 30, \sigma_M = 3$

Arts homework:

$\mu_A = 40, \sigma_A = 4$

What is the probability that the average time it takes to complete both homework assignments is greater than 82 minutes?

Here, we have a sum of normal variables. The mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances. So

$\mu = \mu_M + \mu_A = 30 + 40 = 70$