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3 years ago

Find the volume of this right rectangular prism. [type your answer as a number]

Mathematics

2 answers:

Luden [163]3 years ago

5 0

Answer:

200 cubic meters

Step-by-step explanation:

larisa [96]3 years ago

3 0

Answer:

200

Step-by-step explanation:

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Sarah is fighting a sinus infection. Her doctor prescribed a nasal spray and an antibiotic to fight the infection. The active in

eimsori [14]

Answer:

a) The antibiotic is made with a greater initial amount of active ingredient.

b) The time when both medications will have the same amount of active ingredients in the bloodstream = 8 hours.

Step-by-step explanation:

Nasal spray's active ingredient left in the bloodstream is modelled as

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

Antibiotic's active ingredient left in the bloodstream is modelled as

a(t) = 9/(t+3)

with t in hours.

a) Determine which drug is made with a greater initial amount of active ingredient. Justify your answer.

At the instance of usage, the active ingredient for both drugs are at their pure concentration.

So, we find the amount of active ingredient for each drug in the bloodstream at t=0 and compare.

For nasal spray,

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

At t = 0

n(0) = (1/5) + (18/15) = 1.4

For antibiotics,

a(t) = 9/(t+3)

At t=0

a(0) = (9/3) = 3

3 > 1.4

Hence, the antibiotic is evidently made with a greater initial amount of active ingredient.

b) Determine algebraically the number of hours after taking the medications when both medications will have the same amount of active ingredient remaining in her bloodstream

At the time when both medications will have the same amount of active ingredients in the bloodstream, n(t) = a(t)

n(t) = ((t + 1)/(t + 5)) + (18/(t² + 8t + 15))

a(t) = 9/(t+3)

Note that (t² + 8t + 15) = (t + 3)(t + 5)

When n(t) = a(t)

((t + 1)/(t + 5)) + (18/(t² + 8t + 15)) = 9/(t+3)

Multiplying through by (t² + 8t + 15) or more properly written as (t + 3)(t + 5)

(t+1)(t+3) + 18 = 9(t+5)

t² + 4t + 3 + 18 = 9t + 45

t² - 5t - 24 = 0

Solving the quadratic equation

t = 8 or t = -3

Time cannot be negative, hence, t = 8 hours.

Hope this Helps!!!

3 0

3 years ago

Find the area of a triangle whose vertices are located at (-2,5), (-4, -3), and (3,1). Evaluate the determinant using diagonals.

myrzilka [38]

Answer:

The area of the triangle is 48 unit²

Step-by-step explanation:

The given vertices of the triangle are;

(-2, 5), (-4, -3), and (3, 1)

The formula for finding the area of a triangle with given coordinates of the vertices is as follows;

$\Delta = \dfrac{1}{2}\times \begin{vmatrix}x_1 & y_1 & 1\\ x_2 & y_2 & 1\\ x_3 & y_3 & 1\end{vmatrix} = \dfrac{1}{2}\times \left | x_1\cdot y_2 - x_2\cdot y_1 + x_2\cdot y_3 - x_3\cdot y_2 + x_3\cdot y_1 - x_1\cdot y_3\right |$

Substituting gives;

$\Delta = \dfrac{1}{2}\times \begin{vmatrix}-2& 5 & 1\\ -4 & -3 & 1\\ 3 & 1 & 1\end{vmatrix} \\\Delta = \dfrac{1}{2}\times \left | (-2)\times (-3) - ((-4)\times 5) + (-4)\times 1 - 3\times (-3) + 3 \times 5 - (-2)\times 1\right | \\\Delta = \dfrac{1}{2}\times \left | 6 +20 -4 +9 + 15+2\right | = 48$