Mathematics, 08.04.2020 05:26 hmccush8

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Answer from: erinbrewster1299

$\large \boxed{\text{1. 24 doses; 2. 4614 mL}}$

Step-by-step explanation:

1. Prescription

(a) Calculate the volume of the mouthwash

Tetracycline 0 mL (it's a solid)

Nystatin 40

Diphenhydramine 60

Dexamethasone 140

TOTAL 240 mL

(b) Calculate the number of doses

1 tsp = 5 mL, so a dose of

2 tsp = 10 mL

$\text{No. of doses} = \text{240 mL} \times \dfrac{\text{1 dose}}{\text{10 mL}} = \text{24 doses}\\\\\text{There are $\large \boxed{\textbf{24 doses}}$ in the prescription.}$

2. Punch

You must convert gallons, pints, and cups to millilitres.

The conversion factors are

1 US gal = 3785 mL

1 US pt = 473 mL

1 US c = 237 mL

(a) Gallons to millilitres

$\text{No. of millilitres} = \frac{3}{4}\text{ gal} \times \dfrac{\text{3785 mL}}{\text{1 gal}} = \text{2839 mL}$

(b) Pints to millilitres

$\text{No. of millilitres } = \text{3 pt} \times \dfrac{\text{473 mL}}{\text{1 pt}} = \text{1419 mL }$

$\text{No. of millilitres} = \text{1.5 c } \times \dfrac{\text{237 mL}}{\text{1 c}} = \text{356 mL}$

(d) Volume of punch

Orange juice = ¾ gal = 2839 mL

Ginger ale = 3 pt = 1419

Pineapple juice = 1½ c = 356

TOTAL = 4614 mL

$\text{The final volume of the punch is $\large \boxed{\textbf{4614 mL}}$}$

Answer from: Quest

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Answer from: Quest

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

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