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amid [387]
3 years ago
7

Malachy, Sushil and Fiona share some sweets in the ratio 7:1:1. Malachy gets 90 more sweets than Fiona. How many sweets does Sus

hil get?
Mathematics
1 answer:
VashaNatasha [74]3 years ago
3 0

Answer:

15

Step-by-step explanation:

Fiona (F) = Sushi (S)

Malachy (M) = 7 Fiona (F)

M = F + 90

F + 90 = 7F

6F = 90

F (Fiona) = 15

S (Sushi) = 15

check: Malachy (M) = 15 * 7 = 105

M-F = 105 - 15 = 90

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Sarah has $18.00 and she earns $7.25 an hour at work. what’s the equations
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Answer:

y = 7.25x + 18

Step-by-step explanation:

18 is the base. so it goes last.

7.25 is the amount being raised per a certain amount (hours) so its 7.25x

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3 years ago
Simplify the following expression. √14 / √18
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Tan x-1/tan x+1=1-cot x/1+cotx
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\dfrac{\tan x-1}{\tan x+1}=\dfrac{\frac{\sin x}{\cos x}-1}{\frac{\sin x}{\cos x}+1}=\dfrac{\sin x-\cos x}{\sin x+\cos x}=\dfrac{1-\frac{\cos x}{\sin x}}{1+\frac{\cos x}{\sin x}}=\dfrac{1-\cot x}{1+\cot x}
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3 years ago
. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum
Drupady [299]

Answer:

r=1.05\ \text{ft}

h=2.12\ \text{ft}

20.91\ \text{ft}^3

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = 7.35\ \text{ft}^3

V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}

Surface area is given by

A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}

Differentiating with respect to radius we get

\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}

Equating with zero we get

0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05

\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0

So, the value of the function is minimum at r=1.05

h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3

The minimum surface area is 20.91\ \text{ft}^3.

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What makes a unit rate different from other rates
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A unit rate is when it is in simplest form
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