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3 years ago

Sheila only has $10 to spend on muffins. If muffins are $1.50 each, how many muffins can she

Mathematics

1 answer:

KIM [24]3 years ago

5 0

Answer:

Step-by-step explanation:

10 divided by 1.50 equals 6

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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0

2 years ago

Difference between<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B5%7D%20%20-%20%20%5Cfrac%7B3%7D%7B10%7D%20" id="TexF

vampirchik [111]

Step-by-step explanation:

see below

$\longrightarrow \: \frac{4}{5} - \frac{3}{10}$

$\longrightarrow \: \frac{8 - 3}{10}$

$\longrightarrow \: \cancel{\frac{5}{10} }$

$\longrightarrow \: \frac{1}{2}$

3 0

1 year ago

Read 2 more answers

Evaluate 2a + 4b<br> if a = 10 and b = 6

iris [78.8K]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

A baseball has a diameter of 6 cm. If you wanted to replace the inside of the baseball with air, how much would be needed in cub

e-lub [12.9K]

This is just another way of asking "what is the volume of a sphere of 6cm"
The volume of a sphere is $V= \frac{3}{4} \pi R^{3}$
The R is 3cm in this problem since the diameter is twice the radius. For a 3cm radius sphere this is 113.1cm^3

3 0

2 years ago

Read 2 more answers

B) Express 0.6363......as a rational number in its lowest term.

bulgar [2K]

Answer:

$\frac{7}{11}$

Step-by-step explanation:

We require 2 equations with the repeating digits (63) placed after the decimal point.

let x = 0.636363..... (1) multiply both sides by 100

100x = 63.6363... (2)

Subtract (1) from (2) thus eliminating the repeating digits

99x = 63 ( divide both sides by 99 )

x = $\frac{63}{99}$ = $\frac{7}{11}$ ← in simplest form

8 0

2 years ago