Please help. Find the product or quotient in simplified form. Explain how to multiply and divide fractions.

1 answer:

7 0

<span>5 1/6 x 1/3
</span>first convert 5 1/6 (which is a mixed fraction) into an improper fraction ...
=> 6*5+1/6 = 31/6
=>now we have ... 31/6 * 1/3
=> to multiply fractions we multiply the numerators ( top numbers ) with each other and the denominators (bottom numbers ) also the same way ...
=> 31/6 * 1/3 => 31*1 / 6*3 => 31/18
=> then divide them to get answer as mixed fraction ..
=> 1 13/18 ..

<span>3 1/2 / 1 1/3
</span>=> here also first convert 3 1/2 and 1 1/3 into improper fractions ..
=> 3 1/2 => 2*3+1/2 => 7/2
=> 1 1/3 => 3*1+1/3=> 4/3
=> now divide them ..
=> 7/2/4/3
=> for dividing fractions we take the reciprocal of one fraction and then multiply ..
=> 7/2 * 3/4
=> now multiply these two fractions ..
=> 7*3/2*4 => 21/8
=> answer as mixed fraction = 2 5/8 ...

Hope it helps !!!

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I hope that my answer helped you!

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laila [671]

Answer:

Question 1: 0.081 min⁻¹

Question 2: 168ºF

Explanation:

The missing equation is:

$T=T_a+(T_0-T_a)e^{-kt}$

You are given:

Ta = the temperature surrounding the object = 73ºF
T₀ = the initial temperature of the object = 204ºF
t = 2.5 min
T after 2.5 min = 180ºF

Question 1: Find the the value of k.

Substitute the data into the equation and solve for k:

$180\º=73\º+(204\º-73\º)e^{-k\cdot 2.5min}\\ \\ 107\º=131\ºe^{-k\cdot 2.5min}\\\\-k\cdot 2.5min=\ln (107/131)\\\\k=0.081min^{-1}$

Question 2: Find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.

Subsititute into the formula and compute:

$T=73\ºF+(204\ºF-73\ºF)e^{-0.081min^{-1}\times 4min}\\ \\ T=73\ºF+(131\ºF)(0.72325024)\\\\T=168\ºF$

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3 years ago

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis. What is the volume of the figure?

Luden [163]

Given:

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.

To find:

The volume of the figure.

Solution:

Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.

Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.

If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.

Volume of a cone is

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