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Jobisdone [24]
3 years ago
14

Jamal filled his gas tank and then use 7/16 of the tank for traveling to visit his grandfather. He then used 1/3 of the remainin

g gas in the tank to run errands around town. What fraction of the tank is filled with gasoline
Mathematics
1 answer:
alisha [4.7K]3 years ago
8 0

Answer:

The fraction of the tank is filled with gasoline is \frac{3}{8}.

Step-by-step explanation:

Consider the provided information.

Jamal filled his gas tank and then use 7/16 of the tank for traveling to visit his grandfather.

After his first traveling the amount of gas left can be calculated as:

1-\frac{7}{16}

\frac{16-7}{16}

\frac{9}{16}

He then used 1/3 of the remaining gas in the tank to run around town.

That means he left with 2/3 of gas.

\frac{9}{16}\times \frac{2}{3}

\frac{3}{8}

Hence, the fraction of the tank is filled with gasoline is \frac{3}{8}.

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Please help me!<br> Look at this diagram.
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Step-by-step explanation:

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8 0
2 years ago
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ludmilkaskok [199]
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3 years ago
Integrate the following
enot [183]

I suppose you mean to have the entire numerator under the square root?

\displaystyle\int_2^4\frac{\sqrt{x^2-4}}{x^2}\,\mathrm dx

We can use a trigonometric substitution to start:

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\displaystyle\int_0^{\pi/3}\frac{\sqrt{(2\sec t)^2-4}}{(2\sec t)^2}(2\sec t\tan t)\,\mathrm dt=\int_0^{\pi/3}\frac{\tan^2t}{\sec t}\,\mathrm dt

We can write

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Cramer's rule works as follows:
x+3y=16
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Then 
x=Dx/D
y=Dy/D
where Dx,Dy,D are 2x2 matrices formed from of coefficients and right hand side.
D=
1 3
3 1
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Dx=matrix D with first column replaced by the vector [16,8]=
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8 1
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Dy=matrix D with second column replaced by the vector [16,8]=
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Therefore
x=-8/-8=1
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Check:
x+3y=1+3(5)=16
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