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3 years ago

A water tank is 1/8 full the tank is 3/4 full when 42 gallons are added to the tank how much water was originally in the tank

1 answer:

8 0

A water tank is 1/8 full. The tank is 3/4 full when 42 gallons are added to the tank. How much water was originally in the tank? (I rewrote it, your wording was messed up)

3/4 = 6/8
1/8 + 6/8 = 7/8 = 42 gallons
42 divided by 8 = 5 1/4

So, the answer is 5 1/4. The tank originally 5.25 gallons of water.

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So here's the question

Lesechka [4]

Yes, is subtraction, to get their "difference".

first off, let's convert the mixed fractions, to "improper", and then subtract.

$\bf \stackrel{red~yarn}{9\frac{1}{5}}-\stackrel{blue~yarn}{3\frac{11}{25}}$

$\bf -------------------------------\\\\
\stackrel{mixed}{9\frac{1}{5}}\implies \cfrac{9\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{46}{5}}
\\\\\\
\stackrel{mixed}{3\frac{11}{25}}\implies \cfrac{3\cdot 25+11}{25}\implies \stackrel{improper}{\cfrac{86}{25}}\\\\
-------------------------------\\\\
\cfrac{46}{5}-\cfrac{86}{25}\impliedby \textit{our LCD is 25}\implies \cfrac{(5\cdot 46)~~-~~(1\cdot 86)}{25}
\\\\\\
\cfrac{230~-~86}{25}\implies \cfrac{144}{25}\implies 5\frac{19}{25}$

4 0

3 years ago

What is 19.6 divided by 7

Lemur [1.5K]

19 divided by 7 = 2.8

7 0

3 years ago

A 20° sector in a circle has an area of 21.51 pi yd?.

kodGreya [7K]

Answer

____________________________________________________________

This would be 21.5π * 360 / 20 yd^2 = 1215.18 yd^2 ( using pi = 3.14)

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5 0

3 years ago

Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

3 years ago

I need help.6\10 - 1\2?

spin [16.1K]

6/10 - 1/2...common denominator is 10
6/10 - 5/10 = 1/10 <==

6 0

4 years ago

Read 2 more answers