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babymother [125]

3 years ago

14

Kallie drank 12.75 gallons of water in 3 weeks. She drank the same amount of water each day. Estimate how many gallons she drank

in one day.

2 answers:

scZoUnD [109]3 years ago

6 0

Answer:

607 miltliters per day

Step-by-step explanation:

Step one:

given data

Kallie drank 12.75 gallons of water in 3 weeks

if she drank the same amount each day, then in one day she will drink

Note----there are 31 days in 3 weeks (7 days make 1 week)

Step two:

Hence in one day she will drink

= total volume of water/number of days

= 12.75/21

=0.607liters per day

or

607 militliters per day

antiseptic1488 [7]3 years ago

5 0

Answer:

3 1/8

Step-by-step explanation:

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Find the area of the region enclosed by the graphs of these equations. (CALCULUS HELP)

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Answer:

$\displaystyle A = \frac{20\sqrt{15}}{3}$

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Order of Operations: BPEMDAS

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Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

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Step-by-step explanation:

<u>Step 1: Define</u>

F: y = √(15 - x)

G: y = √(15 - 3x)

H: y = 0

<u>Step 2: Find Bounds of Integration</u>

<em>Solve each equation for the x-value for our bounds of integration.</em>

F

Set <em>y</em> = 0: 0 = √(15 - x)
[Equality Property] Square both sides: 0 = 15 - x
[Subtraction Property of Equality] Isolate <em>x</em> term: -x = -15
[Division Property of Equality] Isolate <em>x</em>: x = 15

G

Set y = 0: 0 = √(15 - 3x)
[Equality Property] Square both sides: 0 = 15 - 3x
[Subtraction Property of Equality] Isolate <em>x</em> term: -3x = -15
[Division Property of Equality] Isolate <em>x</em>: x = 5

This tells us that our bounds of integration for function F is from 0 to 15 and our bounds of integration for function G is 0 to 5.

We see that we need to subtract function G from function F to get our area of the region (See attachment graph for visual).

<u>Step 3: Find Area of Region</u>

<em>Integration Part 1</em>

Rewrite Area of Region Formula [Integration Property - Subtraction]: $\displaystyle A = \int\limits^b_a {f(x)} \, dx - \int\limits^d_c {g(x)} \, dx$
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[Area] [Integral] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle A = \int\limits^{15}_0 {(15 - x)^{\frac{1}{2}}} \, dx - \int\limits^5_0 {(15 - 3x)^{\frac{1}{2}}} \, dx$

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u = 15 - x

du = -dx

Integral 2:

z = 15 - 3x

dz = -3dx

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<em>Integration Part 2</em>

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Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Area Under the Curve - Area of a Region (Integration)

Book: College Calculus 10e

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