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3 years ago

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A 18,000 gallon swimming pool contains 7,000 gallons of water when a hose is placed into the pool and begins adding water at a r

ate Of 1100 gallons per hour

1 answer:

SOVA2 [1]3 years ago

7 0

In 3 hours it will be 10,300 gallons of water because add 7000 + 3300 equals 10,300

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Math help rightnow plzzzzzzzzzzzzzzzzzzzzzz 1 attachment answer all

raketka [301]

#1

x-7>10

x>10 + 7

x>17

#2

3x <= 21

x <= 21/3

x<= 7

#3

5a - 2<18

5a < 18 + 2

5a <20

a <20/5

a<4

#4

2t + 8 >= -4(t +1)

2t +8>= -4t -4

2t + 4t >= -4 - 8

6t >= -12

t>= -12/6

t>= -2

6 0

3 years ago

Find the sum or difference <br> 1/2 - 1/14<br> A.3/7<br> B.2/7<br> C.4/7

pogonyaev

Answer:

A.3/7

Step-by-step explanation:

1/2 - 1/14

We need to get a common denominator of 14

1/2 * 7/7 = 7/14

7/14 - 1/14 = 6/14

We can simplify by dividing the top and bottom by 2

3/7

7 0

3 years ago

PLZ HELP WILL GIVE BRAINLIEST 50+25 POINTS!!!<br><br>Graph the following piecewise function.

Luda [366]

We need to graph the given piecewise function.

To graph any piecewise function we do that into parts

Let's graph upper part first which is

$f(x)=x^2+2$

restriction for that is $-5 \leq x < 3$

that means we are free to pick any number for x that is between -5 and 3, including 3.

So we will find few points by plugging random numbers between -5 and 3.

Let's use x=-5, we get:

$f(-5)=(-5)^2+2=25+2=27$

so first point is (-5,27).

similarly we can find other points like (0,2), (2,6), (-1,3) etc.

Now we join those points by a curved line.

$-5 \leq x$ means we use a close circle at -5

x<3 means use open circle at 3

------------

Repeat same process for 2nd part f(x)=x-4

choose any number between 3 and 7 like x=3, 4 etc

so we get points (3,-1), (4,0) etc

Now graph them

So the final graph will look like:

5 0

3 years ago

Read 2 more answers

Find the area of the region enclosed by the graphs of the functions

Vaselesa [24]

Answer:

$\displaystyle A = \frac{8}{21}$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right<u> </u>

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

Terms/Coefficients
Functions
Function Notation
Graphing
Solving systems of equations

<u>Calculus</u>

Area - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

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

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

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

*Note:

<em>Remember that for the Area of a Region, it is top function minus bottom function.</em>

<u />

<u>Step 1: Define</u>

f(x) = x²

g(x) = x⁶

Bounded (Partitioned) by x-axis

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

<em>Find where the functions intersect (x-values) to determine the bounds of integration.</em>

Simply graph the functions to see where the functions intersect (See Graph Attachment).

Interval: [-1, 1]

Lower bound: -1

Upper Bound: 1

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

<em>Integration</em>

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx$
[Area] Rewrite [Integration Property - Subtraction]: $\displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx$
[Area] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}$
[Area] Evaluate [Integration Rule - FTC 1]: $\displaystyle A = \frac{2}{3} - \frac{2}{7}$
[Area] Subtract: $\displaystyle A = \frac{8}{21}$

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

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

Book: College Calculus 10e

6 0

3 years ago

Subtract.<br> (7x2 + 6) - (2x-5)

Annette [7]

Answer:

25-2x

Step-by-step explanation:

(7x2+6)-(2x_5)

(14+6)-2x+5

20_2x+5

4 0

3 years ago

Read 2 more answers