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Oduvanchick [21]

2 years ago

11

A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Creat

e and graph the solution set of the equation for the gallons of water, y, remaining in the barrel in terms of the number of minutes elapsed, x.

2 answers:

emmainna [20.7K]2 years ago

7 0

Answer:

$y=-0.10x+60$

Step-by-step explanation:

Let

y -----> gallons of water remaining in the barrel

x-----> number of minutes elapsed

we know that

Water leaks out of the barrel at a rate of 1 gallon every 10 minutes

so

$1/10=0.10\frac{gal}{min}$

The linear equation that represent this situation is

$y=-0.10x+60$

The graph in the attached figure

Bad White [126]2 years ago

5 0

Answer:

So you t start with 60 because that is how many gallons Jim has. Then you can count by tens until you get to 100. it takes 10 tens to get to 100 which means that for each 10 mins 1 gallon is lost. so the number of gallons lost in 100 mins is 10. so the point would read (100, 50) for every hundred mins, 10 gallons of water are lost. nUntil you hit zero because cannot have negative amounts of water. Even s helps!

Step-by-step explanation:

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Compute i^1+i^2+i^3....i^99+i^100

fgiga [73]

Good morning ☕️

Answer:

<h3>i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰ = 0</h3>

Step-by-step explanation:

Consider the sum S = i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰

S = i¹ + i² + i³ + . . . + i⁹⁹ + i¹⁰⁰

S = a₁ + a₂ + a₃ +. . . + a₉₉ + a₁₀₀

then, S is the sum of 100 consecutive terms of a geometric sequence (an)

where the first term a1 = i¹ = i and the common ratio = i

FORMULA:______________________

$S=(term1)*\frac{1-(common.ratio)^{number.of.terms}}{1-(common.ratio)}$

_______________________________

then

$S=i*\frac{1-i^{100} }{1-i}$

or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1 (we know that i⁴ = 1)

Hence

S = 0

7 0

2 years ago

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achi

lubasha [3.4K]

Answer:

Shift 2 unit left

Flip the graph about y-axis

Stretch horizontally by factor 2

Shift vertically up by 2 units

Step-by-step explanation:

Given:

Parent function: $f(x)=\log x$

Transformation function: $f(x)=\log(-2x-4)+2$

Take -2 common from transform function f(x)

$f(x)=\log[-2(x+2)]+2$

Now we see the step-by-step translation

$f(x)=\log x$

Shift 2 unit left ( x → x+2 )

$f(x)=\log(x+2)$

Flip the graph about y-axis ( (x+2) → - (x+2) )

$f(x)=\log[-(x+2)]$

Stretch horizontally by factor 2 [ -x(x+2) → -2(x+2) ]

$f(x)=\log[-2(x+2)]$

Shift vertically up by 2 units [ f(x) → f(x) + 2 ]

$f(x)=\log[-2(x+2)]+2$

Simplify the function:

$f(x)=\log(-2x-4)+2$

Hence, Using four step of transformation to get new function $f(x)=\log(-2x-4)+2$

3 0

1 year ago

Read 2 more answers

brian filled 72 glasses with apple juice for a school party if each glass holds 1 cup of juice how many quarts of apple juice di

GaryK [48]

4 cups in a quart so you would have 72 cups divided by 4 and get 18

5 0

2 years ago

You have a small marble statue of Mozart that is 10 inches tall and is made of 16 cu. inches of marble. The original statue in V

vagabundo [1.1K]

Answer:

0.08 cubic feet.

Step-by-step explanation:

You have a small marble statue of Mozart that is 10 inches tall and is made of 16 cu. inches of marble.

The original statue in Vienna is 7 feet tall.

First we will convert this to inches as one relation is given in inches.

1 feet = 12 inches

7 feet = $12\times7=84$ inches

Let the amount of marble used for 84 inches statue be = x

We can relate both the conditions in the following way:

$\frac{10}{16} =\frac{84}{x}$

$10x=16\times84$

$10x=1344$

x = 134.40 cubic inches

Now, 1 cubic inch = $\frac{1}{1728}$ cubic foot

So, 134.40 cubic inches = $\frac{134.40}{1728}$ cubic foot

= 0.0777 cubic feet rounding to 0.08 cubic feet.

6 0

2 years ago

Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Digiron [165]

Answer:

(3)11

Step-by-step explanation:

We are given that

$(x^2-12x+35)(x^2+10x+24)=504$

We have to find the sum of positive roots of the equation.

$x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504$

$x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504$

$x^4-2x^3-61x^2+62x+840-504=0$

$x^4-2x^3-61x^2+62x+336=0$

Factor of 336

2,3,4,6,8,7,

Let x=2

$2^4-2^4-61(2^2)+62(2)+336\neq0$

x=2 is not the root of equation

x=-2

$(-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0$

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

$3^4-2(3^3)-61(3^2)+62(3)+336=0$

Therefore, x=3 is the root of equation.

$(x+2)(x-3)(x^2-x-56)=0$

$(x+2)(x-3)(x^2-8x+7x-56)=0$

$(x+2)(x-3)(x(x-8)+7(x-8))=0$

$(x+2)(x-3)(x-8)(x+7)=0$

$x-8=0\implies x=8$

$x+7=0\implies x=-7$

Positive roots are 3 and 8

Sum of positive roots=3+8=11

Option (3) is true.

4 0

1 year ago