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kipiarov [429]
2 years ago
9

A contaminant is leaking into a lake at a rate of R(t) = 1400e0.06t gallons/h. Enzymes have been added to the lake that neutrali

ze the contaminant over time so that after t hours the fraction that remains is S(t) = e−0.32t. If there are currently 10,000 gallons of the contaminant in the lake, how many gallons are present in the lake 18 hours from now? (Round your answer to the nearest whole number.) gal
Mathematics
1 answer:
ruslelena [56]2 years ago
5 0

Answer:

Step-by-step explanation:

Rate of leakage, R(t) = 1400 e^0.06t gallons/h

fraction remains , S(t) = e^(-0.32t)

initial contaminant = 1000 gallon

gallons contaminant present after t hour is S(t) R(t)

G(t) = S(t) R(t)

G(t) = 1400 e^{0.06t}\times e^{-0.32t}

G(t) = 1400 e^{- 0.26t}

Put t = 18 hours

G(t) = 1400 e^{- 0.26\times 18}

Taking log on both the sides

ln G = ln 1400 - 0.26 x 18

ln G = 7.244 - 4.68

ln G = 2.564

G = 13 gallons

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Bob's bill for dinner at surefire steak house was $45. In addition he piad 5°\° of the bill in tax and he left a tip for 15°\° o
Anuta_ua [19.1K]

Answer:

$54

Step-by-step explanation:

First

45 times .05= 2.25

Second

45 plus 2.25

Third

45 times .15= 6.75

Fourth

45+2.25+6.75

5 0
2 years ago
Write a two step equation involving division and addition that has a solution of x = 25
Tamiku [17]
Start with the solution
x=-25
use the reverse of what they asked
they wanted division and addition
we use multiplication and subtract

ok
x=-25
we can use subtraction and multiplication in any order
minus 10 from both sides
x-10=-35
multiply both sides by 4
4(x-10)=-140
4x-40=-140 is a possible equation
6 0
2 years ago
Use the double intercept approach to find the graph of –1 = –y + x. A. B. C. D.
navik [9.2K]

Answer:

Intercepts at (-1, 0) and (0, 1).

Step-by-step explanation:

The double intercept form for the equation of a line is

ax + by = 1

-1 = -y + x

<em> y = 0 </em>

<em> </em>x = -1     Multiply each side by -1

-x = 1

The <em>x-intercept</em> is at (-1, 0).

=====

<em> x = 0 </em>

-1 = -y     Multiply each side by -1

y = 1

The <em>y-intercept</em> is at (0, 1).

=====

The graph (see below) is a straight line passing through the points (-1, 0) and (0, 1).


5 0
2 years ago
Consider the first five steps of the derivation of The Quadratic function
Burka [1]

Answer:

Step-by-step explanation:

  • pick like terms

x² +  b²/4a² = -c / a + b²/4a²

  • b²/4a² = (b/2a)²

x² + (b/2a)² = -c/a + (b/2a)²

(x + b/2a)² = -c/a + (b/2a)² =  -c / a + b²/4a² = (-4ac+ b²)/4a²

(x + b/2a)² =  (-4ac+ b²)/4a²

  • square root both sides

√{(x + b/2a)²} = √{(-4ac+ b²)/4a²}

x + b/2a = √(-4ac+ b²) / √(4a²) = √(-4ac+ b²) / 2a = √( b²-4ac) / 2a

x + b/2a  =  √( b²-4ac) / 2a

  • subtract b/2a from both sides

x + b/2a -b/2a  =  {√( b²-4ac) / 2a } -b/2a

x = -b/2a +   {√( b²-4ac) / 2a }

  • the l.c.m is the same

x = {-b±√( b²-4ac)}/2a

7 0
2 years ago
Given CS=2x+1, SB=6x, CR=7.5, and RA=18. What must the value of x be in order to prove SR || BA? Justify your answer
dangina [55]
The picture in the attached figure

we know that
In similar triangles. The ratio of the lengths of the sides CS and CB must be equal to the ratio of the lengths of sides CR and CA.   CS / CB = CR / CA
which can also be written as, 
CS / (CS + SB) = CR / (CR + RA)
CS*(CR+RA)=CR*(CS+RA)
CS=2x+1
SB=6x
CR=7.5
RA=18
(2x+1)*[7.5+18]=7.5*[2x+1+18]
(2x+1)*[25.5]=7.5*[2x+19]
(51x+25.5)=15x+142.5
51x-15x=142.5-25.5
36x=117
x=117/36
x=3.25

the answer is 
x=3.25

4 0
2 years ago
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