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Pavel [41]
3 years ago
7

If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures

the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.

The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)

Mathematics
1 answer:
klio [65]3 years ago
7 0

Answer:

Second Option

The transformation that will cause p(t) to have an intercept with the y = p(t) axis is p(t) =-log_{10}(t+1)

Step-by-step explanation:

If we have the function p(t) = -log_{10}(t) as the parent function then we must find out which of the transformations shown must be performed to the function so that it has an intersection on the y axis.

The main function p(t) = -log_{10}(t) because if we do t = 0 then p(t) is not defined because the log(0) is not defined.

Then, if we transform the function by doing y = p(t) +1 then we will obtain:

p(t) =-log_{10}(t)+1

This transformation moves the parent function 1 unit up. Therefore, if the original function had no interception in y, then it will not have an intercept either.

 

Then, if we transform the function by doing y = p(t + 1) then we will get:

p(t) =-log_{10}(t+1)

This function moves the parent function one unit to the left on the x axis. Therefore it will have an intercept in p(t) = 0

The transformation -1*p (t) only reflects the function p(t) on the x axis.  But if the main function has no intercept on the y-axis then the reflected function will also have no intercept on the y-axis

Therefore the correct option is the second one. The transformation that will cause p(t) to have an intercept with the y = p(t) axis is p(t) =-log_{10}(t+1)

Observe the attached image

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Solve the equation 2 3/5 × 1 3/7
Airida [17]

Answer:

26/7

Step-by-step explanation:

2\frac{3}{5} * 1\frac{3}{7}=

\frac{13}{5}* \frac{10}{3}  =

\frac{130}{35}=

simplify= 26/7

8 0
3 years ago
A triangle has one side measuring 5 feet and two sides measuring 7 feet. What kind of
Svetllana [295]

Answer:

isoceles but not equilateral

Step-by-step explanation:

it has two sides that are the same length, but not all three sides are the same length

An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal

8 0
3 years ago
$13,168is invested, part at 13%and the rest at
Kryger [21]

Answer: the amount invested at 13% is $9748

the amount invested at 5% is $3420

Step-by-step explanation:

Let x represent the amount invested at 13%.

Let y represent the amount invested at 5%.

$13,168 is invested, part at 13 % and the rest at 5%. This means that

x + y = 13168

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested at 13%,

P = x

R = 13%

T =1 year

I = (x × 13 × 1)/100 = 0.13x

Considering the amount invested at 5%,

P = y

R = 5%

T = 1 year

I = (x × 5 × 1)/100 = 0.05y

If the interest earned from the amount invested at

13% exceeds the interest earned from the amount invested at

5% by $1438.24, it means that

0.13x - 0.05y = 1438.24 - - -- - - - - -1

Substituting x = 13168 - y into equation 1, it becomes

0.13(13168 - y) - 0.05y = 1438.24

1711.84 - 0.13y - 0.05y = 1438.24

- 0.13y - 0.05y = 1438.24 - 1711.84

- 0.08y = - 273.6

y = - 273.6/- 0.08

y = 3420

x = 13168 - y = 13168 - 3420

x = 9748

7 0
3 years ago
What is the inverse of the function f(x) = x – 12?
igor_vitrenko [27]
F (x)= x+12 is the inverse of the function
7 0
3 years ago
8 + 8r = 3 + 3r can anyone can help me out​
MAVERICK [17]

Answer:r = -1

Step-by-step explanation:

8+8r-(3+3r)=0

We add all the numbers together, and all the variables

8r-(3r+3)+8=0

We get rid of parentheses

8r-3r-3+8=0

We add all the numbers together, and all the variables

5r+5=0

We move all terms containing r to the left, all other terms to the right

5r=-5

r=-5/5

r=-1

Hope this helps

6 0
3 years ago
Read 2 more answers
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