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Marta_Voda [28]
3 years ago
15

BellaBought a small smoothie at the Point Coffee Shop and gave the barsta a 10% tip she spent 2.75 in all. How much did the smoo

thie cost before the tip
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
5 0
$2.50 was the original price
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2. The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise
rusak2 [61]

Answer:

hey have made this a little more confusing than it has to be. Usually we use H+ in chemistry instead of t, but you can also use X, Y if it's easier where Y = -log(X) where X= hydronium and Y = pH.

Which also means Y=p(t) and X = t.

To graph this, I would suggest using values for X like 0.1, 0.2, 0.5, 0.7, 1.0, 1.5, or similar numbers. Then use your calculator to calculate Y values for each of these X values and plot them. You can also use a spreadsheet. If you have Excel I can help you to use it. Either way you can then use your graph to answer the questions in part 1 where Y = 0 and Y=1 and just read off the X values.

Part 2 is worded badly. It's ambiguous to say "raised by 0.5" since if you raise hydronium (= X) by 0.5, the change in pH (=Y) will vary depending on where you start. They meant "raise to 0.5", though they do say this at the end of the question. Anyway, you can easily read it off your graph using 0.5 as the X value.

Now to set up the exponential function this is much easier than it sounds. Just remember that a logarithm is the inverse of an exponent so they cancel each other out:  As an example log(10X) = X.

So applying here, just take this equation  Y = -log(X) and raise 10 to both sides of the equation:

10Y = 10-log(X)    which gives you 10Y = 1/X or more usefully X = 10-Y where again X= hydronium and Y = pH

Part 3, these questions actually have no relationship to anything in chemical reality, but are just exercises to see if you can manipulate the graph and function. But they do illustrate at least one interesting point. Note that in the equation

X = 10-Y

X can never =0. This makes sense since there is nothing you can raise 10 to that will make it zero. It also makes sense chemically since in water you can never have zero hydronium. Similarly using the other form

Y = -log(X)

You know X can also never be zero since you can't have log(0).

Now when they ask for a "Y intercept" they are asking for when X=0 which as stated is never in the above case. However when you transform the equation the ways they want you to, then maybe sometimes you can:

So for p(t) + 1 that really means Y = -log(x) + 1.  Still here you can not have a Y intercept (X can't =0) since you would still have log(0) which is forbidden.

But p(t+1) really means Y = -log(X+1). Here of course X can be zero since that just gives you log(1). So you have a Y-intercept.

I'll leave it for you to figure out the third one, the question being if you set X=0, will you get log(0)? If so, that's forbidden. If not, you will have a Y intercept.

5 0
2 years ago
4 x 2x 4 being length and 2x being width
kow [346]

Answer:

1/4

Step-by-step explanation:

4 0
3 years ago
I need help
zhenek [66]

Answer:

10 miles

Step-by-step explanation:

35/7 ?/2   2x35=70/7=10 butterfly cross multiply and divide

4 0
2 years ago
Read 2 more answers
The function f(x) = x2 - 4x + 5 is shown on the graph.
Xelga [282]

Answer:

4. The range of the function is all

real numbers less than or equal to 9.

3 0
2 years ago
Find the area of the blue shape below. Use 3.14 for π
Anika [276]

Answer:

1413.86 ft^2.

Step-by-step explanation:

The diameter of the circle = 50 - 2(18)

= 50-36

=  14 ft.

So its radius is 7 ft.

The total area of the blue shape

= 2(35 * 18) + 3.14*7^2

= 1413.86 ft^2.

7 0
1 year ago
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