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Setler79 [48]
3 years ago
11

Solve for 'p'

Mathematics
1 answer:
Darina [25.2K]3 years ago
6 0
\left(\dfrac{9a^{-4}}{25}\right)^p=\dfrac3{5a^2}
\left(\dfrac9{25a^4}\right)^p=\dfrac3{5a^2}

One way to find p is to notice that the part on the left hand side within the parentheses can be written as a square:

\dfrac9{25a^4}=\dfrac{3^2}{5^2(a^2)^2}=\left(\dfrac3{5a^2}\right)^2

So you could write

\left(\left(\dfrac3{5a^2}\right)^2\right)^p=\left(\dfrac3{5a^2}\right)^{2p}=\dfrac3{5a^2}

Since these two expressions are equal, and the bases are the same, you know the exponents must be equal, with the exponent on the right hand side being 1. So 2p=1, or p=\dfrac12.
You might be interested in
What is the solution to the inequality? -2/3(2x - 1/2) ≤ 1/5x - 1 Express your answer in interval notation.
almond37 [142]

ANSWER


-\frac{2}{3}(2x-\frac{1}{2})\le \frac{1}{5}x-1


Multiply through by LCM of 15


(15) \times -\frac{2}{3}(2x-\frac{1}{2})\le 15(\frac{1}{5}x-1)





-10(2x-\frac{1}{2})\le 3x-15



Expand brackets to obtain,



-20x+5\le 3x-15



Group like terms



15+5\le 20x+3x




20\le 23x


\frac{20}{23}\le x




x\ge \frac{20}{23}


In interval form it is written as


[\frac{20}{23}, \infty)







8 0
3 years ago
Help me pls I’ve been posting this question all day
Rama09 [41]

Answer:

19.5 sq. inches

Step-by-step explanation:

This one is fairly simple. The area of a rhombus is the same as that of a parallelogram, which is side * height. In this case, we have 6.5 (side) *3 (height) = 19.5 sq. inches. Hope this helps!

6 0
2 years ago
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
There are 30 names in a hat. If two names are picked without replacement, which expression shows the probability that Jack and J
Darya [45]

Answer: Choice C)

(1/30)*(1/29)

Explanation:

Jack has a 1/30 chance of being picked since he is 1 person out of 30 total. After his name is picked, and not put back, there are 30-1 = 29 names left. The chances Jill is picked is 1/29. The two fractions are multiplied to get the overall probability both are picked.

7 0
3 years ago
On Monday, Kym spent 15 minutes folding the clothes. She took a bath for 25 minutes and then took 10 minutes to make her bed. Ky
Brut [27]
Ok. First, Kym went to bed at 8:30. There are only 60 minutes in an hour. 10 minutes to make her bed. 8:30 - 10 = 8:20. She had a 25 minute bath "jeez that's long" 8:20 - 25 = 7:55. Kym spent 15 minutes folding clothes: 7:55 - 15 = 7:40. She began to start folding clothes at 7:40.

Answer:<span> B. 7:40 p.m.
Or you could do it the easy way.
15 + 25 + 10 = 50

50 - 8:30 = 7:40
</span>

7 0
3 years ago
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