Answer:
dang I'm sorry I'm only in middle school but dang that's a lot
The solution to the equation is p = 1/3 and q = undefined
<h3>How to solve the equation?</h3>
The equation is given as:
p^2 - 2qp + 1/q = (p - 1/3)
The best way to solve the above equation is by the use of a graphing calculator i.e. graphically
However, it can be solved algebraically too (to some extent)
Recall that the equation is given as:
p^2 - 2qp + 1/q = (p - 1/3)
Split the equation
So, we have
p^2 - 2qp + 1/q = 0
p - 1/3 = 0
Solve for p in p - 1/3 = 0
p = 1/3
Substitute p = 1/3 in p^2 - 2qp + 1/q = 0
So, we have
(1/3)^2 - 2q(1/3) + 1/q = 0
This gives
1/9 - 2/3q + 1/q = 0
This gives
2/3q + 1/q = -1/9
Multiply though by q
So, we have
2/3q^2 + 1 = -1/9q
Multiply through by 9
6q^2 + 9 = -q
So, we have
6q^2 + q + 9 = 0
Using the graphing calculator, we have
q = undefined
Hence. the solution to the equation is p = 1/3 and q = undefined
Read more about equations at:
brainly.com/question/13763238
#SPJ1
Answer:
Y = 60 degrees and X = 12
Step-by-step explanation:
x+3 and 15 are congruent so x+3 = 15, 12+3 = 15 therefore x = 12
y = 60 vertically opposite angles are equal. :D
<h3>
Answer: -2</h3>
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Work Shown:


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Explanation:
In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.
I'm using the rule that

where k is some positive real number constant.
Using that rule will simplify the expression greatly to leave us with -2/1 or simply -2 as the answer.
In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.
This effectively means,

I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.
Answer:
The period of given function is 
So, Option B is correct.
Step-by-step explanation:
In this question we need to find the period of the function y= 3 sin x/8
The formula used to find period of function is: 
We need to know the value of b.
To find the value of b we compare the standard equation with the equation of function given.
Standard Equation: y = a sin(bx - c) +d
Given Equation: y= 3 sin(x/8)
Comparing we get:
a= 3
b= 1/8
c= 0
d=0
So, we get the value of b i.e 1/8. Putting it in the formula to find period of given function.


Solving,


So, the period of given function is 