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Mariulka [41]
2 years ago
5

Q.1 What value of p will make this equation true?

Mathematics
1 answer:
gtnhenbr [62]2 years ago
4 0

Answer:

1. \: p = 10 \\ 2. \: x = 4

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Describe the following variation: y/x2=5
Firdavs [7]
We are asked to describe the variation \displaystyle{ \frac{y}{x^2}=5, 

that is y=5x^2

for x≠0, in which case x=y=0, we distinguish the following intervals:

I   = (-infinity, -1]
II  = (-1, 0)
III = (0, 1)
III = [1, infinity)

Case I, consider the cases (examples)   x= -5, and x= -6

5(-6)^2\ \textgreater \ 5(-5)^2, so we can conclude that the greater the x, the smaller the y.

Case II, consider x= -1/2 < x=-1/3

5(-\frac{1}{2})^2= \frac{5}{4}\\\\ 5(-\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \  \frac{5}{4}

thus, the greater the x, the smaller the y.


Case III, consider the cases (examples)   x= 5, and x= 6

5(6)^2\ \textgreater \ 5(5)^2, so we can conclude that the greater the x, the greater the y.

Case III, consider x= 1/3 < x=1/2

5(\frac{1}{2})^2= \frac{5}{4}\\\\ 5(\frac{1}{3})^2= \frac{5}{9}\\\\\frac{5}{9}\ \textless \ \frac{5}{4}

thus, the greater the x, the greater the y.


Conclusion:

y=0 only if x is 0. Otherwise y>0 always:

for x<0,   x and y are inversely proportional

for x>0,   x and y are directly proportional.


Remark, an other possible consideration in cases could be x<0 and x>0 only.


Remark, 
another approach is considering the graph of y=5x^2, which is a parabola, with the vertex at (0, 0) opening upwards.

From the graph we can find the same conclusion. That is we can see that the farer we get away from the y-axis, in both direction, the larger the values of y become.

4 0
3 years ago
Which of the following expressions could give the total amount of a $45 restaurant bill with a 15% tip added on? (0.15)($45) (0.
Akimi4 [234]
The correct answer is 45+45(0.15). This is because you need to first count the price, and then add on the tip which is a certain percentage of that price. Hope this helped!
6 0
3 years ago
Find the minimum and maximum possible areas of a rectangle measuring 6 km by 11 km.
defon
Area of rectangle=length * breadth
=6*11=66kmOR,6000m*11000m=66000000m
4 0
3 years ago
An equilateral triangle has a perimeter of 15x + 3. What is the length of each side of the triangle?
maw [93]

An equilateral triangle have 3 congruent sides.

Divide the total (15x +3) by 3

(15x + 3)/3 = 5x + 1

Each side's length is 5x + 1

hope this helps

6 0
3 years ago
Which of the following are solutions to the equation below?
Over [174]
B and E are correct.
5 0
2 years ago
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