Answer:
The interval for which <em>y</em> is a decreasing function of <em>x</em> is:
Or as an inequality:
Step-by-step explanation:
We are given the equation:
And we want to find the range of values <em>x</em> for which <em>y</em> is a decreasing function of <em>x</em>.
<em>y</em> is decreasing whenever <em>y'</em> is negative. Find <em>y'</em> using the Quotient Rule:
Differentiate:
<em>y</em> is decreasing whenever <em>y'</em> is negative. Thus:
Multiply both sides by <em>x²</em>. This is always positive so we do not need to change the sign:
Factor:
e<em>ˣ</em> is always positive. So:
Adding one to both sides produces:
Therefore, <em>y</em> is a decreasing function of <em>x</em> when <em>x</em> is less than one (and greater than 0).
In interval notation:
Or as an inequality:
<u>Given</u>:
The line graph shows the number of marks Stacey scored in her homeworks.
We need to determine the Stacey's mean score.
<u>Mean score:</u>
The total number of marks is given by
Simplifying, we get;
Thus, the total number of marks is 40.
Sum of the number of marks scored is given by
Thus, the sum of the marks scored is 20.
The mean is given by
Therefore, Stacey's mean score is 2 marks.
Answer:
· This image may result from the construction of <em>an angle congruent to a given angle</em>.
· The next step in this construction is to set the compass width to <em>arc JK and draw an arc centered at L intersecting the existing arc through L</em>.
Step-by-step explanation:
If the step shown above results in point of intersection P, and the construction is completed by drawing ray DP, then this construction produces triangle DLP congruent to triangle BKJ. The angle at D will be congruent to the angle at B because CPCTC. Hence an angle congruent to a given angle will have been constructed.
Second, fourth and fifth.
2^4 = 2*2*2*2 =16
4^2= 4*4 =16
16^1= 16=16
The question was incomplete. Below you will find the missing content.
The square root function f(x) is x <= 7
Options are :
A. 7 is subtracted from the x-term inside the radical.
B. The radical is multiplied by a negative number.
C. 7 is added to the radical term.
D. The x-term inside the radical has a negative coefficient.
Option D is correct, which is : The x-term inside the radical has a negative coefficient.
Given, the domain of the square root function f(x) is x <= 7
Consider the function y = √x.
The domain of this function is x ≥ 0 and the range is y ≥ 0.
The expression inside the radical must be greater than or equal to zero.
Now, if x ≤ 7
x - 7 ≤ 0
7 - x ≥ 0
And the function y = √(7-x) will have the domain x ≤ 7.
This implies that the x-term inside the radical has a negative coefficient.
Therefore, the statement that the x-term inside the radical has a negative coefficient must be true.
Learn more about function here :
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