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:
Answer:
144
Step-by-step explanation:
Answer:
their hopes will come true
Step-by-step explanation:
Using the formula for calculating amount expressed as;
A = P(1+r)^t
Given
P = $15000
r = 9.6% = 0.096
t = 15years (18-3)
Substitute;
A = 15,000(1+0.096)^15
A = 15,000(1.096)^15
A = 15000(3.9551)
A = 59,326.6
As we can see, the money is even more than twice the original amount, this shows that their hopes will come true
The steps to construct a regular hexagon inscribed in a circle using a compass and straightedge are given as follows:
1. <span>Construct a circle with its center at point H.
2. </span><span>Construct horizontal line l and point H on line l
3. </span>Label
the point of intersection of the circle and line l to the left of point
H, point J, and label the point of intersection of the circle and line l
to the right of point H, point K.<span>
4. Construct
a circle with its center at point J and having radius HJ .
Construct a circle with its center at point K having radius HJ
5. </span><span>Label
the point of intersection of circles H and J that lies above line l,
point M, and the point of their intersection that lies below line l,
point N. Label the point of intersection of circles H and K that lies
above line l, point O, and the point of their intersection that lies
below line l, point P.
6. </span><span>Construct and JM⎯⎯⎯⎯⎯, MO⎯⎯⎯⎯⎯⎯⎯, OK⎯⎯⎯⎯⎯⎯⎯, KP⎯⎯⎯⎯⎯, PN⎯⎯⎯⎯⎯⎯, and NJ⎯⎯⎯⎯⎯ to complete regular hexagon JMOKPN .</span>
