Answer:
dy/dx=1
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If f(x) and its inverse function, fx), are both plotted on the same coordinate plane, what is their point of intersection?
1 answer:
Answer: (3, 3)
Step-by-step explanation:
the graphs of and
are flipped: if the point
is on the graph of
, then the point
is on the graph of
.
Any points of intersection will satisfy . A point that satisfies this property must have the same x and y coordinate. (Think about it.) The only point on
like that is
, so that is the point of intersection.
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We can see that revolving the region formed by intersecting 3 lines, we will get 2 cones that are connected their bases.
Volume of the cone V=1/3 *πr²*h
1) small cone has r=5, and h=5
Volume small cone V1= 1/3 *π*5²*5 = 5³/3 *π
2) large cone has r=5, and h=21-6=15, h=15
Volume large cone V2= 1/3 *π*5²*15 = 5³*π
3) whole volume
5³/3 *π + 5³*π=5³π(1/3+1)=((5³*4)/3)π=(500/3)π≈166.7π≈523.6
Area
we see 2 right triangles,
Area of the triangle=1/2*b*h, where b -base, h -height
1) small one, b=5, h=5
A1=(1/2)*5*5=25/2
2)large one, b=5, h=15
A2=(1/2)*5*15=75/2
3) whole area=A1+A2=25/2+75/2=100/2=50
Volume of the cone V=1/3 *πr²*h
1) small cone has r=5, and h=5
Volume small cone V1= 1/3 *π*5²*5 = 5³/3 *π
2) large cone has r=5, and h=21-6=15, h=15
Volume large cone V2= 1/3 *π*5²*15 = 5³*π
3) whole volume
5³/3 *π + 5³*π=5³π(1/3+1)=((5³*4)/3)π=(500/3)π≈166.7π≈523.6
Area
we see 2 right triangles,
Area of the triangle=1/2*b*h, where b -base, h -height
1) small one, b=5, h=5
A1=(1/2)*5*5=25/2
2)large one, b=5, h=15
A2=(1/2)*5*15=75/2
3) whole area=A1+A2=25/2+75/2=100/2=50
Answer:
a) growth
b) $500
c) 6% = 0.06
d)
e) $595.51
Step-by-step explanation:
<u />
<u>Part (a)</u>
Exponential GROWTH, since interest is applied to the account each year.
<u>Part (b)</u>
Initial amount = $500
<u>Part (c)</u>
Growth factor = 6% = 0.06 (in decimal form)
<u>Part (d)</u>
General form of exponential growth function:
where:
- a = initial amount
- r = rate of growth (in decimal form)
- x = time (in years)
Given:
- a = 500
- r = 0.06
<u>Part (e)</u>
when x = 3