Factor completely: 81x^4 – 1A. (9x + 1)(9x – 1)
B. (9x^2 + 1)(9x^2 – 1)
C. (3x^2 + 1)^3(3x – 1)
D. (9x^2 + 1)(3x + 1)(3x – 1)
Answers
Using this: a²-b²=(a+b)(a-b)
81x^4-1=
(9x²)²-1=
(9x²-1)(9x²+1)= (in the bold half we use the formula again)
(3x+1)(3x-1)(9x²+1)
So the answer is D
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A trailer hauling wood weighs 2/3 ton.The trailer weighs 1/4 ton without the wood. What is the weight of the wood?
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Answers
A = the future value at withdraw
P = the initial deposit
r = the annual interest rate (decimal)
t = the number of years the money is invested for
so the equation is A = 3000 (1.08) ^ 3, which is $3779.14
Answers
20
If you draw that out on a coordinate grid, you get a trapezoid with one base 6 units long, one base 4 units long and a height of 4. Using the formula for area of a trapezoid
h(b1 + b2)/2
where h is the height, 4, b1 is a base, 6, b2 is the other base, 4, we get
4(4+6)/2
which is 4(10)/2 or 40/2
which gets us the answer, 20
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-3 -3
-5y=-40
y=8
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Answer:
3 miles per hour.
Step-by-step explanation:
15 divided by 5 is 3
each hour he would have covered 3 miles of distance.
Answer:
3 miles per hour
Step-by-step explanation:
The formula for average speed is: R being rate, D being distance, T being time. We substitute the values to get
Simplified 3. Her average speed was 3 miles per hour. Hope this helps!
2.y=4x^3+3x^2+2
3.y=2x+3+8/x
4.y=x^3-9x^2-21x+11
5.y=9x^2/3-2x+5
Please provide full working out, thanks.
Answers
y=x²+2x
we have to calculate the first derived
y´=2x+2
we equal to "0" the first derived and find out the value of "X"
2x+2=0
x=-2/2=-1
we have to calculate de second derived
y´´=2>0 ⇒we have a minimun at x=-1
we calculate y
y=(-1)²+2(-1)=1-2=-1
Answer: we have a minimum at (-1,-1)
2)
y=4x³+3x²+2
we have to calculate the first derived
y´=12x²+6x
we equalize to "0" the first derived and find out the value of "X"
12x²+6x=0
6x(2x+1)=0
6x=0 ⇒x=0
2x+1=0 ⇒x=-1/2
we have to calculate de second derived
y´´=24x+6
y``(0)=24(0)+6=6 >0 ⇒we have a minimun at x=0
y``(-1/2)=24(-1/2)+6=-12+6=-6 ⇒we have a maximum at x=-1/2
we calculate y
if x=0, y=2
if x=-1/2; y=4(-1/2)³+3(-1/2)²+2=9/4.
we have to equalize the second derived to "0" and find out the value of "x"
24x+6=0
x=-6/24=-1/4; in x=-1/4 we have an inflection point.
y=4(-1/4)³+3(-1/4)²+2=31/16
Answer: we have a minimum at (0,2), a maximum at (-1/2, 9/4) and a inflection point at (-1/4, 31/16).
3.
y=2x+3+8/x
y=(2x²+3x+8)/ x
we have to calculate the first derived
y´= [(4x+3)x-(2x²+3x+8)] / x²=(4x²+3x-2x²-3x-8) / x²=(2x²-8)/x²
we equal to "0" the first derived and find out the value of "X"
(2x²-8) / x²=0
2x²-8=0
x=⁺₋2
we have to calculate de second derived
y´´=[(4x)x²-2x(2x²-8)] / x⁴=(4x³-4x³+16x)/x⁴)=16/x³
y``(-2)=16/(-2)³=-2>0 ⇒ at x=-2 exist a maximum
y´´(2)=16/(2)³=2<0 ⇒ at x=2 exist a minimum
we calculate y
y(-2)=-4+3-4=-5
y(2)=4+3+4=11
Answer: we have a maximum at (-2,-5 ) and a minimun at (2,11)
4)
y=x³-9x²-21x+11
we have to calculate the first derived
y´=3x²-18x-21
we equal to "0" the first derived and find out the value of "X"
3x²-18x-21=0
x²-6x-7=0
x=[6⁺₋√(36+28)]/2=(6⁺₋8)/2
x₁=-1
x₂=7
we have to calculate de second derived
y´´=6x-18
y``(-1)=-6-18=-24<0 ⇒at x=-1 exist a maximum
y´´(7)=42-18=24>0 ⇒ at x=7 exist a minimum.
we calculate y
y(-1)=-1-9+21+11=22
y(7)=343-441-147+11=-234
We equalize the second derive to 0, and find out the value of "x"
6x-18=0
x=3 in x=3 exist an inflection point
y=27-81-63+11=-106
Answer: we have a minimum at (7,-234), a maximum at (-1,22) and an inflection point at (3,-106).
5)
y=9x²/³-2x+5
we have to calculate the first derived
y´=6x⁻¹/³-2
we equal to "0" the first derived and find out the value of "X"
6x⁻¹/³-2=0
x⁻¹/³=1/3
x¹/³=3
x=27
we have to calculate de second derived
y´´=-2x^(-4/3)
y´´(27)=-0.024<0 ⇒ at x=27 exist a maximum
we calculate y
y=32
Answer: we have a maximum at (27,32)