Answer:
440
The attached file is how I would have done it.
Answer: 8x³ - 46x² - 15x + 18
Step-by-step explanation:
To find the volume of a rectangular prism we will multiply each of the three dimensions given
First, let's multiply 4x+3 by x-6: (4x+3)(x-6) = 4x² - 21x - 18
Then we will multiply 4x²... by 2x-1: (4x²-21x-18)(2x-1) = 8x³ - 46x² - 15x + 18
The maximum height that the pendulum can reach will be 45 meters.
<h3>How to calculate the height?</h3>
It should be noted that the total energy at A should be equal to the total energy at B.
Therefore, this will be calculated thus:
1/2(14)² + 10(35) = 1/2(0)² + mgH
98 + 350 = 10H
448 = 10H
H = 448/10
H = 44.8 meters
H = 45 meters approximately
Learn mote about height on:
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I haven't learned antiderivitives yet but I can try to logic it
<span>First find f′ and then find f. f′′(x)=3x^3+6x^2−x+2, f′(1)=9, f(1)=−7.
we reverse chain rule
3x^3, we know that it was a 4th degree thing, and the coefient is 3, so
4*what=3?, answer is 3/4
3/4x^4
6x^2
we know it was x^3, and the coefient is now 6 so
3*what=6? what=2
2x^3
-1x, the power was 2 and coefient is now -1, so
2 times what=-1?, -1/2
-1/2x^2
2, that is from 2x
so
</span>
<span>3/4x^4+2x^3-1/2x^2+2x=f'(x)
test x=1
(3/4)(1)+2(1)-(1/2)(1)+2(1)=
3/4+2-2/4+2=
4 and 1/4 we need to get it to 9
4 and 1/4 +what=9
answer is 4 and 3/4
so we add that to the end since it will become 0 from derivitive
</span>
<span>f'(x)=3/4x^4+2x^3-1/2x^2+2x+4 and 3/4
now reverse drivitive again
3/4x^4
exponent is 5 and coefient is 3/4
5 times what=3/4? answer is 3/20
3/20x^5
2x^3
exponent should be 4 and coefient is 2
4 times what=2? answer is 1/2
1/2x^4
-1/2x^2
exponent should be 3 and coefient is -1/2
3 times what=-1/2? answer is -1/6
-1/6x^3
2x
exponent should be 2 and coefient is 2
2 times what=2? answer is 1
1x^2
4 and 3/4 turns to (4 and 3/4)x
</span>
<span>f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+(4 and 3/4)x
try evaluating it for x=1
f(1)=(3/20)+(10/20)-(10/50)+1+(19/4)
f(1)=6 and 7/30
what do we add to get -7
-13 and 7/30
</span>
<span><span>f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+(4 and 3/4)x-13 and 7/30
</span>
</span>ANSWER
<span>f'(x)=3/4x^4+2x^3-1/2x^2+2x+19/4
</span><span>f(x)=3/20x^5+1/2x^4-1/6x^3+x^2+19/4x-187/30</span>
I'm in a hurry to get home.
My car is almost out of gas.
I pull into a gas station.
I have $10 in my pocket.
Gas is selling for $2.36⁹ per gallon.
How many gallons can I buy.
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Even better:
My car gets 25 miles to the gallon.
How many miles can I buy ?
