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2 answers:
Answer: The farmers have to plough 1680 acres of land.
Step-by-step explanation:
Let the expected time to complete the plowing be 'x'.
In x days, a group of farmers had to plough = 112 acres
According to question, on exceeding the schedule by 8 acres per day, the farmers finished plowing one day earlier than expected.
So, New time = x-1
Number of acres of land becomes
So, According to question, it becomes,
So, Total acres of land the farmers have to plough is given by
Hence, the farmers have to plough 1680 acres of land.
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A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
<h3>What is a quadratic equation?</h3>A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The complete question is:
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth.
The time at which the height of the ball is 16 feet can be found by,
h = 2 + 31t - 16t²
16 = 2 + 31t - 16t²
16 - 2 - 31t + 16t² = 0
16t² - 31t + 14 = 0
t = 0.717 , 1.221
Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.
Learn more about Quadratic Equations:
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Given Equation:
Let us remove parenthesis first.
In order to remove parenthesis, we need to distribute -4 over parenthesis (2/3 h -3).
Distributing -4 over (2/3 h -3), we get,
-4*2/3 h - 4*-3 = -8/3 h + 12.
Substituting this value in original equation, we get
Now, in order to make the equation easy to solve, we always remove fractions. In order to remove fraction, we need to find the lowest common denominator of all terms(lcd).
The fraction terms has 3 in denominators, so we could multiply each and every term by 3 to remove 3's from denominators.
Multiplying each equation by 3, we get,
On simplfying this step, we get
Combining like terms on left side, we get
-7h +36 = 2h -18.
Subtracting 36 from both sides, we get
-7h +36 -36= 2h -18-36.
-7h=2h-54
Subtracting 2h from both sides, we get
-7h-2h=2h-54-2h
-9h = -54
Dividing both sides by -9.
-9h/-9 = -54/-9
h = 6.
Therefore, final answer is h=6.