Apply a 90 degree rotation to the point (1, 2)
2 answers:
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Answer:
The highest altitude that the object reaches is 576 feet.
Step-by-step explanation:
The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be , the first and second derivatives are, respectively:
First Derivative
Second Derivative
Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:
(Critical value)
The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:
The highest altitude that the object reaches is 576 feet.
Answer:
Morgan family picked 144 Braeburn apples, 96 Cortland apples, 72 Fuji apples and 48 Rome apples.
Step-by-step explanation:
Let B, C, F and R represent Braeburn apples, Cortland apples, Fuji apples, and Rome apples respectively.
We have been given that Morgan family picked a total of 360 apples. We can represent this information in an equation as:
We are told that Morgan family picked twice as many Braeburn as Fuji. We can represent this information in an equation as:
We are told that Morgan family picked twice as many Cortland as Rome, that is:
We are told that Morgan family picked 50% more Fuji than Rome, that is:
Upon substituting equation (4) in equation (2), we will get:
Now, each apple in in terms of Rome apples, so we will get:
Let us solve for R.
Therefore, Morgan family picked 48 Rome apples.
Upon substituting in (3), we will get:
Therefore, Morgan family picked 96 Cortland apples.
Upon substituting in (4), we will get:
Therefore, Morgan family picked 72 Fuji apples.
Upon substituting in (2), we will get:
Therefore, Morgan family picked 144 Braeburn apples.