Step-by-step explanation:
xy + 10 = 0. => y = -10/x.
2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.
When -10/x = -2/3 x + 7/3,
-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.
=> 2x² - 7x - 30 = 0
=> (2x + 5)(x - 6) = 0
=> x = -2.5 or x = 6.
dy/dx = d/dx [-10/x] = 10/x².
When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.
When x = 6, dy/dx = 10 / (6)² = 5/18.
Hence the gradients at the points are 1.6 and 5/18.
Answer:
Step-by-step explanation:
A prime number is a positive integer that only has a factor of one and itself. Factors are the numbers we multiply together to get another number.
Example: 11 is a prime number. To get 11, we can only multiply 1x11.
A composite number is a positive integer that has factors other than one and itself.
Example: 12 is a composite number. To get 12, you can multiply together 1x12, 2x6, and 3x4. 1, 2, 3, 4, 6, and 12 are all factors of 12.
In the problem you are trying to solve, Mrs. Evans wants to hang 13 pictures with the same number of pictures in each row. Find all of the factors of 13: 1, 13. Those are the only numbers we can multiply together to get 13. Since its factors are only 1 and itself, 13 is a prime number. Because 13 is a prime number, there are no other possible ways she can arrange her pictures into rows with the same number of pictures in each.
Do inverse operation. Divide 15.00 from 32.40. You will get the answer of 2.16. That is the other factor. To check, just multiply 15.00 and 2.16. Your answer will be 32.40.
I’m positive it’s thee third one
Answer:
option (A) 900 ft²
Step-by-step explanation:
Let the length be L and width of the area be 'B'
now,
Perimeter of the fence = 2 (L + B)
also,
2 (L + B) = 120 feet
or
L + B = 60 ft
or
L = 60 - B ft
Now,
The area of the fencing ground, A = LB
or
A = (60 - B)B
A = 60B - B²
now,
differentiating the area with respect to width B, we get
or
= 60 - 2B
for point of maxima or minima, put = 0
thus,
60 - 2B = 0
or
2B = 60
or
B = 30 ft
to check for maxima or minima
= - 2
since,
is negative, B = 30 ft is point of maxima
therefore,
L = 60 - B = 60 - 30 = 30 ft
Thus,
Maximum area of the fencing ground = 30 × 30 = 900 ft²
Hence,
The correct answer is option (A) 900 ft²
