9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
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The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
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This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
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<em>Additional comment</em>
With these values, the function becomes ...
Answer:
is the question correct, you end up with no X's
3x -4x + x = 9
or I've got it wrong
Let "x" represent the number of units
5x = the number of tomato plants in Inessa's garden
6x = the number of tomato plants in Ralph's garden
the question says that half (1/2 x (5x)) of Inessa's tomato plants are taken from her garden and put into Ralph's garden
this means that Ralph has a total of 850 tomato plants in his garden
using all of this information, we get the following (which we have to solve):
(1/2)(5x) + 6x = 850
when we solve for "x", we find that:
"x" = 100
so, going back to the original statement, if Ralph started out with (6x) tomato plants, and "x" = 100, we have to multiply 6 by 100
doing so gives us our final answer:
Ralph had 600 tomato plants in the beginning
Answer:
X ≤ 50
Step-by-step explanation:
Since the additional fee for a piece of luggage is only charged if it weighs more than 50 lbs, than Michael's suitcase weight must be less than, or equal to, 50 lbs. Using 'X' as the weight of Michael's suitcase in pounds:
X ≤ 50
'X' is less than or equal to 50 lbs
The factors of
375: 1; 3; 5; 15; 25, 75, 125, 375
66: 1; 2; 3; 6, 11, 22, 33, 66
33: 1, 3, 11, 33
