find the values for c and d that make the function differentiable:f(x) = 5x^2 + c if x = or < than 3dx^2 - 3 if x > 3
1 answer:
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
__
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.
_____
<em>Additional comment</em>
With these values, the function becomes ...
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Answer: 5y + 4x = - 10
Step-by-step explanation:
Two lines are said to be perpendicular if the product of their gradients = -1.
If the gradient of the first line is and the gradient of the second line is
, if the lines are perpendicular, them
x
= -1 , that is
=
The equation of the line given is 5x - 4y = -3 , we need to write this equation in slope - intercept form in order to find the slope.
The equation in slope -intercept form is given as :
y =mx + c , where m is the slope and c is the y - intercept.
Writing the equation in this form , we have
5x - 4y = + 3
4y = 5x -+3
y = 5x/4 + 3/4
comparing with the equation y = mx + c , then = 5/4
Which means that = -4/5 and the line passes through the point ( -5 , 2 ).
Using the equation of line in slope - point form to find the equation of the line;
y - = m ( x -
)
y - 2 = -4/5 ( x +5)
5(y - 2 ) = -4 ( x + 5 )
5y - 10 = -4x - 20
5y + 4x = - 10
Answer:
13
Step-by-step explanation:
Given parameters:
Number of oranges processed by grower = 2330 oranges
Number of oranges per crate = 96
Unknown:
Number unpacked oranges
Solution:
To solve this problem, divide the total number of oranges by the number of oranges per crate;
Number of unpacked oranges =
Number of unpacked oranges = 24
The remaining unpacked is 13.
The possible solution is 12 cats and 4 dogs in Sarah's store.
Let x represent the number of cats and y represent the number of dogs.
Since Sarah's Pet Store never has more than a combined total of 16 cats and dogs. Hence:
- x + y ≤ 16
Also, She also never has more than 9 cats. Therefore:
- x > 9
The solution to the inequality is graphed. From the graph, the possible solution is 12 cats and 4 dogs
Find out more on inequalities at: brainly.com/question/24372553
