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.
_____
<em>Additional comment</em>
With these values, the function becomes ...
The amount of blue color in the green paint is an illustration of ratios and proportions.
Cheryl's green paint has more blue color
The proportion of blue color is calculated as:
So, we have:
Express as percentage
Express as percentage
By comparison: 40% >37.5%
Hence, Cheryl's green paint has more blue color
Read more about proportions at:
brainly.com/question/21126582
Answer:
(1/2, -1.8) belongs in quadrant 4
quadrant 4 is a (positive, negative)
Answer:
⅛
Step-by-step explanation:
Each mark (x) on the plot presents the distance that each student jumped.
There are 24 marks there, so it means there is a total of 24 students whose distance jumped were recorded.
Number of students that jumped 5½ ft = 3
Fraction of the students that jumped 5½ ft = no of students that jumped 5½ ft / total number of students
= 3/24
Simplify/reduce the fraction
= 1/8
Answer:
<em>y = -2x - 4</em>
Step-by-step explanation:
<em>y + 1 = -2x - 3</em>
<em>Subtract 1 from both sides to get the y by itself</em>
<em>y = -2x - 3 - 1</em>
<em>Simplify (Combine Like terms)</em>
<em>y = -2x - 4</em>