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Shalnov [3]
3 years ago
5

Prove, using the second derivative, that the general quadratic y= ax^2+bx+c, is:

Mathematics
1 answer:
lozanna [386]3 years ago
3 0

There are three things you have to know:

  • A function is convex when its second derivative f''(x)>0
  • A function is concave when it second derivative f''(x)
  • The derivative of a power, x^n, is nx^{n-1}

So, the first derivative is

y'=2ax+b

and the second derivative is

y''=2a

This implies that the second derivative of a parabola is constant, and of course that 2 doesn't change the sign of a.

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Find the missing side length XI. round your answer to the nearest tenth.​
lianna [129]

Answer: XI = 10.35 mm

Step-by-step explanation:

Considering the given triangle XIF, to determine XI, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

XI/SinF = XF/SinI = FI/SinX

The sum of the angles in a triangle is 180°. It means that

F + 63 + 52 = 180

F = 180 - (63 + 52)

F = 65°

Therefore

XI/Sin 65 = 9/Sin 52

Cross multiplying, it becomes

XISin52 = 9Sin65

0.788XI = 9 × 0.906

0.788XI = 8.154

XI = 8.154/0.788

XI = 10.35

7 0
3 years ago
Sandy is ordering bread rolls for her party. She wants 3/5 of the rolls to be whole wheat. What other fractions can represent th
Vsevolod [243]
9/15 rolls would be wheat
7 0
4 years ago
Suppose we call a number funny if it is the product of three prime factors, of which exactly two are the same. (For example: 12=
Schach [20]

Step-by-step explanation:

31 37 41 43 47 51 53 57 59

are the prime numbers between 30 and 60

6 0
3 years ago
What is 45% in a decimal
Grace [21]

Answer:

0.45

Step-by-step explanation:

Percent is per 100, so the fraction is 45/100.

The decimal is the numerator, but you need to swoop 2 times.

Therefore, the answer is 0.45.

7 0
4 years ago
Read 2 more answers
There is only one freshman in the cast of a high school play. There are 6 sophomores and 11 juniors. One third of the cast are s
Rudik [331]

Let X = total students in musical


 

Then (1/3) X = number of seniors


 

  1 + 6 + 11 + (1/3)X = X


 

              18 + (1/3)X = X


 

                           18 = (2/3)X


 

                 (3/2)(18) = X


 

                          27 = X


 

27 students in musical of which one third are seniors,  

there are 9 seniors in musical


hope this helped!

6 0
3 years ago
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