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AfilCa [17]
2 years ago
10

(a). Consider the parabolic function f(x) = ax² +bx+c, where a ±0, b and care constants. For what values of a, band c is f

Mathematics
1 answer:
ki77a [65]2 years ago
5 0

Information about concavity is contained in the second derivative of a function. Given f(x) = ax² + bx + c, we have

f'(x) = 2ax + b

and

f''(x) = 2a

Concavity changes at a function's inflection points, which can occur wherever the second derivative is zero or undefined. In this case, since a ≠ 0, the function's concavity is uniform over its entire domain.

(i) f is concave up when f'' > 0, which occurs when a > 0.

(ii) f is concave down when f'' < 0, and this is the case if a < 0.

In Mathematica, define f by entering

f[x_] := a*x^2 + b*x + c

Then solve for intervals over which the second derivative is positive or negative, respectively, using

Reduce[f''[x] > 0, x]

Reduce[f''[x] < 0, x]

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Pls help me with this​
Free_Kalibri [48]

Answer:

\boxed{\sf \frac{15}{22} }

Step-by-step explanation:

The radius of the circle is 7 cm.

The two legs of the triangles are 7cm as well.

Area of a trinagle is ( base × height )/2.

\frac{7 \times 7}{2} =24.5

Multiply the value by 2 since there are two triangles.

24.5 \times 2 = 49

Calculate the area of the circle.

\pi r^2

The radius is given.

\pi (7)^2

Take \pi as \frac{22}{7}

49(\frac{22}{7} )

=154

Subtract the area of the two triangles from the area of the whole circle.

154-49=105

The area of the shaded part is 105 cm². The total area of the shape is 154cm².

\frac{105}{154} =\frac{15}{22}

5 0
3 years ago
Which expression is equivalent to -7(y - 2)
Neko [114]

The expression equivalent to -7(y - 2) is -7y + 14

<h3>Which expression is equivalent to -7(y - 2)?</h3>

Given the expression; -7(y - 2)

We expand the expression by multiplying each element inside the parentheses the element out i.e -7

-7(y - 2)

[ -7 × y and -7 × -2 ]

-7y + 14

Therefore, the expression equivalent to -7(y - 2) is -7y + 14.

Learn more about expressions here: brainly.com/question/13947055

#SPJ1

5 0
1 year ago
Factor completely: 64x^3+1
pantera1 [17]

Answer:

Step-by-step explanation:

Sum of cubes is a^3+b^3=(a+b)(a^2-ab+b^2)

64x^3+1

(4x+1)(16x^2-4x+1)

6 0
3 years ago
Hiii how are you guys doing if you answer this I’ll give you points and make you brainly or what ever it’s called and how do you
baherus [9]

Answer:

Hi how is your day going?

Step-by-step explanation:

I have some jokes and I hope you like them.

Knock Knock.

Who's There?

Scold.

Scold who?

Scold outside, let me in!

Knock Knock.

Who's there?

Tank.

Tank who?

You're Welcome!

7 0
2 years ago
Point W has coordinates (4, -7). If it is reflected over the y -axis, what are the coordinates of its image?
Korolek [52]

Answer:

I thank it is D

Step-by-step explanation:

4 0
2 years ago
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