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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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Antonio drops a glass marble into a pond and creates ripples that form concentric circles on the surface of the water. The radiu
photoshop1234 [79]

Answer:

is it multiple answer?

Step-by-step explanation:

8 0
3 years ago
Which choices are equivalent to the fraction below? check all that apply 16/36
kenny6666 [7]

Answer:

\frac{16}{36} = \frac{8}{18} = \frac{4}{9}

Step-by-step explanation:

\frac{16}{36} = \frac{16/4.5}{36/4.5} = \frac{3.5555}{8} \neq  \frac{3}{8} \\\\\frac{16}{36} = \frac{16/12}{36/12} = \frac{1.3333}{3} \neq  \frac{1}{3} \\\\\frac{16}{36} = \frac{16/9}{36/9} = \frac{1.7777}{4} \neq  \frac{1}{4} \\\\\frac{16}{36} = \frac{16/4}{36/4} = \frac{4}{9} \\\\\frac{16}{36} = \frac{16/7.2}{36/7.2} = \frac{2,2222}{5} \neq  \frac{2}{5} \\\\\frac{16}{36} = \frac{16/2}{36/2} = \frac{8}{18} \\\\

3 0
3 years ago
Finding original price with 75 percent of discount and $55.50 sale price
Andre45 [30]
This is pretty much 75% of 55.5 which is 41.625. Rounding that up would make $41.63.
4 0
3 years ago
PLEASE HELP!!
olga_2 [115]

The value of a = 2.17 and b = 1.95.

<h3>What is regression line?</h3>

A regression line is a graphic representation of the regression equation expressing the hypothesized relationship between an outcome or dependent variable and one or more predictors or independent variables;

y=2.01*1.93^{x}

Correlation:

r=0.964

R-squared:

r²=0.9292

Hence, value of a and b is 2.17 and 1.95.

learn more about regression line here:

brainly.com/question/11340674

#SPJ1

8 0
2 years ago
Last month, when Joe took his puppy to the veterinarian, the puppy weighed 5.4 pounds. This month, the puppy weighed 7.56 pounds
tino4ka555 [31]

<u>Answer:</u>

40%

<u>Step-by-step explanation:</u>

We are given that last month, Joe's puppy weight 5.4 pounds while this month, the puppy weighed 7.56 pounds.

We are to find the percentage increase of the weight of the puppy

We know that the formula of percentage increase if given by:

<em>Percentage increase = (new value - initial value)/initial value × 100</em>

So substituting the given values to get:

Percentage increase in puppy's weight = \frac{7.56-5.4}{5.4} \times 100 = 40%

7 0
3 years ago
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