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Leno4ka [110]
2 years ago
8

Calculate the average rate of change of the function f(x) = 3x2 over the interval 1 ≤ x ≤ 5.

Mathematics
1 answer:
rewona [7]2 years ago
8 0
Average rate of change is delta y / delta x

(f(5)-f(1))/(5-1)

(75-3)/4

72/4

18
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Can you help me create a polynomial function matching the criteria on the left please and thanks
Olenka [21]

Answer:

f(x) = \dfrac{1}{8}(x + 4)^2(x + 1)(x - 3)

Step-by-step explanation:

From inspection of the graph, we can see that the curve intercepts the x-axis at (-4, 0), (-1, 0) and (3, 0)

Therefore,

x = -4 ⇒ x + 4 = 0

x = -1 ⇒ x + 1 = 0

x = 3 ⇒ x - 3 = 0

Because (-4, 0) touches the x-axis, then (x + 4)² will be a factor

So (x + 4)², (x + 1) and (x - 3) are all factors of the polynomial

\implies f(x) = \dfrac{1}{n}(x + 4)^2(x + 1)(x - 3)

If we multiply the constants, this will give us the y-intercept:

⇒ 4² x 1 x -3 = -48

From inspection of the graph, the y-intercept is -6

So to get from -48 to -6 we need to multiply -48 by 1/8

Therefore, n = 1/8

\implies f(x) = \dfrac{1}{8}(x + 4)^2(x + 1)(x - 3)

7 0
2 years ago
Read 2 more answers
A triangular prism has a volume of 2500 cubic feet. What is the length of the prism if its triangular bases are right triangles,
seraphim [82]

Answer:

25 ft

Step-by-step explanation:

V = AH, where A = area of the base, and H = height (length) of the prism

A = bh/2 for a triangle

V = bh/2 × H

2500 = (10)(20)/2 × H

2500 = 100H

H = 25

Answer: 25 ft

5 0
2 years ago
Consider the absolute value function f(x) = a[x]. Would the values of a produce a shrink or a stretch? So
Rom4ik [11]

Answer:

Shrink:

a=1/4

a=0.3

Stretch:

a=60

a=2.5

a=1.1

Step-by-step explanation:

7 0
3 years ago
4/5G + 42 = 2.8G + 18<br> Plz solve with an explanation
inysia [295]

Answer:

12

Step-by-step explanation:

Simplify  \frac{4}{5}G

​5

​

​4

​​ G  to  \frac{4G}{5}

​5

​

​4G

​​ .

\frac{4G}{5}+42=2.8G+18

​5

​

​4G

​​ +42=2.8G+18

Multiply both sides by 5.

4g + 210 = 14g + 90

Simplify  

 14G + 90 - 4G to 10G + 90

Subtract 90 from both sides.

210-90=10G210−90=10G

Simplify  210-90210−90  to  120120.

120=10G120=10G

Divide both sides by 1010.

\frac{120}{10}=G

​10

​

​120

​​ =G

Simplify  \frac{120}{10}

​10

​

​120

​​   to  1212.

12=G12=G

Switch sides.

G=12G=12

SORRY ABOUT ALL THIS WORK...

3 0
2 years ago
Read 2 more answers
Which is the best estimate of the circumference of this circle?
Ann [662]

Answer:

To what circle?mm

Step-by-step explanation:

any pictures?

6 0
3 years ago
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