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3 years ago

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Mathematics

1 answer:

AnnZ [28]3 years ago

4 0

Answer:

The average rate of change of $f(x) = x^2 +6x+13$ is 12

The average rate of change of $f(x) =- x^2 +6x+13$ is 10

Step-by-step explanation:

The average rate of change of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.

We can calculate the average rate of change between the 2 points by

$\frac{f(b) - f(a)}{b -a}$ -------------------(1)

(1) The average rate of change of the function $f(x) = x^2 +6x+13$ over the interval 1 ≤ x ≤ 5

f(a) = f(1)

$f(1) = (1)^2 +6(1) + 13$

f(1) =1+6+13

f(a) = 20---------------------(2)

f(b) = f(5)

$f(5) = (5)^2 +6(5)+13$

f(5) = 25 +30 +13

f(5) = 68-----------------------(3)

The average rate of change between (1 ,20) and (5 ,68 ) is

Substituting eq(2) and(3) in (1)

= $\frac{f(5) - f(1)}{5-1}$

= $\frac{68 -20}{5-1}$

= $\frac{48}{4}$

=12

This means that the average of all the slopes of lines tangent to the graph of f(x) between (1 ,20) and (5 ,68 ) is 12

(2) The average rate of change of the function $f(x) = -x^2 +6x+13$ over the interval -1 ≤ x ≤ 5

f(a) = f(-1)

$f(1) = (-1)^2 +6(-1) + 13$

f(1) =1-6+13

f(1) = 8---------------------(4)

f(b) = f(5)

$f(5) = (5)^2 +6(5)+13$

f(5) = 25 +30 +13

f(5) = 68-----------------------(5)

The average rate of change between (-1 ,8) and (5 ,68 ) is

Equation (1) becomes

$\frac{f(5) - f(-1)}{5-(-1)}$

On substituting the values

= $\frac{68 - 8}{5-(-1)}$

= $\frac{60}{5+1}$

= $\frac{60}{6}$

= 10

This means that the average of all the slopes of lines tangent to the graph of f(x) between (-1 ,8) and (5 ,68 ) is 10

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Given that triangle ABC is a right triangle, select a set of possible side length measurements

Elza [17]

Answer:

4,5,6 / 6,8,10 / 5,12,13 / ....

Step-by-step explanation:

Base on the pythagorean theorem, we have : a² + b² = c².
The first set : 4,5,6 - 4² + 5² = 6² (a possible set)
The second set : 6² + 8² = 10² (another possible set)
The last set : 5² + 12² = 13² (also possible)

There are a lot more sets, but I'll only list 3. Hope this helps :)

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1 year ago

Anna made 20/28 free throws in basketball this season.To the nearest thousands,what is her free-throw average?

Afina-wow [57]

Answer:

0.714 free throws.

Step-by-step explanation:

Anna made 20 out of 28 free throws.

Free-throw average = $\frac{20}{28}$ = 0.7142857143 free throws.

This equals 0.714 free throws (answer rounded up to the nearest thousandths)

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3 years ago

Julio believes that the quotient of 6 divided by 1/2 = 3. Explain Julios error and tell how to find the correct answer.

Gnom [1K]

Answer:

it can be written as 6/1 divided by 1/2

then you'll use the keep, switch, flip method. keep 6/1, switch division to multiplication, and flip 1/2 to become 2/1 or 2

now your equation is 6 x 2 = 12

Julio did 6 divided by 2. which could've been fixed if he changed the division sign to multiplication and multiplied

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2 years ago

The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest

Ksenya-84 [330]

Answer:

a) 0.7287

b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( port handles less than 5 million tons of cargo per week)

P(x < 5)

$P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)$

Calculation the value from standard normal z table, we have,

$P(x < 5) =0.7287= 72.87\%$

b) P( port handles 3 or more million tons of cargo per week)

$P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)$

Calculating the value from the standard normal table we have,

$1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%$

c)P( port handles between 3 million and 4 million tons of cargo per week)

$P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%$

$P(3 \leq x \leq 4) = 23.7\%$

d) P(X=x) = 0.85

We have to find the value of x such that the probability is 0.85.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85$

$= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85$

$=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.036) = 0.15$

$\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65$

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

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2 years ago

The area of a trapezium is 800 cm2

svlad2 [7]

Answer:

The distance between the parallel sides is 20cm.

Step-by-step explanation:

Area of a trapezoid:

$A=\frac{a+b}{2}\times h$

where a and b are the 2 bases, and h is the height. The value we're trying to find here is the height.

3 of the 4 variables in this equation are already given:

A = 800

a = 48

b = 32

Just plug those in and solve for h:

$\rightarrow 800=\frac{48+32}{2}\times h\\\rightarrow 800=\frac{80}{2}\times h\\\rightarrow 800=40\times h\\\rightarrow 800\div40=h\\\rightarrow h=20$

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2 years ago

Read 2 more answers