Help please: (n^4)^-3(n^4)^-1

AnnZ [28]

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

4 0

3 years ago

Solve for x pls: Options: a) -11 b) 80 c) 51 d) -14

myrzilka [38]

Answer:

x = -11

Step-by-step explanation:

Let the Triangle be named 'ABC'

In Triangle ABC,

∠A = x + 51

∠B = 80 (Intersecting lines, Vertically opposite Angles)

∠C = 60 (Intersecting lines, Vertically opposite Angles)

∠A + ∠B + ∠C = 180 (Sum of angles of Triangle = 180)

x + 51 + 80 + 60 = 180

=> x + 191 = 180

=> x = 180 - 191

=> x = -11

4 0

2 years ago

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Select the two values of x that are roots of this equation. x + 2x - 6 = 0

VLD [36.1K]

For this case we must solve the following quadratic equation:

$x ^ 2 + 2x-6 = 0$

Where:

$a = 1\\b = 2\\c = -6$

The solution is given by:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

Substituting:

$x = \frac {-2 \pm \sqrt {2 ^ 2-4 (1) (- 6)}} {2 (1)}\\x = \frac {-2 \pm \sqrt {4 + 24}} {2}\\x = \frac {-2 \pm \sqrt {28}} {2}\\x = \frac {-2 \pm \sqrt {2 ^ 2 * 7}} {2}\\x = \frac {-2 \pm2 \sqrt {7}} {2}\\x = -1 \pm \sqrt {7}$

Thus, we have two roots:

$x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}$

ANswer:

$x_ {1} = - 1+ \sqrt {7}\\x_ {2} = - 1- \sqrt {7}$

8 0

3 years ago

(find unit rate) Julio runs 18.6 miles in 3 hours

Romashka-Z-Leto [24]

You do 18.6 ÷ 3 and that equals 6.2

6 0

2 years ago

EAZY POINTS PLS ANSWER THIS ASAP

Elan Coil [88]

Answer:

Monthly payment would be $99.01

Total repayment would be $5,940.30

Interest payed would be $940.30

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers