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Nookie1986 [14]

2 years ago

10

Let f(x)=ln(3x)+2.5 .

2 answers:

Cerrena [4.2K]2 years ago

5 0

For this case what we should do is evaluate the function in each of the points from 2 to 7 and then find the average.
We have then:
f (x) = ln (3x) +2.5.
f (2) = ln (3 * 2) + 2.5 = 4.291759469
f (3) = ln (3 * 3) + 2.5 = 4.697224577
f (4) = ln (3 * 4) + 2.5 = 4.98490665
f (5) = ln (3 * 5) + 2.5 = 5.208050201
f (6) = ln (3 * 6) + 2.5 = 5.390371758
f (7) = ln (3 * 7) + 2.5 = 5.544522438
Then the average is:
Average = (4.291759469 + 4.697224577 + 4.98490665 + 5.208050201 + 5.390371758 + 5.544522438) / (6) = 5.019472516
nearest hundredth
5.02
Answer:
the average rate of change of f (x) from 2 to 7 is 5.02

ANTONII [103]2 years ago

4 0

Answer:

The answer is 0.25 I just took the quiz.

Step-by-step explanation:

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Step-by-step explanation:

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Equation: -5 3/4- 3 1/2 Please help meh.

vampirchik [111]

Answer:

$-9\frac{1}{4}$

Step-by-step explanation:

$-5\frac{3}{4}-3\frac{1}{2}$

Step 1: Factor out the common term $-1$

$=-\left(5\frac{3}{4}+3\frac{1}{2}\right)$

Step 2: Add the whole numbers

$5 + 3 = 8$

Step 3: Combine the fractions:

$\frac{3}{4}+\frac{1}{2} = \frac{5}{4}\\\\=-\left(8+\frac{5}{4}\right)$

Step 4: Convert the improper fractions to mixed numbers

$\frac{5}{4} = 1\frac{1}{4}\\\\=-\left(8+1\frac{1}{4}\right)$

Step 5: Add the numbers

$8 + 1 =9 \\\\=-9\frac{1}{4}$

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Read 2 more answers

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

Yuri [45]

Let the curve C be the intersection of the cylinder

$16x^2+y^2=16$

and the plane

$x+y+z=1$

The projection of C on to the x-y plane is the ellipse

$16x^2+y^2=16$

To see clearly that this is an ellipse, le us divide through by 16, to get

$\frac{x^2}{1}+ \frac{y^2}{16}=1$

or

$\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1$ ,

We can write the following parametric equations,

$x=cos(t), y=4sin(t)$

for

$0\le t \le 2\pi$

Since C lies on the plane,

$x+y+z=1$

it must satisfy its equation.

Let us make z the subject first,

$z=1-x-y$

This implies that,

$z=1-sin(t)-4cos(t)$

We can now write the vector equation of C, to obtain,

$r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))$

The length of the curve of the intersection of the cylinder and the plane is now given by,

$\int\limits^{2\pi}_0 {|r'(t)|} \, dt$

But

$r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))$

$|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}$

$\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184$

Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

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