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3 years ago

Find the volume 12 poir 2.2 cm

Mathematics

1 answer:

Tanzania [10]3 years ago

6 0

Answer: 26.4
To find the volume u multiply 12x2.2=26.4

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Given f(x) = (lnx)^3 find the line tangent to f at x = 3

kirill [66]

Explanation

We must the tangent line at x = 3 of the function:

$f(x)=(\ln x)^3.$

The tangent line is given by:

$y=m*(x-h)+k.$

Where:

• m is the slope of the tangent line of f(x) at x = h,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

$f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.$

2) By evaluating the result of f'(x) at x = h = 3, we get:

$m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.$

3) The value of k is:

$k=f(3)=(\ln3)^3$

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

$y=(\ln3)^2*(x-3)+(\ln3)^3.$

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

$y=(\ln3)^2*(x-3)+(\ln3)^3$

6 0

1 year ago

Combine Like Terms: 3(p+5) - 8 + 11p

kykrilka [37]

Answer:

14p+7

Step-by-step explanation:

Distribute

3p+15-8+11p

6 0

4 years ago

Read 2 more answers

Which of these numbers has the least value? A. 3,213,213 B. 7.8 x 10 C. 6.3 x 10 D. 11,014,114

Mumz [18]

The correct answer is C. 6.3 x 10.

3 0

3 years ago

Read 2 more answers

Please see attachment

Dafna11 [192]

Answer:

a) The value of absolute minimum value = - 0.3536

b) which is attained at $x = \frac{1}{\sqrt{2} }$

Step-by-step explanation:

Step(i):-

Given function

$f(x) = \frac{-x}{2x^{2} +1}$ ...(i)

Differentiating equation (i) with respective to 'x'

$f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2} }$ ...(ii)

$f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} }$

Equating Zero

$f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0$

$\frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0$

$2 x^{2}-1 = 0$

$2 x^{2} = 1$

$x^{2} = \frac{1}{2}$

$x = \frac{-1}{\sqrt{2} } , x = \frac{1}{\sqrt{2} }$

Step(ii):-

Again Differentiating equation (ii) with respective to 'x'

$f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4} }$

put

$x = \frac{1}{\sqrt{2} }$

$f^{ll} (x) > 0$

The absolute minimum value at $x = \frac{1}{\sqrt{2} }$

Step(iii):-

The value of absolute minimum value

$f(x) = \frac{-x}{2x^{2} +1}$

$f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}$

on calculation we get

The value of absolute minimum value = - 0.3536

Final answer:-

a) The value of absolute minimum value = - 0.3536

b) which is attained at $x = \frac{1}{\sqrt{2} }$

3 0

3 years ago

Write an expression the represents the statement "Add 9 and 3, then multiply by 6"

ELEN [110]

Answer:

6(9+3)

Explanation:

Add 9 and 3 which is 9 + 3

THEN multiply by 6 which is 6(9 + 3)

I put parentheses because it's sayings to add first and then multiply!

3 0

2 years ago