4x+x+6=11x-6x+6 what is the value for x

Find f. f ″(x) = x^−2, x > 0, f(1) = 0, f(6) = 0

marin [14]

If you do in fact mean $f(1)=f(6)=0$ (as opposed to one of these being the derivative of $f$ at some point), then integrating twice gives

$f''(x) = -\dfrac1{x^2}$

$f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1$

$f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2$

From the initial conditions, we find

$f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0$

$f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)$

Eliminating $C_2$ , we get

$(C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))$

$-5C_1 = \ln(6)$

$C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)$

Then

$\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}$

3 0

2 years ago

What is the formula of LSD in a cuboid?

7nadin3 [17]

Answer: The volume of a cuboid is given by the formula V = LWH, and the surface area of a cuboid is given by the formula SA = 2lh + 2wh + 2lw where l = length, w = width, and h = height.

And i was just learning this a few days back lol

8 0

4 years ago

8 - (7/10)t = 6 - (1/5)t

rosijanka [135]

Answer:

t = 4

Step-by-step explanation:

Solve for t:

8 - (7 t)/10 = 6 - t/5

Hint: | Put the fractions in 8 - (7 t)/10 over a common denominator.

Put each term in 8 - (7 t)/10 over the common denominator 10: 8 - (7 t)/10 = 80/10 - (7 t)/10:

80/10 - (7 t)/10 = 6 - t/5

Hint: | Combine 80/10 - (7 t)/10 into a single fraction.

80/10 - (7 t)/10 = (80 - 7 t)/10:

1/10 (80 - 7 t) = 6 - t/5

Hint: | Put the fractions in 6 - t/5 over a common denominator.

Put each term in 6 - t/5 over the common denominator 5: 6 - t/5 = 30/5 - t/5:

(80 - 7 t)/10 = 30/5 - t/5

Hint: | Combine 30/5 - t/5 into a single fraction.

30/5 - t/5 = (30 - t)/5:

(80 - 7 t)/10 = (30 - t)/5

Hint: | Make (80 - 7 t)/10 = (30 - t)/5 simpler by multiplying both sides by a constant.

Multiply both sides by 10:

(10 (80 - 7 t))/10 = (10 (30 - t))/5

Hint: | Cancel common terms in the numerator and denominator of (10 (80 - 7 t))/10.

(10 (80 - 7 t))/10 = 10/10×(80 - 7 t) = 80 - 7 t:

80 - 7 t = (10 (30 - t))/5

Hint: | In (10 (30 - t))/5, divide 10 in the numerator by 5 in the denominator.

10/5 = (5×2)/5 = 2:

80 - 7 t = 2 (30 - t)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

80 - 7 t = 60 - 2 t

Hint: | Move terms with t to the left hand side.

Add 2 t to both sides:

2 t - 7 t + 80 = (2 t - 2 t) + 60

Hint: | Look for the difference of two identical terms.

2 t - 2 t = 0:

2 t - 7 t + 80 = 60

Hint: | Group like terms in 2 t - 7 t + 80.

Grouping like terms, 2 t - 7 t + 80 = 80 + (2 t - 7 t):

80 + (2 t - 7 t) = 60

Hint: | Combine like terms in 2 t - 7 t.

2 t - 7 t = -5 t:

-5 t + 80 = 60

Hint: | Isolate terms with t to the left hand side.

Subtract 80 from both sides:

(80 - 80) - 5 t = 60 - 80

Hint: | Look for the difference of two identical terms.

80 - 80 = 0:

-5 t = 60 - 80

Hint: | Evaluate 60 - 80.

60 - 80 = -20:

-5 t = -20

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -5 t = -20 by -5:

(-5 t)/(-5) = (-20)/(-5)

Hint: | Any nonzero number divided by itself is one.

(-5)/(-5) = 1:

t = (-20)/(-5)

Hint: | Reduce (-20)/(-5) to lowest terms. Start by finding the GCD of -20 and -5.

The gcd of -20 and -5 is -5, so (-20)/(-5) = (-5×4)/(-5×1) = (-5)/(-5)×4 = 4:

Answer: t = 4

6 0

3 years ago

9(x + 3) = 108 what does 9x equal and i need major help on how to do this in genral

Andreas93 [3]

9(x + 3) = 108

First distribute the 9 to everything inside the parenthesis by multiplying them.
9x + 27 = 108

Now subtract 27 from both sides

9x + 27 (-27) = 108 (-27)

9x = 81

divide 9 from both sides

9x/9 = 81/9

x = 9

9x = 81

hope this helps

6 0

3 years ago

Read 2 more answers

Circumference involves u its or squate units

kodGreya [7K]

Circumference has the answer in square units.

5 0

4 years ago