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devlian [24]
2 years ago
7

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

Mathematics
1 answer:
marin [14]2 years ago
3 0

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)}

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A triangle has angles measuring 108 and 24 degrees. What is the measure of the third angle?
Novosadov [1.4K]
Since a triangle’s total degrees equals 180 you would do 180-108-24 and you would get 48° for your answer
5 0
2 years ago
Consider the quadratic function f(x)=2x^2-8x-10
Slav-nsk [51]

Answer:

f(x) = 2x² - 8x - 10.

This is a parabola open upward (since a>0) with an axis of symmetry = -b/2a:

a) axis of symmetry: x = -(-8)/(2*2) = 8/4 = 2. Then x = 2, which is the x component of the vertex

b) for x =  2, f(x) = f(2) = - 18 (component of y of the vertex)

c) VERTEX(2, - 18)

d) DISCRIMINENT: b² - 4.a.c = 64 - 4*2*(-10) = 144

Hope this helps! :)

6 0
3 years ago
Problem 5
ddd [48]

Answer:

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Step-by-step explanation:

it is on gole

3 0
2 years ago
10. Choose all fractions equivalent to 36/40 <br><br><br><br> A) 3/4 B) 9/10 C) 9/40 D) 18/20
Talja [164]

Answer:

B, D

Step-by-step explanation:

36/40 simplified is 9/10

9/10 x 2  = 18/20

I hope this helps!

5 0
2 years ago
Read 2 more answers
Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?
nalin [4]

Answer:

9 cm²

Step-by-step explanation:

Two wires are attached 6 feet up a tree and 3 feet from the base of the tree. About how much TOTAL wire was used?

We solve the above question, using the Area of a Triangle

Area = 1/2 × Base × Height

Area = 1/2 × 3 × 6

Area = 9 cm²

Therefore, the total wore that was used was 9cm² of wire

3 0
3 years ago
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