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alex41 [277]
2 years ago
8

Hi Help me with question 6b) pls

Mathematics
1 answer:
Romashka-Z-Leto [24]2 years ago
5 0

Answer:

k = 9

Step-by-step explanation:

Consider the pattern on the right side , that is

T_{k} = k(k + 2) + 1 = k² + 2k + 1

Equating

k² + 2k + 1 = 100 ( subtract 100 from both sides )

k² + 2k - 99 = 0 ← in standard form

(k + 11)(k - 9) = 0 ← in factored form

Equate each factor to zero and solve for k

k + 11 = 0 ⇒ k = - 11

k - 9 = 0 ⇒ k = 9

But k > 0 , then k = 9

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Integrate 1 - x / x(x2 + 1) d x by partial fractions.
solniwko [45]

Answer:

log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x

Step-by-step explanation:

step 1:-   by using partial fractions

[tex]\frac{1-x}{x(x^{2}+1) } =\frac{A(x^{2}+1)+(Bx+C)(x }{x(x^{2}+1) }......(1)

<u>step 2:-</u>

solving on both sides

1-x=A(x^{2} +1)+(Bx+C)x......(2)

substitute x =0 value in equation (2)

1=A(1)+0

<u>A=1</u>

comparing x^2 co-efficient on both sides (in equation 2)

0 = A+B

0 = 1+B

B=-1

comparing x co-efficient on both sides (in equation 2)

<u>-</u>1  =  C

<u>step 3:-</u>

substitute A,B,C values in equation (1)

now  

\\\int\limits^ {} \, \frac{1-x}{x(x^{2}+1) } d x =\int\limits^ {} \frac{1}{x} d x +\int\limits^ {} \frac{-x}{x^{2}+1 }  d x -\int\limits \frac{1}{x^{2}+1 }  d x

by using integration formulas

i)  by using \int\limits \frac{1}{x}   d x =log x+c........(a)\\\int\limits \frac{f^{1}(x) }{f(x)} d x= log(f(x)+c\\.....(b)

\int\limits tan^{-1}x  dx =\frac{1}{1+x^{2} } +C.....(c)

<u>step 4:-</u>

by using above integration formulas (a,b,and c)

we get answer is

log x-\frac{log(x^{2}+1) }{2}-tan^{-1} x

6 0
3 years ago
What is the solution to the linear equation?
patriot [66]
Equation:  2/5 + p = 4/5 + 3/5p

Simplify Both Sides:
p + 2/5 = 3/5p + 4/5

Subtract 3/5p from both sides:
p + 2/5 - 3/5p = 3/5p + 4/5 - 3/5p

2/5p + 2/5 = 4/5

Subtract 2/5 from both sides:
2/5p + 2/5 - 2/5 = 4/5 - 2/5

2/5p = 2/5

Multiply both sides by 5/2

(5/2) * (2/5p) = (5/2) * (2/5)

p  =  1


Answer:  p  =  1





Hope that helps!!! (Answer:   Letter Choice (A),  p  =  1







8 0
3 years ago
10. Express the following as a single fraction.<br> x-1 +x+2 + x<br>2<br>5<br>4<br>​
Margaret [11]

Answer:

x+x+x=3x

2-1=1

3x+1

this is ansver

3 0
3 years ago
Bella wants to know how long her dog is. She measure its body and finds that it is 54 cm long. Then she measures the tail and fi
Nady [450]

Answer:

88 cm

Step-by-step explanation:

body to tail = length of body + length of tail

body to tail = 54 cm + 34 cm

body to tail = 88 cm

7 0
2 years ago
You have a handful of dimes and quarters that totals 26 coins and is worth $5.15. How many of each do you have?
borishaifa [10]

Answer:

9 dimes and 17 quarters

Step-by-step explanation:

9+17=26 coins

9 dimes = 90 cents

17 = 425 cents

90+425= 515 cents or $5.15

Hope this helps! :)

5 0
3 years ago
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