1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tester [92]
3 years ago
10

Solve the following question

Mathematics
1 answer:
White raven [17]3 years ago
3 0

Answer:

g) u^{4}\cdot v^{-1}\cdot z^{3}, h) \frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}

Step-by-step explanation:

We proceed to solve each equation by algebraic means:

g) \frac{u^{5}\cdot v}{z}\div  \frac{u\cdot v^{2}}{z^{4}}

1) \frac{u^{5}\cdot v}{z}\div  \frac{u\cdot v^{2}}{z^{4}} Given

2) \frac{\frac{u^{5}\cdot v}{z} }{\frac{u\cdot v^{2}}{z^{4}} } Definition of division

3) \frac{u^{5}\cdot v\cdot z^{4}}{u\cdot v^{2}\cdot z}   \frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}

4) \left(\frac{u^{5}}{u} \right)\cdot \left(\frac{v}{v^{2}} \right)\cdot \left(\frac{z^{4}}{z} \right)  Associative property

5) u^{4}\cdot v^{-1}\cdot z^{3}   \frac{a^{m}}{a^{n}} = a^{m-n}/Result

h) \frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}

1) \frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10} Given

2) \frac{\frac{x^{2}-16}{x^{2}-10\cdot x+25} }{\frac{3\cdot x - 12}{x^{2}-3\cdot x - 10} } Definition of division

3) \frac{(x^{2}-16)\cdot (x^{2}-3\cdot x -10)}{(x^{2}-10\cdot x + 25)\cdot (3\cdot x - 12)}  \frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}

4) \frac{(x+4)\cdot (x-4)\cdot (x-5)\cdot (x+2)}{3\cdot (x-5)^{2}\cdot (x-4) } Factorization/Distributive property

5) \left(\frac{1}{3} \right)\cdot (x+4)\cdot (x+2)\cdot \left(\frac{x-4}{x-4} \right)\cdot \left[\frac{x-5}{(x-5)^{2}} \right] Modulative and commutative properties/Associative property

6) \frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}  \frac{a^{m}}{a^{n}} = a^{m-n}/\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot c}{b\cdot d}/Definition of division/Result

You might be interested in
What is the slope-intercept equation for the line below?
Veronika [31]

Answer:

Answer is C

Step-by-step explanation:

8 0
3 years ago
Find two linearly independent power series solutions about the point x0 = 0 of
aksik [14]

Assume a solution of the form

y=\displaystyle\sum_{n\ge0}a_nx^n

with derivatives

y'=\displaystyle\sum_{n\ge0}(n+1)a_{n+1}x^n

y''=\displaystyle\sum_{n\ge0}(n+2)(n+1)a_{n+2}x^n

Substituting into the ODE, which appears to be

(x^2-4)y''+3xy'+y=0,

gives

\displaystyle\sum_{n\ge0}\bigg((n+2)(n+1)a_{n+2}x^{n+2}-4(n+2)(n+1)a_{n+2}x^n+3(n+1)a_{n+1}x^{n+1}+a_nx^n\bigg)=0

\displaystyle\sum_{n\ge2}n(n-1)a_nx^n-4\sum_{n\ge0}(n+2)(n+1)a_{n+2}x^n+3\sum_{n\ge1}na_nx^n+\sum_{n\g0}a_nx^n=0

(a_0-8a_2)+(4a_1-24a_3)x+\displaystyle\sum_{n\ge2}\bigg[(n+1)^2a_n-4(n+2)(n+1)a_{n+2}\bigg]x^n=0

which gives the recurrence for the coefficients a_n,

\begin{cases}a_0=a_0\\a_1=a_1\\4(n+2)a_{n+2}=(n+1)a_n&\text{for }n\ge0\end{cases}

There's dependency between coefficients that are 2 indices apart, so we consider 2 cases.

  • If n=2k, where k\ge0 is an integer, then

k=0\implies n=0\implies a_0=a_0

k=1\implies n=2\implies a_2=\dfrac1{4\cdot2}a_0=\dfrac2{4\cdot2^2}a_0=\dfrac{2!}{2^4}a_0

k=2\implies n=4\implies a_4=\dfrac3{4\cdot4}a_2=\dfrac3{4^2\cdot4\cdot2}a_0=\dfrac{4!}{2^8(2!)^2}a_0

k=3\implies n=6\implies a_6=\dfrac5{4\cdot6}a_4=\dfrac{5\cdot3}{4^3\cdot6\cdot4\cdot2}a_0=\dfrac{6!}{2^{12}(3!)^2}a_0

and so on, with the general pattern

a_{2k}=\dfrac{(2k)!}{2^{4k}(k!)^2}a_0

  • If n=2k+1, then

k=0\implies n=1\implies a_1=a_1

k=1\implies n=3\implies a_3=\dfrac2{4\cdot3}a_1=\dfrac{2^2}{2^2\cdot3\cdot2}a_1=\dfrac1{(3!)^2}a_1

k=2\implies n=5\implies a_5=\dfrac4{4\cdot5}a_3=\dfrac{4\cdot2}{4^2\cdot5\cdot3}a_1=\dfrac{(2!)^2}{5!}a_1

k=3\implies n=7\implies a_7=\dfrac6{4\cdot7}a_5=\dfrac{6\cdot4\cdot2}{4^3\cdot7\cdot5\cdot3}a_1=\dfrac{(3!)^2}{7!}a_1

and so on, with

a_{2k+1}=\dfrac{(k!)^2}{(2k+1)!}a_1

Then the two independent solutions to the ODE are

\boxed{y_1(x)=\displaystyle a_0\sum_{k\ge0}\frac{(2k)!}{2^{4k}(k!)^2}x^{2k}}

and

\boxed{y_2(x)=\displaystyle a_1\sum_{k\ge0}\frac{(k!)^2}{(2k+1)!}x^{2k+1}}

By the ratio test, both series converge for |x|, which also can be deduced from the fact that x=\pm2 are singular points for this ODE.

6 0
3 years ago
Find the product of 4/5 and 5/12 put in simplest form
kotegsom [21]

Hello!

The answer is 20/60 simplest form is 1/3

To get 20/60 you must multiply the Numerator by Numerator (4*5) and Denominator by Denominator (5*12). Your answer will be 20/60.

To get 1/3 you must simplify a number that can go into 20 and 60 (which is 10). Divide 20/10 and 60/10 and get 2/6. Simplify 2/6 by 2 and get 1/3.

3 0
3 years ago
Translating Algebraic Expressions
lord [1]

Answer:

1. \frac{4}{5} n+7

2. \frac{1}{3} (g+8)+3c

3. \frac{1}{6} m+9

Step-by-step explanation:

1. The word "of" means "to multiply" so it would be \frac{4}{5} *n which can also be written as \frac{4}{5} n then you plus 7

2. this would be 1/3 times in parenthesis, g+8, and then added to 3c

3. this would be 1/6 times m, then plus 9

6 0
4 years ago
What’s the correct answer ??
Artyom0805 [142]

Im finding it...

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • 800+150? please tell me
    14·2 answers
  • Which number is a factor of both 12 and 42?
    15·1 answer
  • I need help with this math problem
    14·1 answer
  • 13+7*12+9= How would I show my work and get the answer to this problem
    9·1 answer
  • What type of number is -1/3
    13·1 answer
  • Which is more economical: purchasing the economy size of a detergent at 7 kilograms for $7.15 or purchasing the regular size at
    12·2 answers
  • Whats the proper abbreviation for twenty-five micrograms
    15·1 answer
  • Find a number such that the sum of the number and its reciprocal is 68/8
    7·1 answer
  • If sin theta= 4/5 and theta is in quadrant 2, the value of cot theta is . if necessary, use the slash mark ( / ) for a fraction
    10·1 answer
  • Given that ​3x^2-3x+2 find each of the following. ​a) ​g(0) ​b) ​g(​) ​c) ​g(​) ​d) ​g(​x) ​e) ​g(1​t)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!