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2 years ago

Complete the solution of the equation. Find the value of y when x equals 24. -2x + 2y = -56

Mathematics

1 answer:

bixtya [17]2 years ago

5 0

Answer:

Step-by-step explanation:

$Put\ x=24\ to\ the\ equation\ -2x+2y=-56,\ and\ solve\ it\ for\ y:\\\\-2(24)+2y=-56\\\\-48+2y=-56\qquad\text{add 48 to both sides}\\\\-48+48+2y=-56+48\\\\2y=-8\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}=\dfrac{-8}{2}\\\\y=-4$

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Now, lets evaluate the same integral using power series. first, find the power series for the function f(x = \frac{32}{x^2+4}. t

BlackZzzverrR [31]

No idea what the previous part of the problem is, but you have

$f(x)=\dfrac{32}{x^2+4}=\dfrac8{1-\left(-\frac{x^2}4\right)}=\displaystyle8\sum_{n\ge0}\left(-\frac{x^2}4\right)^n$
$f(x)=\displaystyle8\sum_{n\ge0}\left(-\dfrac14\right)^nx^{2n}$

which is valid for $\left|-\dfrac{x^2}4\right|$ , or $|x|$ . So the integral from 0 to 2 is

$\displaystyle\int_0^2f(x)\,\mathrm dx=\int_0^28\sum_{n\ge0}\left(-\frac14\right)^nx^{2n}\,\mathrm dx$
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\int_0^2x^{2n}\,\mathrm dx$

Note that since the power series only converges on the interval if $x$ is strictly less than 2, which means we have to treat this as an improper integral.

$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\int_0^tx^{2n}\,\mathrm dx$ [/tex]
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\frac{x^{2n+1}}{2n+1}\bigg|_{x=0}^{x=t}$
$=\displaystyle8\sum_{n\ge0}\frac{(-1)^n}{2^{2n}(2n+1)}\lim_{t\to2^-}t^{2n+1}$
$=\displaystyle16\sum_{n\ge0}\frac{(-1)^n}{2n+1}$
$=16-\dfrac{16}3+\dfrac{16}5-\dfrac{16}7+\dfrac{16}9+\cdots$

6 0

2 years ago

Identify the place value of digit 9 in each given number.

Ostrovityanka [42]

Step-by-step explanation:

1) Thousands

2) 100 thousands

3) tens

5 0

3 years ago

0.10 x 37.7 explain please

kodGreya [7K]

Answer: The answer is 3.77.

Explanation: Since 0.10 is 10 times smaller than 1, we know that if we divide 37.7 by 10, we will get the same answer as 0.10 x 37.7.

5 0

2 years ago

John and Andrew have £3.40 between them. John has £1.20 more than Andrew. John has £u and Andrew £v

Dahasolnce [82]

In the given question, there are several information's of immense importance and they can be used to find the necessary answers. It is already given that John and Andrew have 3.40 pound together. It is also given that John has 1.20 pound more than Andrew. It is also assumed that John has"u" pound and Andrew has "v" pounds.
Then we can write the two equations as
u + v = 3.40
u = v + 1.20
To find the values of u and v, we can replace the u in the first equation with the value of u in the second equation. Then
u + v = 3.40
(v + 1.20) + v = 3.40
2v + 1.20 = 3.40
2v = 3.40 - 1.20
2v = 2.2
v = 2.2/2
= 1.1
Now we replace the value of v in the first equation to find the value of u.
u + v = 3.40
u + 1.1 = 3.40
u = 3.40 - 1.1
u = 2.3

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3 years ago

(3m±4/5n)2<br>solve this question<br>

sukhopar [10]

Answer:

(3m-4/5)2

Final result :

(15m - 4)2

——————————

Step by step solution :

Step 1 :

Simplify —

Equation at the end of step 1 :

(3m - —)2

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 5 as the denominator :

3m 3m • 5

3m = —— = ——————

1 5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3m • 5 - (4) 15m - 4

———————————— = ———————

5 5

Equation at the end of step 2 :

(15m - 4)

(—————————)2

Step 3 :

Final result :

(15m - 4)2

———

Step-by-step explanation:

5 0

2 years ago