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3 years ago

4 − 1 − 5h = 9(–2h + 9)

Mathematics

2 answers:

sergeinik [125]3 years ago

5 0

Answer:

$4 - 1 - 5h = 9( - 2h + 9) \\ 3 - 5h = - 18h + 81 \\ 18h - 5h = 81 - 3 \\ 13h = 78 \\h = \frac{78}{13} \\ \therefore \: h = 6$

Cerrena [4.2K]3 years ago

4 0

Answer:

Step-by-step explanation:

First, we'll need to remove the parentheses: 3 - 5h = -18h + 81.

Then, we will move the variable to the left-hand side and change its sign, giving us 3 - 5h + 18h = 81

Then we must collect like terms, giving us 13h = 81 - 3

Finally, to get our answer, we must divide both sides of the equation by 13, giving us the answer of 6.

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Please help me with the below question.

VMariaS [17]

By letting

$y = \displaystyle \sum_{n=0}^\infty c_n x^{n+r}$

we get derivatives

$y' = \displaystyle \sum_{n=0}^\infty (n+r) c_n x^{n+r-1}$

$y'' = \displaystyle \sum_{n=0}^\infty (n+r) (n+r-1) c_n x^{n+r-2}$

a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

$5r(r-1) c_0 x^{r-1} + \displaystyle \sum_{n=1}^\infty \bigg( (n+r+1) c_n + (n + r + 1) (5n + 5r + 1) c_{n+1} \bigg) x^{n+r} = 0$

Examine the lowest degree term $\left(x^{r-1}\right)$ , which gives rise to the indicial equation,

$5r (r - 1) + r = 0 \implies 5r^2 - 4r = r (5r - 4) = 0$

with roots at r = 0 and r = 4/5.

b) The recurrence for the coefficients $c_k$ is

$(k+r+1) c_k + (k + r + 1) (5k + 5r + 1) c_{k+1} = 0 \implies c_{k+1} = -\dfrac{c_k}{5k+5r+1}$

so that with r = 4/5, the coefficients are governed by

$c_{k+1} = -\dfrac{c_k}{5k+5} \implies \boxed{g(k) = -\dfrac1{5k+5}}$

c) Starting with $c_0=1$ , we find

$c_1 = -\dfrac{c_0}5 = -\dfrac15$

$c_2 = -\dfrac{c_1}{10} = \dfrac1{50}$

so that the first three terms of the solution are

$\displaystyle \sum_{n=0}^2 c_n x^{n + 4/5} = \boxed{x^{4/5} - \dfrac15 x^{9/5} + \frac1{50} x^{13/5}}$

4 0

2 years ago

N minus 6 divided by 3 equals negative 4

igor_vitrenko [27]

N=-6
-6 minus 6 is -12
-12 /3 is -4 since the negative doesn’t cancel out

5 0

3 years ago

Fundamental theorem of calculus<br> <img src="https://tex.z-dn.net/?f=g%28s%29%3D%5Cint%5Climits%5Es_6%20%7B%28t-t%5E4%29%5E6%7D

mr_godi [17]

Answer:

$\displaystyle g'(s) = (s-s^4)^6$

Step-by-step explanation:

The Fundamental Theorem of Calculus states that:
$\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)$

Where <em>a</em> is some constant.

We can let:
$\displaystyle g(t) = (t-t^4)^6$

By substitution:

$\displaystyle g(s) = \int_6^s g(t)\, dt$

Taking the derivative of both sides results in:
$\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]$

Hence, by the Fundamental Theorem:

$\displaystyle \begin{aligned} g'(s) & = g(s) \\ \\ & = (s-s^4)^6\end{aligned}$

3 0

2 years ago

What is the surface area of the regular pyramid given below?

VARVARA [1.3K]

Each trianglar side has an area: (1/2)*8*9=36
the base is a square with an area of 8*8=64
so the total surface area is 36+36+36+36+64=208

5 0

4 years ago

Read 2 more answers

Write a function g whose graph represents the indicated transformation of the graph of f(x)=x+2; translation 2 units right

miss Akunina [59]

The function g whose graph represents the indicated transformation of the graph of f(x)=x+2; translation 2 units right is g(x) = x

<h3>Translation of functions</h3>

Translation is a technique used to change the position of an image on an xy-plane. Given the function below;

f(x) = x +2

If the expression is translation 2 units to the right, the translation rule will be:

g(x) = f(x )- 2

Substitute

g(x) = x + 2 - 2

g(x) = x

Hence the function g whose graph represents the indicated transformation of the graph of f(x)=x+2; translation 2 units right is g(x) = x

Learn more on translation here: brainly.com/question/12861087
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2 years ago