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Find all derivatives of y^n of the function y=√x+5

quester [9]

Hello,

As somebody has distroyed my question, (may be he have not understood ?)

i will reply to y=(√x)+5

$\displaystyle \boxed{\dfrac{d^n y}{dx^n} =(-1)^n*n!! *\dfrac{1}{2^n} *x^{-\frac{2n+1}{2} }\\}\\y'=\dfrac{1}{2} *x^{-\frac{1}{2}} \\\\y''=-\dfrac{1}{4} *x^{-\frac{3}{2}} \\...\\$

3 0

3 years ago

Work out the area of Triangle ABC

Tema [17]

The main idea is using the Pythagorean formula to find the length of line segment $DB$ .

Alr so you use the formula $A^2 + B^2 = C^2$

$C^2$ is already given and is $2\sqrt{5}$

and $A^2$ is $3\sqrt{2}$

So using algebraic rules you'll get $B$ as:

$\sqrt{2}$

Now using the formula: $\frac{1}{2} b * h$ , you can find the area of tri ABD and CBD which would be $3$ and $1$ so add them up and you get $4$ !

5 0

3 years ago

The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please

Hitman42 [59]

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

$S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx$

We let the substitution take place.

Therefore, we let $u = 1 + 4x^{2}$

Thus, $du = 8dx.$

So,

$xdx = \frac{1}{8}du$

Also, the interval of the integration changes to [ 37, 65]

Thus,

$S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx$

= $\frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} } }$

= 156.5 units²

8 0

3 years ago

Lina and Michael studied the data in the table. They each wrote an equation to represent the relationship between the number of

valkas [14]

Answer:

10 seconds ago The graph represents Jason's weight loss over 5 months. ... 49 seconds ago Lina and Michael studied the data in the table. They each wrote an equation to represent the relationship between the number of miles and the numbers. of hours ridden by each bicyclist. Data : Miles, m ; Hours, ...

1 answer

Step-by-step explanation:

7 0

3 years ago

Kwan's parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, thei

poizon [28]

A. First let us start with the linear model.

The equation is in the form of y = m x + b

Calculating for the slope m:

m = (309,587 – 50,000) / (2007 – 1997)

m = 25,958.7

Subsituting:

y = 25,958.7 x + b

Taking x = 1997, y = 50,000. Solve for b:

50,000 = 25,958.7 (1997) + b

b = -51,789,523.9

The complete equation is therefore:

y = 25,958.7 x - 51,789,523.9

B. The exponential model has the following form:

y = a b^x

where a and b are constants

Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587

50,000 = a b^1997

309,587 = a b^2007

Combining in terms of a:

50,000 / b^1997 = 309,587 / b^2007

b^2007 / b^1997 = 309,587 / 50,000

b^10 = 6.19174

b = 1.2

Substituting:

y = a 1.2^x

Solving for a:

50,000 = a 1.2^1997

a = 3.75 x 10^-154

The complete equation is:

y = 3.75 x 10^-154 * 1.2^x

3 0

4 years ago