Find the value of the expression 4a^4-2b^2+40 when a = 2 and b=7

If 2x2 + y2 = 17 then evaluate the second derivative of y with respect to x when x = 2 and y = 3. Round your answer to 2 decimal

Vera_Pavlovna [14]

Answer:

y''=-1.26

Step-by-step explanation:

We are given that $2x^2+y^2=17$

We have evaluate the second order derivative of y w.r.t. x when x=2 and y=3.

Differentiate w.r.t x

Then , we get

$4x+2yy'=0$

$2x+yy'=0$

$yy'=-2x$

$y'=-\frac{2x}{y}$

Again differentiate w.r.t.x

Then , we get

$2+(y')^2+yy''=0$ $(u\cdot v)'=u'v+v'u)$

$2+(y')^2+yy''=0$

Using value of y'

$yy''=-2-(-\frac{2x}{y})^2$

$y''=-\frac{2+(-\frac{2x}{y})^2}{y}$

Substitute x=2 and y=3

Then, we get $y''=-\frac{2+(\frac{4}{3})^2}{3}$

$y''=-\frac{18+16}{9\times 3}=-\frac{34}{27}$

Hence,y''=-1.26

6 0

4 years ago

Write the rule for the linear function. Remember a function rule is written using f(x)

Marina CMI [18]

Answer:

The rule for the linear function will be:

$f(x) = -2x+5$

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear

Taking two points from the table to determine the slope

(1, 3)

(2, 1)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(1,\:3\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)$

$m=\frac{1-3}{2-1}$

$m=-2$

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (1, 3)

$y-y_1=m\left(x-x_1\right)$

$y - 3 = -2 (x-1)$

$y-3 = -2x+2$

adding 3 to both sides

$y-3+3 = -2x+2+3$

$y = -2x+5$

or

$f(x) = -2x+5$

Therefore, the rule for the linear function will be:

$f(x) = -2x+5$

4 0

3 years ago

Need help as fast as possible please I will mark BRAINLIST only for correct answers :) Thank you!

zavuch27 [327]

Answer:

a

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the simplified form of the expression -2(-5x - 8)?

Deffense [45]

Answer: 10x+16

Step-by-step explanation:

Use the distributive property a(b+c)= ab+ac

so

-2(-5x-8) = (-2 * -5x) - (-2* -8)

=

10x-(-16)

=10x+16

Hope this helped!

3 0

3 years ago

The price of a

RideAnS [48]

Answer:

$31.5

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers