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2 years ago

What is the slope of the line that contains these points? х 5 6 7 8

Mathematics

1 answer:

marysya [2.9K]2 years ago

5 0

Answer:

-6/5

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ]. Use two of the given points to solve.

-6-6/-5-5

12/-10

-6/5

Got it off the internet hope it helps 8)

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A student was asked to find the equation of the tangent plane to the surface z=x3−y4 at the point (x,y)=(1,3). The student's ans

aliya0001 [1]

Answer:

C) The partial derivatives were not evaluated a the point.

D) The answer is not a linear function.

The correct equation for the tangent plane is $z = 241 + 3 x - 108 y$ or $3x-108y-z+241 = 0$

Step-by-step explanation:

The equation of the tangent plane to a surface given by the function $S=f(x, y)$ in a given point $(x_0, y_0, z_0)$ can be obtained using:

$z-z_0=f_x(x_0,y_0,z_0)(x-x_0)+f_y(x_0,y_0, z_0)(y-y_0)$ (1)

where $f_x(x_0, y_0, z_0)$ and $f_y(x_0, y_0, z_0)$ are the partial derivatives of $f(x,y)$ with respect to $x$ and $y$ respectively and evaluated at the point $(x_0, y_0, z_0)$ .

Therefore we need to find two missing inputs in our problem in order to use equation (1). The $z_0$ coordinate and the partial derivatives $f_x(x_0, y_0, z_0)$ and $f_y(x_0, y_0, z_0)$ . For $z_0$ just evaluating in the given function we obtain $z_0= -80$ and the partial derivatives are:

$\frac{\partial f(x,y)}{\partial x} \equiv f_x(x, y)= 3x^2 \\f_x(x_0, y_0) = f_x(1, 3) = 3$

$\frac{\partial f(x,y)}{\partial y} \equiv f_y(x, y)= -4y^3 \\f_y(x_0, y_0) = f_y(1, 3) = -108$

Now, substituting in (1)

$z-z_0=f_x(x_0,y_0,z_0)(x-x_0)+f_y(x_0,y_0, z_0)(y-y_0)\\z + 80 = 3x^2(x-1) - 4y^3(y-3)\\z = -80 + 3x^2(x-1) - 4y^3(y-3)$

Notice that until this point, we obtain the same equation as the student, however, we have not evaluated the partial derivatives and therefore this is not the equation of the plane and this is not a linear function because it contains the terms ( $x^3$ and $y^4$ )

For finding the right equation of the tangent plane, let's substitute the values of the partial derivatives evaluated at the given point:

$z = -80 + 3x^2(x-1) - 4y^3(y-3)\\z = -80 +3(x-1)-108(y-3)\\z = 241 + 3 x - 108 y$

or $3x-108y-z+241 = 0$

7 0

3 years ago

6(2y - 1) - 4y i need the algebraic expression

Marina CMI [18]

6(2y - 1) - 4y simplified is 8y-6

5 0

4 years ago

Read 2 more answers

A bus and a truck leave a gas station at the same time and are headed to the same destination. If the bus traveled 300 miles in

Andrej [43]

<h3>answer </h3>

they will reach at the same time.

Step-by-step explanation:

first we need to find out total Miles covered by bus and truck per hour,

so,

300÷6=50 miles per hour

200÷4=50 miles per hour

so they both will reach at the same time.

hope this will help you

thanx a lot

6 0

3 years ago

Determime whether each of the following is a prime or composite number

mr_godi [17]

Hi! Since prime numbers only have 1 and themselves as factors, 101 would be prime. 123 has factors of 1,3,41,123, so it would classify as a composite number. I hope this helps!:)

5 0

3 years ago

Thesumoftwopositivenumbersis16.whatisthesmallest possible value of the sum of their squares?

anygoal [31]

X+y=16
the sum of the squares is
x^2+y^2=sum

solve for y in first equation
x+y=16
y=16-x
subsitiute that for y in other equation

x^2+(16-x)^2=sum
x^2+x^2-32x+256=sum
2x^2-32x+256=sum
take derivitive to find the minimum value (or just find the vertex because the parabola opens up)
derivitive is
4x-32=derivitve of sum
the max/min is where the derivitive equals 0
4x-32=0
4x=32
x=8

at x=8
so then y=16-8=8

the smallest value then is 8^2+8^2=64+64=128

5 0

4 years ago