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3 years ago

How to find the slope of a graph

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

5 0

Answer:

There are 2 different ways, depending on the amount of data given;

1st way: When only the line on the graph is given (Without any coordinate points given) then the slope could be found out with the formula of Rise/Run, or Change in y / Change in x

2nd way: When a line and 2 coordinate points are given, the the formula that would be used is: $\frac{Y_2 - Y_1}{X_2 - X_1}$ , where X₁ and Y₁ are the coordinate points of the 1st given point, and X₂ and Y₂ are the coordinate points of the 2nd given point.

Hope this helps!

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Consider the multivariable function f\left(x,y,z\right)=\frac{x^3-2.5y^2+\frac{z}{2}}{z\left(x-y\right)}f ( x , y , z ) = x 3 −

Lelu [443]

Answer:

$f\left(2,3,1\right)=\bold{14}$

Step-by-step explanation:

Given the function:

$f\left(x,y,z\right)=\frac{x^3-2.5y^2+\frac{z}{2}}{z\left(x-y\right)}$

To find:

The value of $f(2, 3, 1)$ = ?

Solution:

$f(2, 3, 1)$ means the values of $x, y\ and\ z$ as:

$x=2\\y=3\\z=1$

Let us put the given values in the given function and let us solve for it:

$\Rightarrow f\left(2,3,1\right)=\dfrac{2^3-2.5\times 3^2+\frac{1}{2}}{1\left(2-3\right)}\\\\\Rightarrow f\left(2,3,1\right)=\dfrac{8-2.5\times 9+0.5}{1\left(-1\right)}\\\\\Rightarrow f\left(2,3,1\right)=\dfrac{8-22.5+0.5}{-1}\\\\\Rightarrow f\left(2,3,1\right)=\dfrac{-14}{-1}\\\\\Rightarrow f\left(2,3,1\right)=\bold{14}$

Therefore, the answer is:

$f\left(2,3,1\right)=\bold{14}$

8 0

3 years ago

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values

Vesnalui [34]

The Lagrangian is

$L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)$

with critical points where the partial derivatives vanish.

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$

$L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda$

$L_\lambda=x^2+y^2-9=0$

Substitute $x,y$ into the last equation and solve for $\lambda$ :

$\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6$

Then we get two critical points,

$(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)$

We get an absolute maximum of $3\sqrt{17}\approx12.369$ at the second point, and an absolute minimum of $-3\sqrt{17}\approx-12.369$ at the first point.

4 0

3 years ago

Trevor has $9100 in an investment account. He withdrew all of his money from the account. He spent $1100 on a plane ticket to Pa

Ilya [14]

Answer:

$6,400

Step-by-step explanation:

9100-1100

8000

8000×1/5

$1600

8000-1600

$6,400

3 0

3 years ago

What is the sum of the measures of the interior angles of a 15-sided polygon?

AlladinOne [14]

Answer:

B. 2340

Step-by-step explanation:

Interior angles of a polygon is given by

(n – 2)180 where n is the number of sides

(15-2) *180

13*180

2340

3 0

4 years ago

A regular polygon has sides all the same length, and angles all the same measure. Find the pelmeter of the regular polygon below

Ede4ka [16]

The perimeter of the regular polygon is 70 inches

<h3>How to determine the perimeter of the regular polygon?</h3>

The sides of the regular polygon is given as:

Side = 10 in

The regular polygon has 7 sides

So, the perimeter of the polygon is calculated as:

P = Side lengths * Number of sides

This gives

P = 10 inches * 7

Evaluate

P = 70 inches

Hence, the perimeter of the regular polygon is 70 inches