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3 years ago

Given f(x) = x - 7 and g(x) = x2. Find g(14))

Mathematics

2 answers:

Alex17521 [72]3 years ago

4 0

Answer:

196

Step-by-step explanation:

g(x) = x^2

Let x = 14

g(14) = 14^2

= 196

Free_Kalibri [48]3 years ago

4 0

Answer: 196

Step-by-step explanation:

F(x)= x-7

G(x)= x2

Find g(14)

G(x)= g(14)

Therefore x=14

Substitute for x in g(x)

G(14)= (14)^2

G(14)= 14×14

G(14)= 196

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y=4/5x+5

Step-by-step explanation:

because this is the answer

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guse lagrange multipliers to find the maximum or minimum values of the function subject to the given constraint. (if an answer d

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Therefore the maximum value of function f(x,y,z)= $x^{2} y^{2} z^{2}$ =1/27

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<h3>What is function?</h3>

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable) (the dependent variable) (the dependent variable). Mathematics uses functions frequently, and functions are essential for specifying physical relationships in the sciences.

Here,

The function is given as:

f(x,y,z)= $x^{2} y^{2} z^{2}$

$x^{2} +y^{2}+ z^{2}$ =1

=> $x^{2} +y^{2}+ z^{2}$ -1=0

Using Lagrange multiplies, we have:

L(x,y,z,λ)=f(x,y,z) +λ(0)

Substitute f(x,y,z)= $x^{2} y^{2} z^{2}$ and $x^{2} +y^{2}+ z^{2}$ -1=0

Differentiate

L(x)= $2xy^{2} z^{2}$ +2λx

L(y)= $2yx^{2} z^{2}$ +2λy

L(z)= $2zx^{2} y^{2}$ +2λz

L(λ)= $x^{2} +y^{2}+ z^{2}$ -1

Equating to 0

$2xy^{2} z^{2}$ +2λx =0

$2yx^{2} z^{2}$ +2λy = 0

$2zx^{2} y^{2}$ +2λz = 0

$x^{2} +y^{2}+ z^{2}$ -1 = 0

Factorize the above expressions

$2xy^{2} z^{2}$ +2λx =0

2x( $y^{2} z^{2}$ +λ)=0

2x=0 and ( $y^{2} z^{2}$ +λ)=0

x=0 and $y^{2} z^{2}$ = -λ

$2yx^{2} z^{2}$ +2λy = 0

2y( $x^{2} z^{2}$ +λ)=0

2y=0 and ( $x^{2} z^{2}$ +λ)=0

y=0 and $x^{2} z^{2}$ = -λ

$2zx^{2} y^{2}$ +2λz = 0

2z( $y^{2} x^{2}$ +λ)=0

2z=0 and ( $x^{2} y^{2}$ +λ)=0

z=0 and $x^{2} y^{2}$ = -λ

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x=0 and $y^{2} z^{2}$ = -λ

y=0 and $x^{2} z^{2}$ = -λ

z=0 and $x^{2} y^{2}$ = -λ

The above expression becomes

x=y=z=0

This means that,

$x^{2} +y^{2}+ z^{2}$ =1

$x^{2} +x^{2}+ x^{2} =1 \\3x^{2 } =1$

x= ±1/ $\sqrt{3}$

So,

y= ±1/ $\sqrt{3}$

z= ±1/ $\sqrt{3}$

The critic points are

x=y=z=±1/ $\sqrt{3}$

x=y=z=0

Therefore the maximum value of function f(x,y,z)= $x^{2} y^{2} z^{2}$ =1/27

And the minimum value is 0

To know more about function , visit

brainly.com/question/12426369

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1 year ago

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Answer:

#1) y = -4x + 1; #2) parallel; #3) y = -1/2x + 5/2; #4) y = 2x + 4; #5) Never

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y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6

Lines that are parallel have the same slope; this means we want a line through (1, -3) with a slope of -4. Using point-slope form,

$y-y_1=m(x-x_1)\\\\y--3=-4(x-1)\\\\y+3=-4(x)-4(-1)\\\\y+3=-4x+4\\\\y+3-3=-4x+4-3\\\\y=-4x+1$

#2) We must first write our second equation in slope-intercept form by isolating the y term:

2x+y=7

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2x+y-2x = 7-2x

y = -2x+7

This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2. To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2. Using point-slope form,

$y-0=\frac{-1}{2}(x-5)\\\\y=\frac{-1}{2}(x)+\frac{-1}{2}(-5)\\\\y=\frac{-1}{2}x+\frac{5}{2}$

#4) The slope of Main Street on the diagram, found by using rise/run, is 2. This means the bike path will also have a slope of 2 in order to be parallel. The park entrance is at (0, 4). This makes the equation y = 2x+4.

#5) Two lines with the same slope are always parallel. They are never perpendicular.

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