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3 years ago

15

The coordinate grid shows the plot of four equations. a coordinate plane is shown with four lines graphed. line a crosses the x

axis at negative 3.5 and the y axis at 7. line b crosses the x axis at 6.5 and the y axis at 4.5. line c is horizontal and crosses the y axis at 1. line d crosses the x axis at 0.5 and the y axis at 1.which set of equations has (−1, 5) as its solution? a and b b and d a and c b and c

2 answers:

hammer [34]3 years ago

8 0

Its A & B

NOT B and D

Digiron [165]3 years ago

6 0

Answer:

A and b is corrects

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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

andrey2020 [161]

Answer:

The maximum value is 1/27 and the minimum value is 0.

Step-by-step explanation:

Note that the given function is equal to $(xyz)^2$ then it means that it is positive i.e $f(x,y,z)\geq 0$ .

Consider the function $F(x,y,z,\lambda)=x^2y^2z^2-\lambda (x^2+y^2+z^2-1)$

We want that the gradient of this function is equal to zero. That is (the calculations in between are omitted)

$\frac{\partial F}{\partial x} = 2x(y^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial y} = 2y(x^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial z} = 2z(x^2y^2 - \lambda)=0$

$\frac{\partial F}{\partial \lambda} = (x^2+y^2+z^2-1)=0$

Note that the last equation is our restriction. The restriction guarantees us that at least one of the variables is non-zero. We've got 3 options, either 1, 2 or none of them are zero.

If any of them is zero, we have that the value of the original function is 0. We just need to check that there exists a value for lambda.

Suppose that x is zero. Then, from the second and third equation we have that

$-2y\lambda = -2z\lambda$ . If lambda is not zero, then y =z. But, since $-2y\lambda=0$ and lambda is not zero, this implies that x=y=z=0 which is not possible. This proofs that if one of the variables is 0, then lambda is zero. So, having one or two variables equal to zero are feasible solutions for the problem.

Suppose that only x is zero, then we have the solution set $y^2+z^2=1$ .

If both x,y are zero, then we have the solution set $z^2=1$ . We can find the different solution sets by choosing the variables that are set to zero.

NOw, suppose that none of the variables are zero.

From the first and second equation we have that

$\lambda = y^2z^2 = x^2z^2$ which implies $x^2=y^2$

Also, from the first and third equation we have that

$\lambda = y^2z^2 = x^2y^2$ which implies $x^2=z^2$

So, in this case, replacing this in the restriction we have $3z^2=1$ , which gives as another solution set. On this set, we have $x^2=y^2=z^2=\frac{1}{3}$ . Over this solution set, we have that the value of our function is $\frac{1}{3^3}= \frac{1}{27}$

4 0

2 years ago

Which polynomial is in standard form?

Elina [12.6K]

the

first equation is the answer of this question.

explanation

where the xy is in sequence so it is the standard form of polynomial

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1 year ago

The drawing below shows the dimensions of skims kite what is the area of Kim's kite

Leno4ka [110]

Answer:

48 square inches

Step-by-step explanation:

Given

See attachment for kite

Required

The area of the kite

The given kite has a triangular shape.

So, the area is:

$Area = 0.5 * base * height$

From the attachment

$base = 12in$

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So:

$Area = 0.5 * 12in* 8in$

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2 years ago

If profit is represented by a polynomial function, and the function is graphed, what do the x - Intercept represent to the reade

Ludmilka [50]

Answer:

Breakeven quantity

Step-by-step explanation:

x intercepts are basically where there's no profit and no loss.

Revenue = cost

Which is also called the break even point

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2 years ago

Find the measure of one interior angle for the following regular polygon

shusha [124]

Answer:

Step-by-step explanation:

I am assuming that by "interior" angle you do not mean the central angle.

This is a 10-sided polygon, a decagon. That means that there are 10 triangles that can extend from the center, with their sides being equal to the radii of the decagon. If we extract one of these triangles we can find what the interior angle is. The vertex angle measures 360/10 which is 36.

Split this triangle in half from the vertex to the base, creating a right triangle. The vertex angle is also split in half, making this angle (the vertex angle is the one at the top of the triangle) 18 degrees. We already know that one angle inside this right triangle is 90 (definition of a right triangle) and to find the other one, we apply the Triangle Angle-Sum Theorem:

180 - 18 - 90 = 72 degrees. That is the measure of the base angle that is NOT the right angle, obviously.

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2 years ago