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2 years ago

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Two numbers whose sum is 44 and whose product is a maximum

1 answer:

Mashcka [7]2 years ago

4 0

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x) Remove the brackets

Max = 44x - x^2 Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x ) Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.

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Solve the system of equations below by graphing. x^2-2x+y-3=0 x2+y=0 What is the solution rounded to the nearest hundredth? (–2.

Olin [163]

Answer:

$(-1.5,-2.25)$

Step-by-step explanation:

The first function is $x^2-2x+y-3=0$ .

We make y the subject of this function to obtain,

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

This is graph will open downwards because $a=-1\:$ .

At y-intercept of this graph, $x=0$ .

$\Rightarrow y=3+2(0)-(0)^2$

$\Rightarrow y=3$

The y-intercept is $(0,3)$ .

At x-intercept $y=0$ .

$0=3+2x-x^2$

$0=(x+1)(x-3)$

$\Rightarrow x=-1,x=3$ .

The x-intercepts are,

$(-1,0),(3,0)$

Also the vertex form of the function is,

$y=-(x-1)^2+4$ .

Therefore the vertex of the parabola is $(1,4)$ .

We plot all the points obtained and draw a smooth curve to obtain the curve as show in the diagram.

The second function is

$x^2+y=0$

$\Rightarrow y=-x^2$

This is the graph of the basic quadratic function $y=x^2$ that has been turned upside down.

This graph also has the vertex,y-intercept and x-intercept all at $(0,0)$ .

We now graph this too on the same graph sheet as the first one to obtain the blue graph as shown in the diagram.

These two graphs intersect at the point, $(-1.5,-2.25)$ .

Therefore the correct answer is B

3 0

3 years ago

A football is kicked toward an end zone with an initial vertical velocity of 30 ft/s. The function h(t) = -16+ 30t models the he

Ulleksa [173]

Answer:

A. The football does not reach a height of 15ft

Step-by-step explanation:

Given

$h(t) = -16t^2 + 30t$

Required

Determine which of the options is true

The option illustrates the height reached by the ball.

To solve this, we make use of maximum of a function

For a function f(x)

Such that:

$f(x) = ax^2 + bx + c$ :

$f(\frac{-b}{2a}) = maximum/minimum$

i.e we first solve for $\frac{-b}{2a}$

Then substitute $\frac{-b}{2a}$ for x in $f(x) = ax^2 + bx + c$

In our case:

First we need to solve $\frac{-b}{2a}$

Then substitute $\frac{-b}{2a}$ for t in $h(t) = -16t^2 + 30t$

By comparison:

$b = 30$

$c = -16$

$\frac{-b}{2a} = \frac{-30}{2 * -16}$

$\frac{-b}{2a} = \frac{-30}{-32}$

$\frac{-b}{2a} = \frac{30}{32}$

$\frac{-b}{2a} = \frac{15}{16}$

Substitute $\frac{15}{16}$ for t in $h(t) = -16t^2 + 30t$

$h(\frac{15}{16}) = -16(\frac{15}{16})^2 + 30(\frac{15}{16})$

$h(\frac{15}{16}) = -16(\frac{225}{256}) + \frac{450}{16}$

$h(\frac{15}{16}) = -(\frac{225}{16}) + \frac{450}{16}$

$h(\frac{15}{16}) = \frac{-225 + 450}{16}$

$h(\frac{15}{16}) = \frac{225}{16}$

$h(\frac{15}{16}) = 14.0625$

This implies that the maximum height reached is 14.0625ft.

So, the option that answers the question is A because $14.0625 < 15$

8 0

2 years ago

Please help..thank you

iVinArrow [24]

Answer:

D

Step-by-step explanation:

To shift down:

F(x)-b

To shift up:

F(x)+b

To shift right:

F(x-b)

To shift left:

F(x+b)

7 0

3 years ago

Read 2 more answers

Use to model the problem draw the block to show your work

natulia [17]

First of all be more spusific in your question

3 0

2 years ago

Graph x^2+60x+256in^2

Softa [21]

Answer:

44

Step-by-step explanation:

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8 0

3 years ago