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4 years ago

11

Find the rate of change of the area of a square with respect to the length z , the diagonal of the square. what is the rate when

z=2?

1 answer:

Reil [10]4 years ago

4 0

The diagonal of a square is equal to the side x times square root of 2, xSqrt(2)
z = xSqrt(2), its rate of change is just Sqrt(2)

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A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

7 0

4 years ago

5. Select All equations that have a solution of 2"

Pachacha [2.7K]

Answer:

none of these have a solution of 2.

Step-by-step explanation:

4x+ 15 = 27

x=3

x + 6 =3

x = 3

2(x+5)=18

x = 4

x + 9 = 6

x = -3

if my understanding of what the equations are supposed to be please let me know what they are supposed to be, because with the way they are typed it is hard to tell :)

6 0

3 years ago

Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value

algol [13]

Answer:

Minimum value of function $C=x+10y$ is 63 occurs at point (3,6).

Step-by-step explanation:

To minimize :

$C=x+10y$

Subject to constraints:

$x\leq 3---(1)\\y\leq 9---(2)\\x+y\geq 9----(3)\\x\geq 0\\y\geq 0$

Eq (1) is in blue in figure attached and region satisfying (1) is on left of blue line

Eq (2) is in green in figure attached and region satisfying (2) is below the green line

Considering $x+y\geq 9$ , corresponding coordinates point to draw line are (0,9) and (9,0).

Eq (3) makes line in orange in figure attached and region satisfying (3) is above the orange line

Feasible region is in triangle ABC with common points A(0,9), B(3,9) and C(3,6)

Now calculate the value of function to be minimized at each of these points.

$C=x+10y$

at A(0,9)

$C=0+10(9)\\C=90$

at B(3,9)

$C=3+10(9)\\C=93$

at C(3,6)

$C=3+10(6)\\C=63$

Minimum value of function $C=x+10y$ is 63 occurs at point C (3,6).

3 0

3 years ago

The wholesale price for a chair is $124. A certain furniture store marks up the wholesale price by 16%. Find the price of the ch

vazorg [7]

Answer:$143.84Step-by-step explanation:Given the following question:Initial price of the chair was $124....Marked up 16% (which means the price has increased by 16%)Find the new price of the chair...In order to find the answer, we find 16% of a given number in till it equals 124 which was the initial price.16% of 143.84 is 124143.84 is already rounded to the nearest centWhich means the new price of the chair is "$143.84"

8 0

2 years ago

Read 2 more answers

What are all the square numbers in 100

Doss [256]

What does that question even meAn

8 0

3 years ago