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3 years ago

Find the length and width of a rectangle with maximum area that has a perimeter of 9P units.

Mathematics

1 answer:

scoundrel [369]3 years ago

4 0

Answer:

l = 9p/4 , l = 9p/4

Step-by-step explanation:

Given:

Perimeter = 9p

Find:

Length and width

Computation:

Assume;

Length = l

Perimeter = 2(l+b)

9p/2 = l+w

w = 9p/2 - l

Area = lb

Area = l(9p/2 - l)

Using differentiation

l = 9p/4

w = 9p/2 - l

w = 9p/2 - 9p/4

w = 9p/4

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2 years ago

Read 2 more answers

Find equation of set of points pieces that its distance from the point 3, 4, -5 and -2, 1, 4 are equal.

Gnesinka [82]

Answer:

Step-by-step explanation:

Suppose we a point $P(x,y,z)$ such that its distance from either the point $A(3,4,-5)$ or $B(-2,1,4)$ is the same.

Using this information we can formula:

distance AP = distance BP

first, let's find the distance from AP, using the distance formula.

$r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}$

$AP = \sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2}$

similarly, we can find the distance BP

$BP = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

since both distances are exactly the same we can equate them

$AP = BP$

$\sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2} = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}$

we can simplify it a bit squaring both sides, and getting rid of the subscripts.

$(3 - x)^2 + (4 - y)^2 + (-5 - z)^2 = (-2 - x)^2 + (1 - y)^2 + (4 - z)^2$

what we have done here is formulated an equation which consists of any point P that will have the same distance from (3,4,-5) and (-2,1,4).

To put it more concretely,

This is the equation of the the plane from that consists of all points (P) from which the distance from both (3,4,-5) and (-2,1,4) are equal.

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3 years ago