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3 years ago

Find two positive numbers whose product is 36 and whose sum is a minimum.

1 answer:

8 0

Let one of the numbers be x. The other number cab then be represented as 36-x (x+36-x = 36).
The product can then be represented as y = x(36-x) or y=36x-x2

The maximum or minimum is always on the axis of symmetry which has the formula x=-b/2a.
In our case, the axis of symmetry is -36/-2, so x=18.

If one number is 18 and the 2 numbers add to 36, the other number is 18 as well.
So the 2 numbers are 18 and 18 and the maximum product is 324,

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tigry1 [53]

Answer:

2.5 second

Step-by-step explanation:

The equation is missing in the question.

The equation is, $h=-8t^2+40t$ , where 'h' is the height and 't' is time measured in second.

Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :

$\frac{dh}{dt} =0$

Now the differentiating the equation with respect to time t, we get

$\frac{dh}{dt}=\frac{d}{dt}(-8t^2+40t)$

$\frac{dh}{dt}=-16t+40$

For maximum height, $\frac{dh}{dt} =0$

So, $-16t+40=0$

$\Rightarrow 16t=40$

$\Rightarrow t=\frac{40}{16}$

$\Rightarrrow t = 2.5$

Therefore, the ball takes 2.5 seconds time to reach the maximum height.

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3 years ago

Can you solve question #36

Sonja [21]

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3 years ago

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Which triangle is a right triangle?

iren [92.7K]

Answer:

A right triangle is always 90 degrees.

Step-by-step explanation:

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3 years ago

A company is manufacturing an open-top rectangular box. They have 30 cm by 16 cm sheets of material. The bins are made by cuttin

Natalija [7]

Answer:

a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm

Step-by-step explanation:

a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.

b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.

So, dV/dx = 0

d(30 - 2x)(16 - 2x)x/dx = 0

-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0

32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0

4x²- 120x + 450 = 0

x²- 30x + 112.5 = 0

Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,

$x = \frac{-(-30)+/-\sqrt{(-30)^{2} - 4 X 1 X 112.5} }{2 X 1} \\= \frac{30+/-\sqrt{900 - 450} }{2}\\ = \frac{30+/-\sqrt{450} }{2}\\ = \frac{30+/-21.21 }{2}\\\\ = \frac{30+21.21 }{2} or \frac{30-21.21 }{2}\\ = \frac{51.21 }{2} or \frac{8.79}{2}\\ = 25.605 or 4.395$

x ≅ 25.61 or 4.4

V = (30 - 2x)(16 - 2x)x

Substituting the values of x into L and B, we have )x

L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22

B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22

Since L and B cannot be negative, we use the other value for x = 4.4, So

L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2

B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2

So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³

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3 years ago

The figure above shows a square inscribed in a rectangle.

slava [35]

Step-by-step explanation:

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