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3 years ago

Estimate V120 to the nearest integer.

Mathematics

1 answer:

mote1985 [20]3 years ago

4 0

Answer:

Step-by-step explanation:

We want to estimate

$\sqrt{120}$

to the nearest integer

Recall that

$\sqrt{121} = 11$

and

$\sqrt{100} = 10$

Since

$\sqrt{120}$

is closer to √121 so the √120 to the nearest integer is 11.

Using calculator, we have

$\sqrt{120} = 10.95445$

We round to the nearest integer to get

$\sqrt{120} \approx11$

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Jude says that the volume of a square pyramid with base edges of 7 in and a height of 7 in is equal to the volume of a cylinder

irakobra [83]

Answer:

Jude is not correct

Step-by-step explanation:

The volume of a square pyramid is given as:

$V = a^2\frac{h}{3}$

where a = base edge and h = height

Hence, the volume of the square pyramid with base edge of 7 in and height of 7 in is:

$V = 7^2*\frac{7}{3}$

V = $114.3 in^3$ ≅ $114 in^3$

The volume of a cylinder is given as:

$V = \pi r^2h$

where r = radius and h = height

Hence, the volume of a cylinder with radius of 7 in and height of 7 in is:

$V = \pi *7^2*7$

V = $1077.57 in^3$ ≅ $1078 in^3$

Since their volumes are not equal, Jude is not correct.

8 0

4 years ago

A rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn that is $400$

Degger [83]

Let us list out the given information:

Cost per foot = $5

Total fencing cost = $1200

Let L be the length of the barn that will maximize the area of the pasture and W be the width of the rectangular cow pasture.

From the given information, we need to do the fencing for three sides covering 1 L and 2 W's because other L will be the fourth side is part of the side of a barn. We need to write the equation based on the cost information.

If cost/foot is $5, then cost of length ' L ' will be 5L dollars and cost of '2W' width equals 10W dollars. Total cost is $1200. We can set up second equation as

5L + 10W = 1200. This can be simplified by dividing throughout the equation by 5 to get L+ 2W= 240. Solving for L we get L = 240 - 2W

Area of a rectangle is given by A = L ×W.

Substituting 240 - 2W for L we get the area function as..

A=(240 - 2W)×W= 240W-2W²

A = -2W²+240W.

When we have a function of the form f(x) = ax^2 + bx + c, then maximum value of the function can be obtained for x = -b/2a. Using that idea we can find the maximum area.

Here in the area function a = -2 and b = 240

For W = -b/2a = -240/2(-2) = -240/-4 = 60 feet, we get maximum area.

The question is asking us to find Length. We can substitute W = 60 in the equation L = 240 - 2W to find the Length.

L = 240 - 2(60) = 240 - 120 = 120 feet.

Conclusion: The length of the side parallel to the barn that will maximize the area of the pasture is 120 feet.

Note: Here the information 400 feet in the sentence "the fourth side is part of the side of a barn that is 400 feet long" given to distract us, we might not require that information to find the Length.