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7 days ago

Sketch the region bounded by the curves y=3x3, x+y=4, and y=0. Find the coordinates of the centroid.

Mathematics

1 answer:

AnnZ [9K]6 days ago

5 0

The attached graph illustrates the region. The centroid's coordinates are (5/3, 1). The centroid's coordinates are determined by averaging the coordinates of the area; Oₓ = (Aₓ+Bₓ+Cₓ)/3 = (0+1+4)/3 = 5/3 and O(y) = (A(y) + B(y) + C(y)) = (0+3+0)/3=3/3=1.

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The graph of f(x) = 2x is shown on the grid. The graph of g(x) = ()x is the graph of f(x) = 2x reflected over the y-axis. Which

zzz [9066]

Response:

The graph in question is linked to g(x) = -2x, though it is not provided.

Detailed explanation:

A reflection across the y-axis changes the sign of the x-coordinate for every point. To derive the new function, we substitute x with -x:

g(x) = f(-x) = 2(-x) = -2x

This leads us to g(x) = -2x.

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20 days ago

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A storage pod has a rectangular floor that measures 19 feet by 13 feet and a flat ceiling that is 5 feet above the floor. Find t

Inessa [8989]

Answer:

Area= 247 feet²

Volume= 1235 feet³

Step-by-step explanation:

The storage pod features a rectangular base measuring 19 feet by 13 feet, with a flat ceiling height of 5 feet above.

Calculating the area of the floor yields: length multiplied by width

Length = 19 feet

Width = 13 feet

Area = 19*13

Area = 247 feet²

The volume of the pod can be found by multiplying the area by the height

Height of the pod = 5 feet

Area = 247 feet²

Volume = 247*5

Volume = 1235 feet³

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16 days ago

Elias’s teacher has given him a rectangle that is 15 feet by 20 feet. She has asked him to create a new rectangle using a scale

Inessa [8989]

No, as the fraction equates to a whole number. Thus, it would actually be an increase.

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11 days ago

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A low-strength children’s/adult chewable aspirin tablet contains 81 mg of aspirin per tablet. How many tablets may be prepared f

Svet_ta [9486]

Answer:

From 1 kg of aspirin, a total of 12,345 tablets can be produced.

Step-by-step explanation:

This query mentions that low-strength chewable aspirin tablets for children and adults contain 81 mg of aspirin each, asking how many tablets can be made from 1 kg of aspirin.

Considering the weight of a tablet measured in kg, we start by converting 81 mg to kg.

Each kg equals 1,000,000 mg. Hence

1 kg - 1,000,000 mg

x kg - 81 mg.

1,000,000x = 81

$x = \frac{81}{1,000,000}$

Therefore, x = 0.000081 kg.

Each tablet essentially contains 0.000081 kg of aspirin. To find out how many tablets this yields from 1 kg of aspirin:

1 tablet - 0.000081 kg

x tablets - 1 kg

0.000081x = 1

$x = \frac{1}{0.000081}$

Thus, x = 12,345 tablets.

Therefore, a total of 12,345 tablets can be manufactured from 1 kg of aspirin.

4 0

10 days ago

A cone is cut out of the center of a pyramid with a rectangular base. The rectangular base has side lengths of 15 and 10 units.

Svet_ta [9486]

Answer:

Volume of the shaded area = (600 - 36π) units³

Step-by-step explanation:

Volume of the shaded area = Volume of pyramid - Volume of cone

Volume of pyramid = ⅓*l*w*h

Where,

l = length of the base of the pyramid = 15 units

w = width of the base of the pyramid = 10 units

h = height of pyramid = 12 units

Substituting the values helps find the volume of the pyramid

Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³

Volume of Cone = ⅓πr²h,

Where,

r = radius = ½ of diameter = ½ of 9 = 3 units

h = height = 12 units

Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12

= π*3*12 = 36π units³

Volume of shaded area = (600 - 36π) units³

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5 days ago