Mathematics : asked on sierravick123owr441

16.01.2022

Arthur wants to make a raised rectangular frame, shown below, to grow basil plants. The basil plants are transplanted, with their soil, from 2-in.-wide pots into the frame. The diagram at the right below shows a top-down view of the frame. Each circle represents a transplanted basil plant with its soil. Arthur will add more soil to the frame until the soil is 3x in. deep.

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Mathematics

Arthur wants to make a raised rectangular frame, shown below, to grow basil plants. The basil plants are transplanted, with their soil, from 2-in.-wide pots into the frame. The diagram at the right below shows a top-down view of the frame. Each circle represents a transplanted basil plant with its soil. Arthur will add more soil to the frame until the soil is 3x in. deep. A cuboid with a height of 3x inches. A rectangle with six circles of two inches diameter placed at equal distance in two rows consisting of three circles each. The distance between

Step-by-step answer

P Answered by PhD

9514 1404 393

V = 36x^3 +102x^2 +(72 -18π)x cubic inches

Step-by-step explanation:

The frame contains 6 pots of diameter 2 inches, so their total area is ...

A = 6(πr^2) = 6(π(1 in)^2) = 6π in^2

The dimensions of the frame, in inches are ...

length: 4x +6

width: 3x +4

The area of the pots will subtract from the area of the frame to give the area covered by soil. The other dimension of the frame is ...

height: 3x

So the volume of soil in the frame is ...

V = (LW - 6π)(3x)

V = ((4x +6)(3x +4) -6π)(3x) = 3x(12x^2 +34x +24 -6π)

V = 36x^3 +102x^2 +(72 -18π)x . . . . cubic inches

Arthur wants to make a raised rectangular frame, shown below, to grow basil plants. The basil plants

Mathematics

Step-by-step answer

P Answered by PhD

9514 1404 393

V = 36x^3 +102x^2 +(72 -18π)x cubic inches

Step-by-step explanation:

The frame contains 6 pots of diameter 2 inches, so their total area is ...

A = 6(πr^2) = 6(π(1 in)^2) = 6π in^2

The dimensions of the frame, in inches are ...

length: 4x +6

width: 3x +4

The area of the pots will subtract from the area of the frame to give the area covered by soil. The other dimension of the frame is ...

height: 3x

So the volume of soil in the frame is ...

V = (LW - 6π)(3x)

V = ((4x +6)(3x +4) -6π)(3x) = 3x(12x^2 +34x +24 -6π)

V = 36x^3 +102x^2 +(72 -18π)x . . . . cubic inches

Mathematics

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Step-by-step answer

P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics

Deanna gets 3 problems incorrect on a math quiz. Her score is 85%. How many questions are on the quiz?

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P Answered by PhD

The answer is in the image

Mathematics

Anthony received $150 for his birthday this year. This was $10 less than half the amount he received last year. How much money did Anthony receive for his birthday last year?

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P Answered by PhD

The answer is in the image

Mathematics

A new school randomly assigns a six-character student code to every prospective student. The school uses the characters 1, 2, 3, 4, 5, X, Y, and Z. If none of the student codes contain a repeated character, what is the total number of codes that can be randomly assigned?

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The total nom of code that can be used is equal to 5+3 = 8

Mathematics

In a parking lot, for every 8 cars there are 7 trucks. What is the ratio of cars to trucks? A)7 : 8 B)8 : 7 C)8 : 15 D)15 : 8

Step-by-step answer

P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics

The ratio of tables to chairs at the furniture store is 1:6. There are 30 chairs. How many tables are there?

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P Answered by PhD

The solution is in the following image

Mathematics

A 4300-N force from a car s engines produces an acceleration of 3.3 m/s2. What is the mass of the car? A. 4300 kg B. 1300 kg C. 14,000 kg D. 390 kg

Step-by-step answer

P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

=4300/3.3

=1303.03kg

Mathematics

A 4300-N force from a car s engines produces an acceleration of 3.3 m/s2. What is the mass of the car? A. 4300 kg B. 1300 kg C. 14,000 kg D. 390 kg

Step-by-step answer

P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

=4300/3.3

=1303.03kg

Approximately it is aqual to 1300kg

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