19.07.2022

Arthur plants 4 basil plants in a square frame like the one shown. The soil in this frame will be 2x in. deep. Write a polynomial function V in standard form to represent the volume of soil in the frame in terms of x.

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11.02.2023, solved by verified expert
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Answer:

V = 18x^3 +48x^2 +(32 -8π)x cubic inches

Step-by-step explanation:

The volume of soil in the frame can be found by finding the volume of the rectangular prism created by the frame subtracting the volume of the pots.

The frame contains 4 pots of diameter 2 inches, so their total area is ...

  A = 4(πr^2) = 4(π(1 in)^2) = 4π in^2

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

  length: (3x +4) inches

  width: (3x +4) inches

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: 2x inches 

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

  V = (LW - 4π)(2x)

  V = ((3x +4)(3x +4) -4π)(2x) = (2x)(9x^2 +24x +16 -4π)

  V = 18x^3 +48x^2 +(32 -8π)x  cubic inches

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Mathematics
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
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
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

tip=18% of 75.45

     =18/100 * 75.45 = $13.581

Tip = $13.581

Mathematics
Step-by-step answer
P Answered by PhD

Cost before sale tax=$46.00

Cost after including tax=$48.76

Sale tax=$48.76-46.00

=$2.76

we know,

sale tax=((sales tax rate)/100) * cost before sale tax

2.76=((sales tax rate)/100) *46.00

sale tax rate=(2.76*100)/46

                   =276/46

                    =6%

There fore sales tax rate=6%

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