09.04.2023

Select the smaller of the two given numbers.
-|19|, -|12|

. 1

Step-by-step answer

24.06.2023, solved by verified expert
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-|12|

Step-by-step explanation:

|19| is 19, -|19| is -19

|12| is 12, -|12| is -12

-12>-19

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Mathematics
Step-by-step answer
P Answered by PhD

-|12|

Step-by-step explanation:

|19| is 19, -|19| is -19

|12| is 12, -|12| is -12

-12>-19

Mathematics
Step-by-step answer
P Answered by PhD

Surface area: 1216

Volume: 4608

Step-by-step explanation:

Scale factor: 5:8

This means that the dimensions of the larger figure are 8/5 of those in the smaller figure.

Surface area:

The surface area is found multiplying the square of the change(8/5) by the original surface area(475). So

S = (\frac{8}{5})^2 \times 475 = \frac{64}{25} \times 475 = 64 \times 19 = 1216

Volume:

The volume is found multiplying the cube of the change(8/5) by the original volume(1125). So

S = (\frac{8}{5})^3 \times 1125 = \frac{512}{125} \times 1125 = 512 \times 9 = 4608

Mathematics
Step-by-step answer
P Answered by PhD

Surface area: 500

Volume: 5500

Step-by-step explanation:

Scale factor: 2:5

This means that the dimensions of the larger figure are 5/2 of those in the smaller figure.

Surface area:

The surface area is found multiplying the square of the change(5/2) by the original surface area(80). So

S = (\frac{5}{2})^2 \times 80 = \frac{25}{4} \times 80 = 25 \times 20 = 500

Volume:

The volume is found multiplying the cube of the change(5/2) by the original volume(352). So

S = (\frac{5}{2})^3 \times 352= \frac{125}{8} \times 352 = 125 \times 44 = 5500

Mathematics
Step-by-step answer
P Answered by PhD

Surface area: 250

Volume: 1375

Step-by-step explanation:

Scale factor: 4:5

This means that the dimensions of the larger figure are 5/4 of those in the smaller figure.

Surface area:

The surface area is found multiplying the square of the change(5/4) by the original surface area(160). So

S = (\frac{5}{4})^2 \times 160 = \frac{25}{16} \times 160 = 25 \times 10 = 250

Volume:

The volume is found multiplying the cube of the change(5/4) by the original volume(704). So

S = (\frac{5}{4})^3 \times 704 = \frac{125}{64} \times 704 = 125 \times 11 = 1375

Mathematics
Step-by-step answer
P Answered by PhD

Surface area: 500

Volume: 5500

Step-by-step explanation:

Scale factor: 2:5

This means that the dimensions of the larger figure are 5/2 of those in the smaller figure.

Surface area:

The surface area is found multiplying the square of the change(5/2) by the original surface area(80). So

S = (\frac{5}{2})^2 \times 80 = \frac{25}{4} \times 80 = 25 \times 20 = 500

Volume:

The volume is found multiplying the cube of the change(5/2) by the original volume(352). So

S = (\frac{5}{2})^3 \times 352= \frac{125}{8} \times 352 = 125 \times 44 = 5500

Physics
Step-by-step answer
P Answered by PhD

1. The two forces of a 3rd law pair always act on different bodies.

TRUE

SO above statement is TRUE because Newton's III law is valid for two different objects where one object will exert force and other body will exert reaction force on it.

2. Part F Given that two bodies interact via some force, the accelerations of these two bodies have the same magnitude but opposite directions. (Assume no other forces act on either body.)

FALSE

This is false because the force of action and Reaction is same on two different objects but for finding acceleration we need to divide the force by mass of two objects and since the mass of two bodies may be different so we can say that acceleration may be different.

3. Part G According to Newton's 3rd law, the force on the (smaller) moon due to the (larger) earth is

(i) greater in magnitude and antiparallel to the force on the earth due to the moon.

(ii) greater in magnitude and parallel to the force on the earth due to the moon.

(iii) equal in magnitude but antiparallel to the force on the earth due to the moon.

(iv) equal in magnitude and parallel to the force on the earth due to the moon.

(v) smaller in magnitude and antiparallel to the force on the earth due to the moon.

(vi) smaller in magnitude and parallel to the force on the earth due to the moon.

Since Earth and moon is an isolated system so here Newton's III law is valid due to which we can say that two forces are equal in magnitude but opposite in sign

so correct answer will be

equal in magnitude but antiparallel to the force on the earth due to the moon.

Physics
Step-by-step answer
P Answered by PhD

1. The two forces of a 3rd law pair always act on different bodies.

TRUE

SO above statement is TRUE because Newton's III law is valid for two different objects where one object will exert force and other body will exert reaction force on it.

2. Part F Given that two bodies interact via some force, the accelerations of these two bodies have the same magnitude but opposite directions. (Assume no other forces act on either body.)

FALSE

This is false because the force of action and Reaction is same on two different objects but for finding acceleration we need to divide the force by mass of two objects and since the mass of two bodies may be different so we can say that acceleration may be different.

3. Part G According to Newton's 3rd law, the force on the (smaller) moon due to the (larger) earth is

(i) greater in magnitude and antiparallel to the force on the earth due to the moon.

(ii) greater in magnitude and parallel to the force on the earth due to the moon.

(iii) equal in magnitude but antiparallel to the force on the earth due to the moon.

(iv) equal in magnitude and parallel to the force on the earth due to the moon.

(v) smaller in magnitude and antiparallel to the force on the earth due to the moon.

(vi) smaller in magnitude and parallel to the force on the earth due to the moon.

Since Earth and moon is an isolated system so here Newton's III law is valid due to which we can say that two forces are equal in magnitude but opposite in sign

so correct answer will be

equal in magnitude but antiparallel to the force on the earth due to the moon.

Mathematics
Step-by-step answer
P Answered by Master

Note: The first file attached contains the clear and complete question

a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7

A(t) has a local maximum at t=7

A(t) has a local minimum at t=1

b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74

D(t) has a local maximum at t=1.59

D(t) has a local minimum at t=7.74

c) A(t) = (-t^3) + 8(t^2) -21t + 40

d) The water level in vat A is rising most rapidly at t = 4 hrs

e) 138 gallons

f) 18 gallons per hour

g) 98 gallons

Step-by-step explanation:

For clarity and easiness of expression, the calculations are handwritten and attached as files below.

Each step is neatly expressed and solutions to each part of the question are clearly written


Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat

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