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Iteru [2.4K]
3 years ago
6

A sphere has a radius of 9 in. An artist creates a replica of the structure that has been scaled up by a factor of 1.5.

Mathematics
2 answers:
vesna_86 [32]3 years ago
7 0

Answer:

Step-by-step explanation:

V=4/3πr³

v = 1.33*3.142*9³

v = 3046.39in³

New scale = 3046.39*1.5

= 4,569.59in³

LuckyWell [14K]3 years ago
5 0

Answer:

V = 10,305.99 in^3

Step-by-step explanation:

A sphere has a radius of 9 in. An artist creates a replica of the structure that has been scaled up by a factor of 1.5.

What is the volume of the replica in cubic inches?

Since we are SCALING UP, the value we are given needs to be multiplied by the scale factor. So, 9 * 1.5 = 13.5. Now we can take the equation to solve for the volume of a circle : V = 4/3 * π * r^3  

And then we plug in our radius (13.5)

V = 4/3 * π * 13.5^3  = 10,305 in^3

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The coordinate will be (5, 12). Then the number of balloons that a group of 5 people pops will be 12.

<h3>What is coordinate geometry?</h3>

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Rami works at a carnival dart game where groups of people try to pop balloons taped to a wall by throwing darts.

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2 years ago
Question 2 of 10
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Answer:

4

Step-by-step explanation:

Since the base angles are the same, the side have to be the same

ML = MN

4x = x+3

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3x= 3

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3 years ago
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Katie solved the equation by completing the square. X2+12x−7=0 which equation shows one of the steps katie could have taken to c
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solution:

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3 years ago
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A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int
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Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}

By expanding the previous equation:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0

Since there is no accumulation within the tank, expression is simplified to this:

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The solution of this equation is:

c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})

The salt concentration after 8 minutes is:

c(8) = 0.166 \frac{pounds}{gallon}

The instantaneous amount of salt in the tank is:

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Answr:

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Step-by-step explanation:

Simplify both sides of the equation.

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1

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Step 2: Subtract 1/2 from both sides.

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−

1

2

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1

2

p=

−7

2

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