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3 years ago

If the ratio between the radii of the two spheres is 3:7, what is the ratio of their volumes?

1 answer:

4 0

Given that the dilation factor or scale factor between the two spheres is equal to 3:7, the ratio between their volumes is calculated by cubing the numbers in the ratio. That is,
3³:7³
This operation will give us an answer of 27:343

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kondor19780726 [428]

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3 years ago

If angle symbol1 and angle symbol2 are complementary angles and if the measure of angle symbol1 is 5454degrees° more than the me

Misha Larkins [42]

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3 years ago

The profits in hundreds of dollars, P(c), that a company can make from a product is modeled by a function of the price, c, they

Jobisdone [24]

The maximum profit is the y-coordinate of the vertex of the parabola represented by the equation.

$P(c)=-20c^2+320c+5120 \\ \\
a=-20 \\
b=320 \\ \\
\hbox{the vertex } (h,k): \\
h=\frac{-b}{2a}=\frac{-320}{2 \times (-20)}=\frac{-320}{-40}=8 \\
k=f(h)=f(8)=-20 \times 8^2+320 \times 8+5120= \\
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The maximum value is 6400, but the profit is given in hundreds of dollars, so multiply the value by 100.

The maximum profit the company can make is $640,000.

4 0

3 years ago

Read 2 more answers

The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485. For each decrease in unit p

ANTONII [103]

Answer:

Demand Equation: q = 15125 - 25p.

Supply Equation: 80p - 24000 = 9q.

Equilibrium Price: $525.

Equilibrium Quantity: 2000 units.

Step-by-step explanation:

To solve this question, first, the demand equation has to be calculated. Let price be on the y-axis and quantity by on the x-axis. It is given that p = $485 when q = 3000 units. This can also be written as (q₁, p₁) = (3000, 485). It is also given that when the price goes down by $20, the quantity increases by 500 units. Therefore, (q₂, p₂) = (3500, 465). Due to the statement "For each decrease in unit price of $20 below $485, the quantity demanded increases by 500 units", the demand function will be linear i.e. a straight line. This is because the word "for each" has been used. Therefore, finding the equation of the demand function:

(p - p₁)/(q - q₁) = (q₂ - q₁)/(p₂ - p₁).

(p - 485)/(q - 3000) = (465 - 485)/(3500 - 3000).

(p - 485)/(q - 3000) = (-20)/(500).

(p - 485)/(q - 3000) = -1/25.

25*(p - 485) = -1*(q - 3000).

25p - 12125 = -q + 3000.

25p + q = 15125.

q = 15125 - 25p. (Demand Equation).

Second, find the supply equation. It is given that the suppliers will not sell the product below or at the price of $300. Therefore, (q₁, p₁) = (0, 300). Also, the suppliers will sell 2000 units if the price is $525. Therefore, (q₂, p₂) = (2000, 525). Since it is mentioned that supply equation is linear, therefore:

(p - p₁)/(q - q₁) = (q₂ - q₁)/(p₂ - p₁).

(p - 300)/(q - 0) = (525 - 300)/(2000 - 0).

(p - 300)/(q) = (225)/(2000).

(p - 300)/(q) = 9/80.

80*(p - 300) = 9*(q).

80p - 24000 = 9q. (Supply Equation).

Equilibrium exists when demand = supply. This means that the demand and the supply equations have to be solved simultaneously. Therefore, put demand equation in supply equation:

80p - 24000 = 9(15125 - 25p).

80p - 24000 = 136125 - 225p.

305p = 160125.

p = $525.

Put p = $525 in demand equation:

q = 15125 - 25p.

q = 15125 - 25(525).

q = 15125 - 13125.

q = 2000 units.

To summarize:

Demand Equation: q = 15125 - 25p!!!

Supply Equation: 80p - 24000 = 9q!!!

Equilibrium Price: $525!!!

Equilibrium Quantity: 2000 units!!!

8 0

3 years ago