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3 years ago

Large cheese pizzas cost $5 each and large one-topping pizzas cost $6 each.

Mathematics

1 answer:

dsp733 years ago

8 0

Answer:

$T=5c+6d$

Step-by-step explanation:

The correct question is

Large cheese pizzas cost $5 each and large one-topping pizzas cost $6 each.

Write an equation that represents the total cost, T, of c large cheese pizzas and d large one-topping pizzas.

Let

T -----> the total cost

c ----> the number of large cheese pizzas

d ---> the number of large one -topping pizzas

we know that

The total cost (T) is equal to the number of large cheese pizzas (c) multiplied by it cost ($5) plus the number of large one -topping pizzas (d) multiplied by it cost ($6)

$T=5c+6d$

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A spherical balloon currently has a radius of 19cm. If the radius is still growing at a rate of 5cm or minute, at what rate is a

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Answer:

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Step-by-step explanation:

Given:

Radius of the balloon at a certain time (r) = 19 cm

Rate of growth of radius is, $\frac{dr}{dt}=5\ cm/min$

The rate at which the air is pumped in the balloon can be calculated by finding the rate of increase in the volume of the balloon.

So, first we find the volume of the sphere in terms of 'r'. As the balloon is spherical in shape, the volume of the balloon is equal to the volume of a sphere. Therefore,

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Now, rate of increase of volume is obtained by differentiating both sides of the equation with respect to time 't'.

Differentiating both sides with respect to time 't', we get:

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Now, plug in 19 cm for 'r', 5 cm per minute for $\frac{dr}{dt}$ and solve for $\frac{dV}{dt}$ . This gives,

$\frac{dV}{dt}=4\pi (19 cm)^2(5\ cm/min)\\\\\frac{dV}{dt}=4\times 3.14\times 361\times 5\ cm^3/min\\\\\frac{dV}{dt}=22670.8\ cm^3/min$

Therefore, the rate at which the air is being pumped into the balloon is 22670.8 cm³/min.

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