Function 1 is defined by the equation p=r + 7.

Mathematics

2 answers:

Vadim26 [7]3 years ago

8 0

Answer:

Step-by-step explanation:

MariettaO [177]3 years ago

4 0

Answer:

Function 2

Step-by-step explanation:

Function 1 has a slope of 1.

Function 2 has a slope of 1.1.

1.1 > 1, so Function 2 has a greater slope.

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Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is i

Romashka-Z-Leto [24]

0.08 cm/min

Step-by-step explanation:

Given:

$\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}$

Find $\frac{dr}{dt}$ when diameter D = 20 cm.

We know that the volume of a sphere is given by

$V = \dfrac{4\pi}{3}r^3$

Taking the time derivative of V, we get

$\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}$

Solving for $\frac{dr}{dt}$ , we get

$\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})$

$\:\:\:\:\:\:\:= 0.08\:\text{cm/min}$

3 0

3 years ago

1) Last Tuesday, Regal Cinemas sold a total of 85 movie tickets. Ticket sales totaled

irakobra [83]

In this question, some of the data is missing so its a complete question and the solution can be defined as follows:

$\bold{\text{m = matinee tickets}} \\\\\bold{\text{s = student tickets}}\\\\\bold{\text{r = regular tickets}}$

By given question, calculating equations are:

$\to \bold{m + s + r = 8500}............................................(a)\\\\\to \bold{5m + 6s + 8.50r = 64600}............................(b)\\\\\to \bold{s = 2m}...................(c)$

Putting the equation (c) value in the equation (a) to calculate value:

$m + 2m + r = 8500\\\\3m + r = 8500\\\\r = 8500 - 3m........................................(d)$

Putting equation (c) and (d) value into equation (b):

$5m + 6(2m) + 8.50(8500 - 3m) = 64600\\\\5m + 12m + 72250 - 25.50m = 64600\\\\-8.50m = 64600 - 72250 \\\\-8.50m = -7650\\\\m = \frac{-7650}{-8.50}\\\\m = \frac{7650}{8.50}\\\\m = 900$