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MAXImum [283]
3 years ago
11

The first number in a pattern is 12. The rule is often pattern is add 5. What is the next term in the pattern.

Mathematics
2 answers:
masha68 [24]3 years ago
8 0

Answer:

17

Step-by-step explanation:

andreyandreev [35.5K]3 years ago
8 0

Answer:17

Step-by-step explanation:

If the starting number is 12, and the rule is to add 5, then you will add 5 to 12 and get 17. To get the next number you will add 5 to 17 and get 22 . Then add five to 22 and so on.

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Gas is escaping from a spherical balloon at the rate of 12 ft3/hr. At what rate (in feet per hour) is the radius of the balloon
bija089 [108]

Answer:

This is the rate at which the radius of the balloon is changing when the volume is 300 ft^3 \frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \:\frac{ft}{h}  \approx -0.05537 \:\frac{ft}{h}

Step-by-step explanation:

Let r be the radius and V the volume.

We know that the gas is escaping from a spherical balloon at the rate of \frac{dV}{dt}=-12\:\frac{ft^3}{h} because the volume is decreasing, and we want to find \frac{dr}{dt}

The two variables are related by the equation

V=\frac{4}{3}\pi r^3

taking the derivative of the equation, we get

\frac{d}{dt}V=\frac{d}{dt}(\frac{4}{3}\pi r^3)\\\\\frac{dV}{dt}=\frac{4}{3}\pi (3r^2)\frac{dr}{dt} \\\\\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}

With the help of the formula for the volume of a sphere and the information given, we find r  

V=\frac{4}{3}\pi r^3\\\\300=\frac{4}{3}\pi r^3\\\\r^3=\frac{225}{\pi }\\\\r=\sqrt[3]{\frac{225}{\pi }}

Substitute the values we know and solve for \frac{dr}{dt}

\frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=-\frac{12}{4\pi (\sqrt[3]{\frac{225}{\pi }})^2} \\\\\frac{dr}{dt}=-\frac{3}{\pi \left(\sqrt[3]{\frac{225}{\pi }}\right)^2}\\\\\frac{dr}{dt}=-\frac{3}{\pi \frac{225^{\frac{2}{3}}}{\pi ^{\frac{2}{3}}}}\\\\\frac{dr}{dt}=-\frac{3}{225^{\frac{2}{3}}\pi ^{\frac{1}{3}}} \approx -0.05537 \:\frac{ft}{h}

7 0
4 years ago
Since customers prefer a lower concentration of lemon juice, Mario measures out 3 grams (g) of lemon juice and adds it to the 50
svet-max [94.6K]

Answer:

Ok so you just ask your teacher, if not ur mom. I feel you can work this one out yourself.

Step-by-step explanation:

7 0
3 years ago
How do u solve 2x - 30000y???????????
Fed [463]

Answer:

2(x-15000y)

Step-by-step explanation:

2x-30000y

2(x-15000y)

4 0
3 years ago
Can someone tell me the answer
lidiya [134]

Answer:

x= 50

Step-by-step explanation:

Add up the other two numbers, 15 and 25, which will get you 40. subtract 40 from 90 and you have 50.

6 0
3 years ago
Is the graph proportional, why or why not?
kenny6666 [7]

Answer: yes

Step-by-step explanation:

because it starts at 0 and continues forward

4 0
3 years ago
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