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3 years ago

what is the exact circumference of the base of a cone that has a volume of 1014 pi in^3 and a height of 18 in.

1 answer:

8 0

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
V=1014\pi \\
h=18
\end{cases}\implies 1041\pi =\cfrac{\pi \cdot r^2\cdot 18}{3}
\\\\\\
1041\pi =6\pi r^2\implies \cfrac{1041\pi }{6\pi }=r^2\implies \cfrac{347}{2}=r^2\implies \boxed{\sqrt{\cfrac{347}{2}}=r}\\\\
-------------------------------\\\\
\textit{circumference of a }\stackrel{cone's}{circle}\\\\
C=2\pi r\qquad \qquad C=2\pi \left( \boxed{\sqrt{\cfrac{347}{2}}} \right)$

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Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?

kramer

Answer:

y = 1/12 (x − 5)²

Step-by-step explanation:

We can solve this graphically without doing calculations.

The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.

The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.

So the answer is A. y = 1/12 (x−5)².

But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:

y = 1/(4p) (x − h)² + k

where (h, k) is the vertex and p is the distance from the vertex to the focus.

The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:

p = (3 − (-3)) / 2

p = 3

k, the y component of the vertex, is the average:

k = (3 + (-3)) / 2

k = 0

And h, the x component of the vertex, is the same as the focus:

h = 5

So:

y = 1/(4×3) (x − 5)² + 0

y = 1/12 (x − 5)²

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3 years ago

The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour. There were initially 500

polet [3.4K]

Answer:

(1.2×3)500

Step-by-step explanation:

the 1.2 factor will be multiplied by the hours given then times that by the starting amount of bacteria.

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4 years ago

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Plz help me with this and plz show ur work!?! :)

Rufina [12.5K]

Answer:

Total height lowered = 75m

No of times balloon lowered = 5

Height lowered in each lowering = Total height lowered / No of times balloon lowered

= 75 / 5

= 15 m

The number indicated that each time balloon is lowered by 15 m

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3 years ago

There are 96 strawberries in a basket. Each of 12 children received an equal number of the strawberries. Which equation gives s,

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3 years ago

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Ng Order of Operations George has $15. He would like to know if he has enough money to see a movie ($9.00) and buy a pretzel ($2

UNO [17]

Answer:

No, George does not have enough money to buy everything.

The correct expression is:

15 - 9 - 2.65 - 1.35 - 2(1.74)

Step-by-step explanation:

Given that:

Money present with George initially = $15

Money required to see the movie = $9

Money required to buy a pretzel = $2.65

Money required to buy a drink = $1.35

Money required to buy 2 veggie cups = $2(1.74)

To find:

Whether there is enough money with George to complete all the tasks.

Solution:

First of all, let us calculate all the money required and then we can subtract all the money from the initial amount to find whether there is enough money present with George.

If the result is in positive, there is enough money with George.

Total money required for all the activities = $9 + $2.65 + $1.35 + $2(1.74) = $16.48

Expression = $15 - $16.48 = -$1.48

The result is negative, therefore there is not enough money.

The correct expression is:

15 - 9 - 2.65 - 1.35 - 2(1.74)

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3 years ago