4. What is the value of a in the following equation: 6a = 54? b. 7 C. 12 d. 8 a. 9

Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shap

gayaneshka [121]

Answer:

0.13 ft/min

Step-by-step explanation:

We are given that

$\frac{dV}{dt}=15ft^3/min$

We have to find the increasing rate of change of height of pile when the pile is 12 ft high.

Let d be the diameter of pile

Height of pile=h

d=h

Radius of pile,r= $\frac{d}{2}=\frac{h}{2}$

Volume of pile= $\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3$

$\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}$

h=12 ft

Substitute the values

$15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}$

$\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}$

$\frac{dh}{dt}=0.13ft/min$

7 0

4 years ago

Some people think it is unlucky if the 13th day of month falls on a Friday. show that in that there year (non-leap or leap) ther

Vlad1618 [11]

There are several ways to do this problem. One of them is to realize that there's only 14 possible calendars for any year (a year may start on any of 7 days, and a year may be either a leap year, or a non-leap year. So 7*2 = 14 possible calendars for any year). And since there's only 14 different possibilities, it's quite easy to perform an exhaustive search to prove that any year has between 1 and 3 Friday the 13ths. Let's first deal with non-leap years. Initially, I'll determine what day of the week the 13th falls for each month for a year that starts on Sunday. Jan - Friday Feb - Monday Mar - Monday Apr - Thursday May - Saturday Jun - Tuesday Jul - Thursday Aug - Sunday Sep - Wednesday Oct - Friday Nov - Monday Dec - Wednesday Now let's count how many times for each weekday, the 13th falls there. Sunday - 1 Monday - 3 Tuesday - 1 Wednesday - 2 Thursday - 2 Friday - 2 Saturday - 1 The key thing to notice is that there is that the number of times the 13th falls upon a weekday is always in the range of 1 to 3 days. And if the non-leap year were to start on any other day of the week, the numbers would simply rotate to the next days. The above list is generated for a year where January 1st falls on a Sunday. If instead it were to fall on a Monday, then the value above for Sunday would be the value for Monday. The value above for Monday would be the value for Tuesday, etc. So we've handled all possible non-leap years. Let's do that again for a leap year starting on a Sunday. We get: Jan - Friday Feb - Monday Mar - Tuesday Apr - Friday May - Sunday Jun - Wednesday Jul - Friday Aug - Monday Sep - Thursday Oct - Saturday Nov - Tuesday Dec - Thursday And the weekday totals are: Sunday - 1 Monday - 2 Tuesday - 2 Wednesday - 1 Thursday - 2 Friday - 3 Saturday - 1 And once again, for every weekday, the total is between 1 and 3. And the same argument applies for every leap year. And since we've covered both leap and non-leap years. Then we've demonstrated that for every possible year, Friday the 13th will happen at least once, and no more than 3 times.

5 0

3 years ago

45 POINTS IF ANSWER!!! Find the value of X in the triangle shown below.

pochemuha

Answer:

The bacterium expels oxygen, making room for

hydrogen peroxide and carbon dioxide. These elements are then combined with solar energy to produce fuel.

Step-by-step explanation:

.

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