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Leviafan [203]
3 years ago
8

Determine the volume of one rectangiular prism v(x)=54x^3+264x^2-738x+420 ?

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
4 0
We have 
<span>v(x)=54x^3+264x^2-738x+420 , and the sum of coefficients are
54+264-738+420=0, so 1 is a zero of v(x), it means v(1)=0
so v(x) can be written as v(x)= (x-1) Q(x)
and obviously, Q(x) = v(x) / (x-1)
</span>Q(x)=54x^3+264x^2-738x+420/(x-1)= (6x+42)(9x-10)
v(x)=(x-1)(6x+42)(9x-10)
<span>
the volume of rectangular prism is V= LxWxH
we can assume tha L=x-1, W=6x+42 and H= 9x-10

</span>
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At his last track meet, Eli ran the 400-meter dash in 54 seconds. His friend Kimberly bet him that he couldn't run a whole kilom
Trava [24]

Answer:

Eli has to run for 2.25 minutes at this pace to win the bet.

Step-by-step explanation:

At his last track meet, Eli ran the 400-meter dash in 54 seconds.

So, the speed of Eli's run is \frac{400}{54} \times 60 = 444.44 meters per minute.

Now, if Eli is determined to run a whole kilometer with the same speed, then it will take Eli to run 1 kilometer within \frac{1000}{444.44} = 2.25 minutes.

Hence, Eli has to run for 2.25 minutes at this pace to win the bet. (Answer)

6 0
3 years ago
How do you solve y= -3+3​
Ilia_Sergeevich [38]
Answer=

y=-3+3
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3 years ago
A certain bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover
riadik2000 [5.3K]

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

(a)

\left[\begin{array}{cccc}T&H&S&P\\S&600&1300&2000\\L&400&300&400\end{array}\right] = A.

In the above matrix A, the columns refers the three type of books and the rows refers the from which stores the books are been sold.

The numbers represents the corresponding sales in the month of January.

The sale is same for the 6 months.

Hence, 6A = \left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right]. This matrix 6A represents the total sales over the 6 months.

(b)

If we denote the books in stock at the starting of January by B, then

B = \left[\begin{array}{cccc}T&H&S&P\\S&1000&3000&6000\\L&1000&6000&3000\end{array}\right].

Each month, the chain restocked the stores from its warehouse by shipping 500 hardcover, 1,400 softcover, and 1,400 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles.

If we represent the amount restocked books at the end of each month by another matrix C, then

C = \left[\begin{array}{cccc}T&H&S&P\\S&500&1400&1400\\L&500&500&500\end{array}\right].

This restocking will be done for 5 times before the end of June.

If there would be no sale, then the stock would be

B + 5C = \left[\begin{array}{cccc}T&H&S&P\\S&1000+2500&3000+7000&6000+7000\\L&1000+2500&6000+2500&3000+2500\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right].

Since, the total sale is given by 6A, at the end of June, the inventory in each store can be shown as following,

B+5C-6A \left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right] - \left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&-100&2200&1000\\L&1100&6700&3100\end{array}\right]

6 0
3 years ago
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Answer:

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