Answer:
- A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
Explanation:
To find a relationship modeled by the given function it is recommendable to factor it.
The function is:
The first step to factor it is to extract common factor 4x:
The second step is to factor the quadratic trinomial.
That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:
Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
- x is the desired (unknown) length
- 4x is 4 times the desired length
- x - 10 is 10 less than the desired length
- x - 8 is 8 less than the desired length
Thus, the volume of the prism is the product of the three factors:
The divergence of <em>F</em> is
div(<em>F</em> ) = ∂(<em>x</em> + <em>yz</em>)/∂<em>x</em> + ∂(<em>y</em> + <em>xz</em>)/∂<em>y</em> + ∂(<em>z</em> + <em>xy</em>)/∂<em>z</em>
div(<em>F</em> ) = 1 + 1 + 1
div(<em>F</em> ) = 3
The decimal number of three cents is 0.03
40,768/52 (weeks per yr)= 784
Step-by-step explanation:
Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t
Now, we are given that the savings is =Rs 500
So, According to our assumption, 2t=500
⇒t=250
Hence, the income of the family is =7×250=Rs 1750
And the expenditure is =Income−Savings
=Rs 1750−Rs 500
=Rs 1250