Mathematics, 18.09.2019 09:30, alen919

The length of the top of the table is 3 m greater than the width. the area is 88m^2. find the dimensions of the table.

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The area of a rectangle is found using the formula A=LW. You need to express the length and width of this table using one variable. Since the length is described in terms of the width, let's call the width w. The length is 3m more than the width, so we can call the length w+3. Put these expressions of the length and width into the formula:
A=LW, A=88m², L= (w+3), w=w substitute:
88=w(w+3) (ok I did WL instead of LW but it's the same thing) Distribute the w:
88 = w²+3w subtract 88 from each side
0 = w²+3w-88 factor. w^2 can only be factored by w*w so set that up:
(w )(w ). Now look at the last term, it is -88. You need to find two factors of -88, and since factors multiply to get the number, you must have one positive and one negative factor to get -88, so go ahead and put them into your parentheses:
(w+ )(w- ). Now find factors of -88 that when added together give you 3, the coefficient of the middle term. -8 and 11 add up to 3, so put those into your factors:
(w+11)(w-8) and remember that this equals 0:
(w+11)(w-8)=0 Now when you multiply two numbers and get a product of 0, at least one of those numbers must equal 0 since any number times 0 equals 0. Either one can be 0, so set each equal to 0:
w+11=0 subtract 11 from each side
w= -11

w-8=0 add 8 to each side
w=8

Now you're asked to give the length and width of the table top. The table can't have a dimension that is negative, so we can discard the solution w= -11. We find that the width of the table is 8 feet. To find the length, go back to how we expressed the length, 3 more than the width:
L=3+w, w=8 substitute
L=3+8 add
L=11.

So the length of your table top is 11m and the width is 8m.

answered: Guest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

answered: Guest

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)

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The length of the top of the table is 3 m greater than the width. the area is 88m^2. find the dimens...