$f(x) =x^2 -2x\:\: and \:\: g(x) = 6x + 4\\(f+g)(x) = f(x) + g(x) \\(f+g)(x) = x^2 -2x+ 6x + 4\\(f+g)(x) = x^2+4x + 4\\(f+g)(x) = (x+2)^2\\ 0 = (x+2)^2...[\because (f+g)(x) =0]\\0 = x+2\\\therefore x = -2$

6 0

3 years ago

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Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 529 square meter

Zielflug [23.3K]

Answer:

$x=23/\sqrt{6}$ ,

$y= \frac{23}{6\sqrt{6}}$

Step-by-step explanation:

From the question we are told that

Surface area is 529 square meters

Generally the dimensions of the cuboid

$v=x^y$

$D=4xy+2x^2 =529$

$V=x^29(\frac{529-6x^2}{4x})$

$V' =529-6x^2/4$

$v'=0$

Therefore

$529=6x^2$

$x=\sqrt{\frac{529}{6} }$

$x=23/\sqrt{6}$

Mathematically

$v''=\frac{12x}{4}$

$v''=-3\frac{23}{\sqrt{6} }$

$y= \frac{529-2*(\frac{529}{6} }{4*\frac{23}{\sqrt{6} } }$

$y= \frac{23}{6\sqrt{6}}$

Therefore

$x=23/\sqrt{6}$

and

$y= \frac{23}{6\sqrt{6}}$

7 0

3 years ago

13. GEOMETRY The formula for the area of a triangle is A = Loh , where A represents the area, b is the base, and his the height

Setler79 [48]

Answer:

Whoa! You made a rectangle that's twice as big as the triangle! The area of the rectangle is bh=4\times 5 = 20bh=4×5=20b, h, equals, 4, times, 5, equals, 20 square units, so the area of the triangle is \dfrac 12 by = \dfrac 12 \times 4 \times 5 = 10

bh=

×4×5=10start fraction, 1, divided by, 2, end fraction, b, h, equal, start fraction, 1, divided by, 2, end fraction, times, 4, times, 5, equals, 10 square units.

Step-by-step explanation:

8 0

3 years ago