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3 years ago

1/6 6% 3/5 60% 6/100 which two values are equivalent to 0.6

Mathematics

1 answer:

earnstyle [38]3 years ago

4 0

Answer:

3/5 and 60%

Step-by-step explanation:

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The surface area of this cube is 96 square meters. what is the value of y?

ELEN [110]

The formula for finding the surface area of a cube is A=6y^2 where y is the side length. we know a=96. so we just isolate y.
96/6= 6y^2 / 6
16=y^2
sqrt (16) = sqrt(y^2)
4=y

So y is 4

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4 years ago

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What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out

Romashka-Z-Leto [24]

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides $12-2x$ and $16-2x$ , and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

$(12-2x)(16-2x)x = 4x^3-56x^2+192x$

The derivative of this function is

$12x^2-112x+192$

and it equals zero if and only if

$12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}$

If we evaluate the volume function at these points, we have

$f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)$

So, the maximum volume is given if you cut a square with side length

$x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7$

5 0

3 years ago

The graph for the first equation of a system is shown in orange. The second equation is: 3y+30=6x What is the solution to the sy

Alik [6]

Answer:

Step-by-step explanation:

(1,-8) sorry if you needed an explanation i am not good at that. Hope this helped!!

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3 years ago

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One more time!

CaHeK987 [17]

Since q(x) is inside p(x), find the x-value that results in q(x) = 1/4

$\frac{1}{4} = 5 - x^2\ \Rightarrow\ x^2 = 5 - \frac{1}{4}\ \Rightarrow\ x^2 = \frac{19}{4}\ \Rightarrow \\
x = \frac{\sqrt{19} }{2}$

so we conclude that
$q(\frac{\sqrt{19} }{2} ) = 1/4$

therefore

$p(1/4) = p\left( q\left(\frac{ \sqrt{19} }{2} \right) \right)$

plug $x=\sqrt{19}/2$ into p( q(x) ) to get answer

$p(1/4) = p\left( q\left( \frac{ \sqrt{19} }{2} \right) \right)\ \Rightarrow\ \dfrac{4 - \left( \frac{\sqrt{19} }{2}\right)^2 }{ \left( \frac{\sqrt{19} }{2}\right)^3 } \Rightarrow \\ \\ \dfrac{4 - \frac{19}{4} }{ \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{8\left(4 - \frac{19}{4}\right) }{ 8 \cdot \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{32 - 38}{19\sqrt{19}} \Rightarrow \dfrac{-6}{19\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}\Rightarrow$

$\dfrac{-6\sqrt{19} }{19 \cdot 19} \\ \\ \Rightarrow -\dfrac{6\sqrt{19} }{361}$

$p(1/4) = -\dfrac{6\sqrt{19} }{361}$

3 0

3 years ago

Simplify what is written here

Inessa05 [86]

When multiplying terms that have the same base (in this case, $x$ ) but different exponents, you can add their exponents to make them one term.