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3 years ago

.49027397189 out of 365 is what? 12 POINTS

Mathematics

1 answer:

erastova [34]3 years ago

4 0

The answer would be

744.4816998808433

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Gloria would like to construct a box with volume of exactly 55ft3 using only metal and wood. The metal costs $7/ft2 and the wood

k0ka [10]

Answer:

The dimensions of the box are:

W=2.97 ft

L = 8.91ft

H=2.08ft

Step-by-step explanation:

Volume of the box= 55ft³

LWH=55

Length of the base, L = 3W

3W*WH=55

3W²H=55

$H= \frac{55}{3W^2}$

Metal costs =$7/ft²

Wood costs =$5/ft².

Area of the Sides= 2(LH+WH)

= $\frac{2*3W*55}{3W^2}+\frac{2*W*55}{3W^2}\\=\frac{110}{W}+\frac{110}{3W}$

Cost of the sides therefore is:

$5(\frac{110}{W}+\frac{110}{3W})\\=\frac{550}{W}+\frac{550}{3W}$

Area of the top and bottom=2LW=2*3W*W=6W²

Cost=7*6W²=42W²

Total Cost, C(W) of the box:

$=\frac{550}{W}+\frac{550}{3W}+42W^2\\=\frac{1650+550+126W^3}{3W}\\=\frac{2200+126W^3}{3W}$

To find the minimum cost, we set the derivative of C(W) to be equal to zero.

$C^{1}W=\frac{-2200+84W^3}{3W^2}$

$\frac{-2200+84W^3}{3W^2}=0$

84W³=2200

W³=26.19

W=2.97 ft

L = 3W=3*2.97=8.91ft

$H= \frac{55}{3X2.97^2}=2.08ft$

The dimensions of the box are:

W=2.97 ft

L = 8.91ft

H=2.08ft

4 0

3 years ago

He shorter leg of a 30°-60°-90° triangle is 6. what is the length of the hypotenuse?

blondinia [14]

the length would be 9

8 0

3 years ago

Which of the following represents fifth root of x squared in exponential form? x to the 2 fifths power x to the 5 over 2 power 5

Semmy [17]

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}
\\\quad \\
% rational negative exponent
a^{-\frac{{ n}}{{ m}}} =
 \cfrac{1}{a^{\frac{{ n}}{{ m}}}} \implies \cfrac{1}{\sqrt[{ m}]{a^{ n}}}\qquad\qquad 
% radical denominator
\cfrac{1}{\sqrt[{ m}]{a^{ n}}}= \cfrac{1}{a^{\frac{{ n}}{{ m}}}}\implies a^{-\frac{{ n}}{{ m}}} \\\\
-----------------------------\\\\
\sqrt[5]{x^2}\iff x^{\frac{2}{5}}$