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2 years ago

1 2.2.5 Quiz: Volume

Mathematics

1 answer:

LUCKY_DIMON [66]2 years ago

6 0

Answer:

12 1/2 cubic units, the formula is Lenght × Width × Hieght

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Please help asap tysm <333

muminat

Answer:

32 yards and 64 feet

Step-by-step explanation:

just multiply them by 32

6 0

2 years ago

An open box is to be constructed so that the length of the base is 3 times larger than the width of the base. If the cost to con

natta225 [31]

Answer:

Step-by-step explanation:

Let assume that the volume = 88 cubic feet

Then:

$L = 3w --- (1)volume = l \times w \times h \\ \\ 88 = (3w) \times w \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\$

The construction cost now is:

$C = 4(l \times w) + 2 ( w \times h) + 2(l \times h) \\ \\ C = 4(3w^2) + 2(w \times \dfrac{88}{3w^2}) + 2(3w \times \dfrac{88}{3w^2}) \\\\ C = 12w^2 + \dfrac{176}{3w} + \dfrac{176}{w}$

Now, to determine the minimum cost:

$\dfrac{dC}{dw}= 0 \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}$

$w = \dfrac{88}{3(3)}^{1/3} \ feet$

Now;

$length = 3 ( \dfrac{88}{3(3)})^{1/3} \ feet$

$height = ( 88})^{1/3} (3)^{1/3} \ feet$

6 0

3 years ago

The resistance, R of a wire varies directly as the length, l, and inversely as the diameter, d, squared. If R is 1.50ohms when l

tatyana61 [14]

Answer:

resistance is 1.5 ohms (1.5 Ω)

Step-by-step explanation:

R varies directly with l

R varies inversely with $d^2$

We can set-up a proportionality statement as shown below:

$R=k\frac{l}{d^2}$

Now, Given,

R = 1.50

l = 2

d = 1.5

We substitute and find k (the proportionality constant):

$R=k\frac{l}{d^2}\\1.5=k\frac{2}{1.5^2}\\1.5=\frac{2k}{2.25}\\2k=1.5*2.25\\2k=3.375\\k=1.6875$

Now, we will use this value of k to solve the problem.

Given,

l = 8

d = 3

and

k = 1.6875

We find R:

$R=k\frac{l}{d^2}\\R=1.6875\frac{8}{3^2}\\R=\frac{1.6875*8}{9}\\R=1.5$

The resistance is 1.5 ohms (1.5 Ω)

3 0

3 years ago

Julio is paid 1.4 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 35 hours and

Harman [31]

<span>Julio is paid 1.4 times his normal hourly rate for every excess hour he works in a week.
last week he worked 35 hours and got 436.60 dollars.
We need to find an equation so we can be able to solve Julio’s earnings:
=> Let X be the value of Julio’s rate
=> 30 * X + 5 x 1.4x = 436.6
=> 30x + 7x = 436.6
=> 37x = 436.6
=> 37x / 37 = 436.6 / 37
=> x = 11.8
Thus the original rate of Julio is 11.8 dollars
=> 1.4 x 11.8 = 16.52 dollars, the rate of Julio with added rate
=> 30 x 11.8 + 5 x 16.52
=> 354 + 82.6
=> 436.6

</span>

3 0

3 years ago

Choose the solutions of the following systems of equations x^2+y^2=6 and x^2-y=6

den301095 [7]

Answer:

The solutions are (-√6,0) and (√6,0)

(-√5,-1) and (√5,-1)

Step-by-step explanation:

The equations are:

${x}^{2} + {y}^{2} = 6$