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2 years ago

Which expressions simplify to a rational answer? Select each correct answer

Mathematics

1 answer:

taurus [48]2 years ago

7 0

Answer:

first and last one

Step-by-step explanation:

first one would be 12 and last one is 10

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PLEASE HELP, Erika is working in solving the exponential equation 50^x = 17 ; however, she is not quite sure where to start. Usi

Furkat [3]

Yes, 50^x = 17 is an exponential equation with base 50, and the task here is to solve it for x.

1) Take the log of both sides: x log 50 = log 17

2) Divide both sides b log 50:

log 17

x = ----------

log 50

3) This last result can't be simplified, but can be evaluated"

x = 1.2304 / 1.6990 = 0.724 (approx.)

7 0

2 years ago

You must design a closed rectangular box of width w, length l and height h, whose volume is 504 cm3. The sides of the box cost 3

Charra [1.4K]

Answer:

Dimensions will be

Length = 7.23 cm

Width = 7.23 cm

Height = 9.64 cm

Step-by-step explanation:

A closed box has length = l cm

width of the box = w cm

height of the box = h cm

Volume of the rectangular box = lwh

504 = lwh

$h=\frac{504}{lw}$

Sides which involve length and width and height, cost = 3 cents per cm²

Top and bottom of the box costs = 4 cents per cm²

Cost of the sides $C_{s}$ = 3[2(l + w)h] = 6(l + w)h

$C_{s}$ = 3[2(l + w)h]

$C_{s}=6(l+w)(\frac{504}{lw} )$

Cost of the top and the bottom $C_{(t,p)}$ = 4(2lw) = 8lw

Total cost of the box C = $3024\frac{(l+w)}{lw}$ + 8lw

= $3024[\frac{1}{l}+\frac{1}{w}]$ + 8lw

To minimize the cost of the sides

$\frac{dC}{dl}=3024(-l^{-2}+0)+8w=0$

$\frac{3024}{l^{2}}=8w$

$\frac{378}{l^{2}}=w$ ---------(1)

$\frac{dC}{dw}=3024(-w^{-2})+8l=0$

$\frac{3024}{w^{2}}=8l$

$\frac{378}{w^{2}}=l$

$w^{2}=\frac{378}{l}$ -------(2)

Now place the value of w from equation (1) to equation (2)

$(\frac{378}{l^{2}})^{2}=\frac{378}{l}$

$\frac{(378)^{2} }{l^{4}}=\frac{378}{l}$

l³ = 378

l = ∛378 = 7.23 cm

From equation (2)

$w^{2}=\frac{378}{7.23}$

$w^{2}=52.28$

w = 7.23 cm

As lwh = 504 cm³

(7.23)²h = 504

$h=\frac{504}{(7.23)^{2}}$

h = 9.64 cm

6 0

3 years ago

Find the common difference for the given sequence<br> 1.2, 1.85, 2.5, 3.15, ...

Kay [80]

Answer:

c)0.65

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

The petrol tank at the local service station has a capacity of 6000L. It is 66.06 percent full. How many litres of petrol are ne

Rina8888 [55]

Since the tank is 66.06% full, it is (100 - 66.06) = 33.94% empty.

Its capacity is 6,000L. So, in order to fill it to capacity, the service station
must order 33.94% of 6,000L .

33.94% = 0.3394
"of" means "times"

0.3394 x 6,000L = <em>2,036.4 liters</em> needed, to fill the tank to the rim.

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3 years ago

a family pass to the amusement park costs $54.using the distributive property , write an expression that can be used to find the

Mandarinka [93]

9 x 6 = 54 is this right I'll do distributive property next time

4 0

2 years ago

Read 2 more answers