5x - 18

The volume of a cube is 216 ft. What is the length of a side?

irina [24]

Answer: 6 in.

Step-by-step explanation:

Hope this helped! :)

3 0

2 years ago

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If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

Then using the change of base formula, we can derive the relationship

$\log_xy=\dfrac{\ln y}{\ln x}=\dfrac1{\frac{\ln x}{\ln y}}=\dfrac1{\log_yx}$

This immediately tells us that

$\log_dc=\dfrac1{\log_cd}=\dfrac12$

Notice that none of $a,b,c,d$ can be equal to 1. This is because

$\log_1x=y\implies1^{\log_1x}=1^y\implies x=1$

for any choice of $y$ . This means we can safely do the following without worrying about division by 0.

$\log_db=\dfrac{\ln b}{\ln d}=\dfrac{\frac{\ln b}{\ln c}}{\frac{\ln d}{\ln c}}=\dfrac{\log_cb}{\log_cd}=\dfrac1{\log_bc\log_cd}$

so that

$\log_db=\dfrac1{-\frac34\cdot2}=-\dfrac23$

Similarly,

$\log_da=\dfrac{\ln a}{\ln d}=\dfrac{\frac{\ln a}{\ln b}}{\frac{\ln d}{\ln b}}=\dfrac{\log_ba}{\log_bd}=\dfrac{\log_db}{\log_ab}$

so that

$\log_da=\dfrac{-\frac23}{\frac89}=-\dfrac34$

So we end up with

$\log_dabc=-\dfrac34-\dfrac23+\dfrac12=-\dfrac{11}{12}$

###

Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

4 0

2 years ago

W/3 =4 find w <br> wwwwwwwwwwwwwwwwww

amid [387]

Answer:

w/3=4

w=12

Step-by-step explanation:

3 x 4 = 12

to undo division, you multiply.

4 0

3 years ago

Read 2 more answers

(x2 - y2)-(-x2 + y2)<br> How do you write that out to show work ?! Help pleAse

Verdich [7]

Answer:

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▀█▌░░░▄░▀█▀░▀ ░░ Copy And Paste Him onto all of ur brainly answers

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do it or he will hunt you down and kill u (lets destroy the moderators!!!!!!!!)

we are slowing them down already! good work soilders!

Step-by-step explanation:

8 0

2 years ago

Curtis threw 15 darts at a dartboard.40% of his darts hit the bull’s eye.how many darts not hit the bulls eye?

Harlamova29_29 [7]

Answer:

9

Step-by-step explanation:

The number of darts that failed to hit the bulls eye is 40% of 15 subtracted from 15

Since 40% of the darts hit the bulls eye .

Therefore

40% of 15

40/100 x 15

0.4 x 15

6

This means that 6 darts hit the bulls eye.

Therefore,number of darts that did not hit the bulls eye is

15 - 6 = 9

9 darts failed to hit the bulls eye

7 0

3 years ago