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3 years ago

Jason is a skilled rapper. He has already rapped a 40-word intro to a song and continues to rap 5 words per second.

Mathematics

1 answer:

-Dominant- [34]3 years ago

7 0

Answer:

5 $t$ + 40 ≤ 500

Step-by-step explanation:

Jason can rap 5 words per second

He can already rap 40 words into the song

There are 500 words to the whole song

500

5 $t$ + 40 ≤ 500

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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

Please help me with this question!!

quester [9]

Answer:

Step-by-step explanation:

a1 = 6

a2 = 10

a3 = 14

The next member of the sequence is 4 more than the current sequence. Therefore d = 4

a1 = 6

d = 4

n = 13

an = a1 + (n - 1)*d

an = 6 + (n - 1)*4

a_13 = 6 + 12*4

a_13 = 6 + 48

a_13 = 54

8 0

2 years ago

Please help What is the value of d?

PtichkaEL [24]

Rule: with any inscribed quadrilateral, the opposite angles are supplementary (they add to 180 degrees)

Based on that rule, we can say
d+100 = 180
d+100-100 = 180-100
d = 80

Answer: 80

8 0

3 years ago

102.8 divided by 4 And how u got it :)

eimsori [14]

Answer:

102.8/4=25.7

I got it because I used a calculator

Step-by-step explanation:

7 0

3 years ago

A salesperson earns a commission of 429$ for selling 3300$ in merchandise.

butalik [34]

Answer:

13%

Step-by-step explanation:

429 commission ÷3300 merchandise sold =0.13 percent

7 0

2 years ago