All categories

3 years ago

Add me in fortnite my epic is “I am the sea 81.”

Mathematics

1 answer:

Lapatulllka [165]3 years ago

7 0

Answer:

Step-by-step explanation:

You might be interested in

Awnser Find the slope of the line that passes through (-34, 81) and (32, 12).

icang [17]

Answer:

-23/22

Step-by-step explanation:

Slope m = (y2-y1)/(x2-x1)

m = (12 - 81)/(32 - -34) = (-69)/(66) = -23/22

7 0

2 years ago

How many different ways can you arrange five people shoulder to shoulder in a line

Liono4ka [1.6K]

I think the answer is 25

3 0

3 years ago

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

3 years ago

Which angle number represents <EHK

kotegsom [21]

Angle #8 represents angle EHK

4 0

3 years ago

A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable. True or

vesna_86 [32]

The answer is true
Let's imagine that we have the following function function:
 $y = x ^ 2 
$
We have to:
Independent variable: x
Dependent variable: y
For x = -1:
 $y = (- 1) ^ 2 = 1 
$
 For x = 1:
 $y = (1) ^ 2 = 1 
$
 We observe that the independent variable can only obtain one result.
Answer:
True

3 0

3 years ago

Read 2 more answers