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3 years ago

A road has a 16.7% grade.Why might we want to warn drivers of a grade like this?

1 answer:

8 0

The higher the percentage, the steeper the grade and the steeper the hill. This warning is issued so drivers are more careful (otherwise they would probably get into more accidents).

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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

What is -4x+y=6 and -5x-y=21 in subsitution

kifflom [539]

Solve for y in the first equation.
y = 4x + 6
Substitute <span>4x + 6 into the second equation.
-5x - (</span><span>4x + 6) = 21
Distribute
-5x - 4x - 6 = 21
Combine like terms
-9x = 27
Divide both sides by -9
x = -3
Substitute back into first equation
-4(-3) + y = 6
Solve for y
y = -6</span>

8 0

3 years ago

don walked 3 3/5 miles on Friday, 3.7 miles on saturday, and 3 5/8 miles on sunday. list the distances from least to greatest

astraxan [27]

Solution:

we are given that

Don walked 3 3/5 miles on Friday

It can be re-written as

$3\frac{3}{5}miles=\frac{18}{5}= 3.6$ miles

3 5/8 miles on sunday.

It can be re-written as

$3\frac{5}{8}miles=\frac{29}{8}= 3.625$ miles

an d He walk 3.7 miles on satarday.

The distances from least to greatest is 3.6, 3.625, 3.7

The distances from least to greatest is $3\frac{3}{5}$ miles, $3\frac{5}{8}$ miles, 3.7 miles.

8 0

3 years ago

What are the answers to these i put them in the picture

tekilochka [14]

The problem to number 1 is a inequality, so
x-2<-7
x<-5
since it is < it will have open dot.
Answer: C

2. x/3>-3
x>-9

Answer: D

3. 5p+26<72
5p<46
p<9.2

Answer: C

4. -3w+3>=18
-3w>=15
x<=-5

5. 15x-21>= 12x+18
x>=13
Answer A

6: |3x|=15
Absolute values positive so {-5,5}
Answer: B
7: |2x-3|=5
x=4,-1
Answer: C

8 0

3 years ago

Please see attached! Surface area

grandymaker [24]

Surface area is 10 cm

8 0

3 years ago