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2 years ago

5

micah and his friends work at a tire factory. The factory manufactures several size tires for different vehicles Fill out the ta

ble below to show how the diameter and the circumference of the tires are related.

2 answers:

Georgia [21]2 years ago

7 0

Every other tire has the same ratio

solmaris [256]2 years ago

5 0

Yes above answer is correct

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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

3 years ago

I need help answer 6 through 7 I can't figure them out

seropon [69]

6. the answer is 4. because u find the diameter by dividing by 2.
7. answer = 8 , the radius is 4 . so u need to multiply 2 times 4. 2 times 4 =8.

6 0

3 years ago

Your credit card has a balance of $3300 and an annual interest rate of 14%. You decided to pay off the balance over two years. I

NARA [144]

9514 1404 393

Answer:

$137.90 more each month
$246.00 less total interest

Step-by-step explanation:

The amortization formula is ...

A = P(r/12)/(1 -(1 +r/12)^(-12t))

for the monthly payment on principal P at annual rate r for t years. Here, we have P=3300, r = 0.14, and t=1, so the monthly payment is ...

A = $3300(0.14/12)/(1 -(1 +0.14/12)^-12) ≈ $296.30

The payment of $296.30 is ...

$295.30 -158.40 = $137.90 . . . more each month

The total amount paid is 12×$296.30 = $3555.60, so 255.60 in interest. This amount is ...

$501.60 -255.60 = $246.00 . . . less total interest

3 0

3 years ago

2/x2-9 - 3x/ x2-5x+6 please show work

Luda [366]

Answer: -3x^3 - 7x^2 - x + 39

Step-by-step explanation:

2/(x^2 -9) - 3x/(x^2-5x+6)

get those denominators factored out

2/(x-3)(x+3) - 3x/(x-3)(x-2)

Multiply both by both denominators

2(x-3)(x-2) - 3x(x-3)(x+3)

Multiply it out

(2x^2 - 10x + 12) - (3x^3 + 9x^2 -9x - 27)

Simplify and it becomes

-3x^3 -7x^2 -x + 39

5 0

3 years ago

Which of the following could be the area of a room?<br> a. 18 m<br> b. 50 ft.<br> c. 29 m

Keith_Richards [23]

Answer:

probley A

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers