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3 years ago

The equation of a circle is x^2 + y^2 - 12x + 6y + 20 = 0. What is the radius of the circle?

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

3 0

The radius of the circle is 5.

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How much would $500 invested at 9% interest compounded annually be

dalvyx [7]

Answer:

$705.79.

Step-by-step explanation:

The formula is

Amount = P(1 + r/100) ^ t so

Amount = 500 (1 + 9/100)^4

= $705.79.

8 0

3 years ago

Read 2 more answers

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

HELP 30 POINTS!!!!!

Tamiku [17]

by pythagorean formula, the last side is √(61)

by cos rule

cos A

$= \frac{ {6}^{2} + 61 - {5}^{2} }{2 \times 6 \times \sqrt{61} } \\ = \frac{72}{12 \sqrt{61} } \\ = \frac{6}{ \sqrt{61} }$

A = 39.81

5 0

3 years ago

If an arithmetic progression satisfies U4=7 , U8=15 .Find U10

Alja [10]

Answer:

U10 = 19

Step-by-step explanation:

The sequence is $Ux=(x*2)-1$

x is the coefficient to U.

So, $U10=(10*2)-1$

Which means $U10=20-1$

Which means $U10=19$

And there is your answer.

Hope this helps. Have a nice day.

6 0

2 years ago

Find 2a for a = 3- 4 = 34

Usimov [2.4K]

Answer:

Step-by-step explanation:

2x34(adding value of a)

8 0

3 years ago