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IgorLugansk [536]

2 years ago

12

Find m∠I. Put the answer below. m∠I =

1 answer:

eimsori [14]2 years ago

7 0

Answer:

∠ I ≈ 24°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanI = $\frac{opposite}{adjacent}$ = $\frac{GH}{GI}$ = $\frac{4}{9}$ , then

∠ I = $tan^{-1}$ ( $\frac{4}{9}$ ) ≈ 24°

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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

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

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2 years ago

Whats the area of a circle with a diameter of 12 cm?

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Answer:

113.1cm

Step-by-step explanation:

area= $\pi$ r²

r= half the diameter r=6

a= $\pi$ 6²

a= $\pi$ 36

a=113.1 cm

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Solve the inequality 3u+3(u+1)>2u+7 and write the solution in interval notation.

strojnjashka [21]

<u>Given</u>:

The given inequality is $3u+3(u+1)>2u+7$

We need to determine the solution of the inequality in interval notation.

<u>Solution of the inequality:</u>

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Thus, we have,

$3u+3u+3>2u+7$

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