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Nana76 [90]
3 years ago
7

If 3 to the power y = x then y = ?

Mathematics
1 answer:
Oksanka [162]3 years ago
6 0

Answer:

y=\log_3(x)


Step-by-step explanation:

3^y=x

\ln(3^y)=\ln(x)

y\ln(3)=\ln(x)

y=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

but if

f(x)=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

then since

f(3)=\frac{\displaystyle\ln(3)}{\displaystyle\ln(3)}=1

f(x)=\log_3(x)

so

y=\log_3(x)


or


3^y=x

\log_3(3^y)=\log_3(x)

y\log_3(3)=\log_3(x)

\text{but }\,\log_3(3)=1, \text{so,}

y=\log_3(x)



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Step-by-step explanation:

When three coins are flipped, we get 8 total outcomes: (HHH,HHT,HTH,HTT,THH,THT,TTH,TTT)

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3 years ago
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Step-by-step explanation:

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There are values of t so that sin t=.35 and cos t=.6
NISA [10]

Recall the fundamental rule of trig:

\sin^2(x)+\cos^2(x)=1 \quad\forall x \in \mathbb{R}

So, there exists an angle t such that

(0.6,0.35)=(\sin(t),\cos(t))

if and only if

\sin^2(t)+\cos^2(t)=0.6^2+0.35^2=1

Working out the numbers, we get

0.6^2+0.35^2=0.36+0.1225=0.4825\neq 1

So, there doesn't exist a number t such that

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7 0
3 years ago
Please solve<br>thanks ​
Korolek [52]

Answer:

1) 250°, 2) 44°

Step-by-step explanation:

1) See attached

If we add a line ⊥ to both AB and DE, we can find x as a sum of 2 internal angles of right triangles and 180°

∠D internal = 360°-312°=48°

x=180°+(90°-62°)+(90°-48°)= 180°+28°+42°= 250°

x=250°

2)

∠ADC= ∠ABC= 180°- ∠ADE= 180°- 110°= 70°

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∠DBC= 44°

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