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4 years ago

What is the approximate solution to the equation 2^t =38

Mathematics

1 answer:

timurjin [86]4 years ago

3 0

2^t =38

take the log of each side

log ( 2^t) = log (38)

the exponent gets multiplies

t log (2) = log (38)

divide by log 2

t = log(38)/log (2)

t≈5.2479

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PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. the length TP in cm is:

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<h3><u>Given</u><u> </u><u>:</u><u>-</u></h3>

PQ = 8cm
Radius = 5cm
Two Tangents = P & Q.

<h3><u>Construction</u><u> </u><u>:</u><u>-</u></h3>

Join OT.

<h3><u>⟼</u><u> </u><u>Solution</u><u> </u><u>:</u><u>-</u></h3>

Here, ΔTPQ is isosceles and TO is the angle bisector of ∠PTO.

[∵ TP=TQ = Tangents from T upon the circle]

⠀⠀⠀⠀⠀⠀⠀⠀∴ OT⊥PQ

So, PR = RQ = 4cm.

⠀⠀⠀

___________________________________________

$\longmapsto{}$ By Applying Pythagoras Theorem in ∆OPR :

OR = √OP² - PR²

OR = √5² - 4²

OR = 3cm

__________________________________________

Now,

$\leadsto$ ∠TPR + ∠RPO = 90° (∵TPO=90°)

$\leadsto$ ∠TPR + ∠PTR (∵TRP=90°)

<u> $\leadsto$ </u><u>∴ ∠RPO = ∠PTR</u>

⠀⠀

<u>∴ Right triangle TRP is similar to the right </u><u>triangle</u><u> </u><u>PR</u><u>O</u><u>.</u> [By A-A Rule of similar triangles]

⟼ $\frac{TP}{PO} = \frac{RP}{RO}$

⟼ $\frac{TP}{5} = \frac{4}{3}$

⟼ $TP= \frac{20}{3}$

<h3>Hence you got your answer here. </h3>

⠀⠀⠀⠀⠀

<h2>-MissAbhi</h2>

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