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3 years ago

Reupload for the other one

Mathematics

1 answer:

Norma-Jean [14]3 years ago

4 0

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AC=<br> Help me please!! Thanks so much

katovenus [111]

Answer:

AC = 6√3 in

Step-by-step explanation:

<h3>Finding the length of the chord:</h3>

Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.

∠A = ∠C = 30.

∠A + ∠C + ∠AOC = 180 {angle sum property of traingle}

30 + 30 + ∠AOC = 180°

∠AOC = 180 -60

∠AOC = Ф = 120°

Find the length of radius using the bellow formula.

$\sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}$

Ф = 120°

Arc length = 4π

$\sf 4\pi =\dfrac{120}{180}*\pi *r\\\\ r =\dfrac{4\pi * 180}{120*\pi }\\\\ r = 6 \ in$

$\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}$

$\sf b = 2*6*Sin \ \dfrac{120}{2}\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}$

$\sf \boxed{\bf AC = 6\sqrt{3} \ in}$

5 0

2 years ago

A thermometer is taken from an inside room to the outside, where the air temperature is 20° f. after 1 minute the thermometer re

fomenos

The change in the temperature is proportional to the difference in temperatures. Let's call the initial temperature of the room and the thermometer $E_0$ and the current temperature $E(t)$ where $t$ is the elapsed time in minutes. The outside temperature is 20 F.

Newton's Law of Cooling:

$E(t) - 20 = (E_0 - 20) e^{- k t}$

We're given $E(1)=70 \textrm{ and } E(5)=45$

$70-20 = (E_0 - 20) e^{-k}$

$45-20 =(E_0 - 20) e^{-5k}$

Dividing,

$\dfrac{50}{25}=e^{4k}$

$k = \dfrac 1 4 \ln 2$

Now,

$E(t) - 20 = (E_0 - 20) e^{- k t}$

$E_0 = 20 + (E(t) - 20)e^{k t}$

$E_0 = 20 + (E(1) - 20)e^{k}$

$E_0 = 20 + (70 - 20)e^{\ln 2/4}$

$E_0 = 20 + 50 \cdot 2^{1/4} \approx 79.46 \textrm{ degrees F}$

3 0

4 years ago

Sprinters who run 100 yards now often run 100 meters.

Marina CMI [18]

Answer:

100 meters is 8.6 meters longer than 100 yards.

Step-by-step explanation:

Conversion of yards to meters.

Each yard has 0.914 meters.

So 100 yards is 100*0.9144 = 91.4 meters.

How many meters longer to the nearest tenth is 100 meters than 100 yards?

100 yards = 91.4 meters

100 - 91.4 = 8.6

So 100 meters is 8.6 meters longer than 100 yards.

5 0

3 years ago

If A is an n× n matrix, then det A = det AT . Verify this theorem for 2 × 2 matrices.

Bond [772]

Answer:

Verified

Step-by-step explanation:

Let A matrix be in the form of

$\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

Then det(A) = ad - bc

Matrix A transposed would be in the form of:

$\left[\begin{array}{cc}a&c\\b&d\end{array}\right]$

Where we can also calculate its determinant:

det(AT) = ad - bc = det(A)

So the determinant of the nxn matrix is the same as its transposed version for 2x2 matrices

4 0

3 years ago

Solve for x.<br> A. 7<br> B. 5<br> C. 0<br> D. 2

xeze [42]

5

Dhhhyabusnuabianosnosnosn

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3 years ago