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vichka [17]
3 years ago
14

MZYX=pi/3 radians. Covert this radian measure to its equivalent degree measure.

Mathematics
2 answers:
vitfil [10]3 years ago
7 0

Answer:

60°

Step-by-step explanation:

Angles can be converted from radians to degrees by multiplying by 180/π.

π/3 * 180°/π = 180°π /3π = 180/3 = 60°

60° is the measure of ZYX in degrees.

Rom4ik [11]3 years ago
6 0

Answer: 60°

Step-by-step explanation:

To convert a radian measure to its equivalent degree measure, we need to multiply 180° and divide by  π .

Now, Given : m\angle{ZYX}=\dfrac{\pi}{3}\text{ radians}

Then , its equivalent degree measure would be :

m\angle{ZYX}=\dfrac{\pi}{3}\times\dfrac{180^{\circ}}{\pi}\\\\\Rightarrow\ m\angle{ZYX}=60^{\circ}

Hence, the equivalent degree measure of m\angle{ZYX}=\dfrac{\pi}{3}\text{ radians} is 60°.

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Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep,
Lina20 [59]

The shortest distance between the tip of the cone and its rim exits 51.11cm.

<h3>What is the shortest distance between the tip of the cone and its rim?​</h3>

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

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Solving the value of x, we get

Multiply both sides by x

$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x

$\cos \left(38.5^{\circ}\right) x=40

Divide both sides by $\cos \left(38.5^{\circ}\right)$

$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}

simplifying the above equation, we get

$x=\frac{40}{\cos \left(38.5^{\circ}\right)}

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The shortest distance between the tip of the cone and its rim exits 51.11cm.

To learn more about right triangles refer to:

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1 year ago
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A simple random sample of size n=14 is obtained from a population with μ=64 and σ=19.
madam [21]

Answer:

a) A. The population must be normally distributed

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Step-by-step explanation:

a) The population is normally distributed having a mean (\mu_x) = 64  and a standard deviation (\sigma_x) = \frac{19}{\sqrt{14} }

b) P(X < 68.2)

First me need to calculate the z score (z). This is given by the equation:

z=\frac{x-\mu_x}{\sigma_x} but μ=64 and σ=19 and n=14,  \mu_x=\mu=64 and \sigma_x=\frac{ \sigma}{\sqrt{n} }=\frac{19}{\sqrt{14} }

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P(X < 68.2) = 0.7967

c) P(X  ≥  65.6)

First me need to calculate the z score (z). This is given by the equation:

z=\frac{x-\mu_x}{\sigma_x}

Therefore: z=\frac{65.6-64}{\frac{19}{\sqrt{14} } }=0.32

From z table,  P(X  ≥  65.6) =  P(z  ≥  0.32) = 1 -  P(z  <  0.32) = 1 - 0.6255 = 0.3745

P(X  ≥  65.6) = 0.3745

P(X < 68.2) = 0.7967

5 0
3 years ago
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