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Vlada [557]
3 years ago
6

Solve on the interval [0,2pi): 2 sin^2 x-3 sin x + 1 = 0

Mathematics
1 answer:
erica [24]3 years ago
7 0

Answer:

How do you solve #2sin^2x+3sinx+1=0# and find all solutions in the interval #[0,2pi)#?

Trigonometry Trigonometric Identities and Equations Solving Trigonometric Equations

Answer:

Explanation:

We may identify this as a quadratic equation in #sinx# and factorise it as a trinomial to obtain the solutions as

<h3>#(2sinx+1)(sinx+1)=0#</h3>

<h3>#thereforesinx=-1/2 or sinx=-1#</h3>

<h3>#therefore x= (7pi)/6 or (11pi)/6 or (3pi)/2#</h3>

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Sally finds a coin with a radius of 1.5 centimeters and a thickness of 0.25 cm. It has a measured mass of 18.54 grams. How can S
mote1985 [20]

Answer:

Silver

Step-by-step explanation:

Find the volume of the coin

<u>Volume of a cylinder</u>

\textsf{V}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

Given:

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  • h = 0.25 cm

Substituting given values into the formula to find the volume:

\sf \implies V=\pi (1.5)^2(0.25)

\sf \implies V=0.5625 \pi \:cm^3

Find the density of the coin given it has a measured mass of 18.54 g

<u>Density formula</u>

\sf \rho=\dfrac{m}{V}

where:

  • \rho = density
  • m = mass
  • V = volume

Given:

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  • \sf V=0.5625 \pi \:cm^3

Substituting given values into the density formula:

\implies \sf \rho=\dfrac{18.54}{0.5625 \pi}

\implies \sf \rho=10.49149385\:g\:cm^{-3}

Given:

  • \textsf{Density of Lead}=\sf 11.3\:g\:cm^{-3}
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Therefore, as \sf \rho=10.49\:g\:cm^{-3} the coin is made from silver.

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