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2 years ago

Find all solutions to 2sin(θ)=√3 on the interval 0≤θ<2π

Mathematics

1 answer:

makkiz [27]2 years ago

7 0

Answer:

2sin(3θ) - √3 = 0

Step-by-step explanation:

sin(3θ) = √3/2

3θ = π/3 + 2kπ or 2π/3 + 2kπ, k = 0, ±1, ±2, ±3,...

θ = π/9 + 2kπ/3, 2π/9 + 2kπ/3

If k = 0, we get θ = π/9, 2π/9

If k = 1, we get θ = 7π/9, 8π/9

If k = 2, we get θ = 13π/9, 14π/9

Other values of k give values of θ lying outside of the interval [0, 2π).

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What is the area of a circle with a diameter of 10

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It would be D because the formula is: pi r^2

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3 years ago

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Adam currently runs about 20 miles per week,aND he wants to increase his weekly mileage by 30% How many miles will Adam run per

mel-nik [20]

20miles increased by 30%=new mileage added

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2 years ago

In triangle ABC, a = 9, c = 5, and angle B = 120°. Find the measure of angle A to the nearest degree. Show your work.

slamgirl [31]

Answer:

Angle A = 39°

Step-by-step explanation:

We are given that there is a triangle ABC where a = 9, c = 5 and angle B = 120° and we are to find the measure of angle A.

But first we need to find the side b using the law of cosine:

$b^2 = a^2 + c^2- 2a*c*cos(120)$

$b^2 = 81 + 25 - 2*9*5*(-0.5)$

$b=\sqrt{151}$

Now finding angle A using law of cosine:

$cos(A) = \frac{b^2+c^2-a^2}{2b*c}$

$cos(A) = \frac{151+25-81}{2*12.29*5}$

$cos A=0.7730$

$A=39.38$

Therefore, the measure of angle A = 39°.

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3 years ago

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Water pours into a tank at the rate of 2000 cm3/min. The tank is cylindrical with radius 2 meters. How fast is the height of wat

Gennadij [26K]

Volume of water in the tank:

$V=\pi (2\,\mathrm m)^2h=\pi(200\,\mathrm{cm})^2h$

Differentiate both sides with respect to time t :

$\dfrac{\mathrm dV}{\mathrm dt}=\pi(200\,\mathrm{cm})^2\dfrac{\mathrm dh}{\mathrm dt}$

V changes at a rate of 2000 cc/min (cubic cm per minute); use this to solve for dh/dt :

$2000\dfrac{\mathrm{cm}^3}{\rm min}=\pi(40,000\,\mathrm{cm}^2)\dfrac{\mathrm dh}{\mathrm dt}$

$\dfrac{\mathrm dh}{\mathrm dt}=\dfrac{2000}{40,000\pi}\dfrac{\rm cm}{\rm min}=\dfrac1{20\pi}\dfrac{\rm cm}{\rm min}$

(The question asks how the height changes at the exact moment the height is 50 cm, but this info is a red herring because the rate of change is constant.)

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3 years ago

In is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says t

Y_Kistochka [10]

Answer:

A. $27.23

B. $467.77

Step-by-step explanation:

Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5 1/2% of the selling price. A.How much commission will the salesperson earn by selling a couch for $495?

B.How much money will the store get from the sale of the couch?

Salesperson commission = 5 1/2%

Price of couch = $495

A. Amount earned by the salesperson = 5 1/2% of $495

= 5.5% × 495

= 0.055 × 495

= 27.225

Approximately

Amount earned by the salesperson = $27.23

B.How much money will the store get from the sale of the couch?

Amount the store get = Total price - amount earned by salesperson

= $495 - $27.23

= $467.77

8 0

3 years ago