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Mathematics

1 answer:

zaharov [31]2 years ago

5 0

Answer:

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Step-by-step explanation:

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The ratio of boys to girls in the ninth grade is 6:5. If there are 185 girls in the class, how many boys are there.

FrozenT [24]

There are 222 boys in the class. You find this by dividing 185 by 5 which gets you 37, so you have to multiply the 6 by 37 to find the amount of boys.

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2 years ago

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Two planes A and B start from the same place and move in different directions making an angle of 50° between them the speed of p

Alika [10]

Answer:

The distance between them is 230.65 miles

Step-by-step explanation:

Here we use the Cosine formula

$a^2 = b^2 + c^2 - 2bc\ cos\ A\\\\a^2 = 200^2 + 300^2 - 2\times 200\times 300cos50^{\circ}\\\\= 40,000 + 90,000 - 120,000cos50^{\circ}\\\\= 130,000 - 120,000 \times 0.64\\\\= 130,000 - 76,800\\\\a^2= 53,200\\\\a = \sqrt{53,200} \\\\= 230.65\ miles\ per\ hour$

Now the distance for one hour is

= 230.65 ÷ 1

= 230.65 miles

4 0

3 years ago

How can the Pythagorean Identity be used to find sin θ, cos θ, or tan θ and the quadrant location of the angle?

Archy [21]

First lets see the pythagorean identities

$sin^2 \Theta + cos^2 \Theta =1$

So if we have to solve for sin theta , first we move cos theta to left side and then take square root to both sides, that is

$sin^2 \Theta = 1-cos^2 \Theta => sin \theta = \pm \sqrt{1-cos^2 \Theta}$

Now we need to check the sign of sin theta

First we have to remember the sign of sin, cos , tan in the quadrants. In first quadrant , all are positive. In second quadrant, only sin and cosine are positive. In third quadrant , only tan and cot are positive and in the last quadrant , only cos and sec are positive.

So if theta is in second quadrant, then we have to positive sign but if theta is in third or fourth quadrant, then we have to use negative sign .

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2 years ago

Find the center of the circle whose equation is x² + y² = 4.

Varvara68 [4.7K]

Answer:

The center of circle is $(0,0)$