A scientist is experimenting with bacteria in his laboratory He starts out with 3 bacteria

Point P is the center of the circle below. What is the exact area

igor_vitrenko [27]

Answer:

$Area =192\pi$

Step-by-step explanation:

Given

$\theta = 120^o$

$r =24$

Required

The area of the shaded sector

This is calculated as:

$Area =\frac{\theta}{360} * \pi r^2$

This gives

$Area =\frac{!20}{360} * \pi *24^2$

$Area =\frac{1}{3} * \pi *576$

$Area =\pi *192$

$Area =192\pi$

6 0

3 years ago

Ellie, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of $1

Ber [7]

Answer:

The weight of the package is 1 kilograms.

It will cost $ 13 by both the couriers services.

Step-by-step explanation:

Let the weight of her package is x kilograms

Now, according to the question:

The charges of first Courier = $10 + $3(x)

and The charges of Second Courier = $7 + $6(x)

Also, for x kilograms, both the charges are equal

⇒ $10 + $3(x) = $7 + $6(x)

or, 10 + 3x = 7 + 6x

or, 10 -7 = 6x - 3x

⇒ 3x = 3, implies x = 3/3 = 1

⇒ The weight of the package is 1 kilograms.

It will cost : 10 + 3(1) = $ 13 = 7 + 6(1) by both the couriers services.

5 0

4 years ago

Find cos q if q is an angle in standard position and the point with coordinates (3, –4) lies on the terminal side of the angle.

gayaneshka [121]

Answer:

cos q = 3/5

Step-by-step explanation:

Standard position means the vertex (point or corner of the angle) is at (0,0) and one side of the angle is glued to the positive x-axis (facts, but not technical math terms) See image. Special triangles have all three sides nice and clean with whole number lengths, we call these Pythagorean triples. 3-4-5 is your most basic Pythagorean triple. So we don't even have to calculate the hypotenuse, see image. Now the triangle shown is easy to work with, using entry-level trig...cos = ADJ/HYP. So we get 3/5=.6 BUUuuuut, the angle q in the original problem is actually the giant angle, marked in yellow (see image) and we're in the fourth quadrant which means there's negative numbers all over the place. So just to be sure the answer is .6 and not -.6 Check your signs. One trick to remember is the ASTC markings in the quadrants. I use All Students Take Calculus, but what it means is in the first quadrant All the trig functions are positive. Only Sine (and fam) are positive in the 2nd quadrant. Tan (and fam) in the 3rd and Cos and fam in the 4th quadrant. It's a good quick check.

cos q = 3/5 OR cos q = .6