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2 years ago

Solve the equations below exactly. Give your answers in radians, and find all

Mathematics

1 answer:

kotegsom [21]2 years ago

8 0

Answer:

See below (along with unit circle attached)

Step-by-step explanation:

$sin(t)=-\frac{\sqrt{3}}{2}$

$t=\frac{4\pi}{3},\frac{5\pi}{3}$

$cos(t)=\frac{1}{2}$

$t=\frac{\pi}{3},\frac{5\pi}{3}$

It really helps to use the unit circle! I've attached it below for your convenience. Keep in mind that a point on the unit circle is defined by $(cos(\theta),sin(\theta))$ where $\theta$ is measured in radians.

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Find the component form for vector AB given the initial point A (1, 7, -9) and terminal point B (-2, 18, 4).

Tanzania [10]

To find each of the components of AB we can find the different between the components on the terminal and initial points, doing that, we find:

AB = (-2 - 1, 18 -7, 4 - (-9)) = (-3, 11, 13).

5 0

3 years ago

Students at Hampton Middle School sold T-shirts as a school fundraiser. Sylvie asked 12 random seventh-grade students how many T

natulia [17]

Answer:

4.1 shirts

Step-by-step explanation:

Mean can be found by adding all data points and dividing that by the total amount of data points.

There are 12 students selling shirt, which gives you 12 data points.

So (3+4+8+5+2+5+0+5+3+4+3+7)/12 = 4.083...

Which rounds to 4.1 shirts

6 0

3 years ago

The vertex of this parabola is at (3,5). When the Y value is 6X value is negative one what is the coefficient of the squared ter

iren2701 [21]

We know that equation of a parabola is given by :-

y = a(x-h)² + k

Where (h,k) is the vertex of parabola and (x,y) is any point on its curve.

Given that vertex of parabola is (3,5) and one point (x,y) is (6,-1).

We can plug the given information in the equation of parabola and solve it for value of 'a' :-

-1 = a(6 - 3)² + 5

-1 = a(3)² + 5

-1 = 9a + 5

9a = -1 -5 = -6

a = $\frac{-6}{9} = \frac{-2}{3}$

a = $\frac{-2}{3}$ is the final answer.

7 0

3 years ago

Hurry pleaseeeeeeeeeeeeeeeeeeeeeee

Setler [38]

Answer:27

Step-by-step explanation:

7 0

3 years ago

What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47+ ...?

Alex

Answer:

$\huge\boxed{18,475}$

Step-by-step explanation:

The terms of this sum make the arithmetic sequence.

The fomula of a sum of <em>n</em> terms of an arithmetic sequence:

$S_n=\dfrac{[2a_1+(n-1)d]\cdot n}{2}$

We have

$a_1=2\\d=17-2=32-12=47-32=15\\n=50$

Substitute:

$S_{50}=\dfrac{[2\cdot2+(50-1)\cdot15]\cdot50}{2}=(4+49\cdot15)\cdot25=(4+735)\cdot25\\\\=739\cdot25=18,475$

3 0

3 years ago