How do I solve 4cos^2 x -1=0

Answers

Answer 1

Answer: $(cosx)^(2) = 1/4$ <=> cosx = +1/2 or cosx = -1/2;
cosx = +1/2 => x = +π/3 + 2kπ, where k is an integer or x = -π/3 + 2kπ, where k is an integer;
cosx = -1/2 => x = +2π/3 + 2kπ, where k is an integer or x = -2π/3 + 2kπ, where k is an integer;

Answer 2

Answer:

Answer:

pi/3? 2pi/3?

Step-by-step explanation:

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3. What is the slope of the table shown? Cars Washed Number Money ($) 5 40 10 80 15 120 20 160

Answers

The slope is 8.
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F (x + 3)2 = 42, what is the approximate positive value of x? 0.48
3.48
5.48
6.48

Answers

Answer:

3.48

Step-by-step explanation:

I took the test.

Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2.

Answers

- Vertex : ( 0, 0 ).
- Focus: ( p/2, 0 );
y² = 1/4 x
y² = 2 p x ⇒ 2 p = 1/4
p = 1/8
p/2 = 1/16
F ( 1/16, 0)
- Directrix:
x = - p/2 x
x = - 1/16 x
- The focal length:
2 p = 2 · 1/8 = 1/4

Answer:

The vertex is (0,0), focus of the parabola is $((1)/(16),0)$ , directrix of the parabola is $y=-(1)/(16)$ , focal width is $(1)/(4)$ .

Step-by-step explanation:

The given equation of parabola is

$x=4y^2$

It can be written as

$y^2=(1)/(4)x$ ....(1)

The general equation of parabola is

$(y-k)^2=4p(x-h)$ ... (2)

Where, (h,k) is vertex, (h+p,k) is focus, y=h-p is directrix and |4p| is focal width.

On comparing (1) and (2), we get

$h=0,k=0$

The vertex is (0,0).

$4p=(1)/(4)$

$p=(1)/(16)$

Focus of the parabola is

$(h+p,k)=(0+(1)/(16),0)=((1)/(16),0)$

Therefore focus of the parabola is $((1)/(16),0)$ .

Directrix of the parabola is

$y=h-p=0-(1)/(16)=-(1)/(16)$

Directrix of the parabola is $y=-(1)/(16)$ .

Focal width is

$|4p|=|4* (1)/(16)|=(1)/(4)$

Focal width is $(1)/(4)$ .

What is the greatest number of acute angles that a triangle can contain?

Answers

Answer:

The greatest number of acute angle a triangle can contain are:

Step-by-step explanation:

We know that a acute angle is a angle whose measure is less than 90°.

Now we know that the sum of all the angles of a triangle is 180°.

Now we have to find such 3 angles which are less than 90° and add up to 180°.

Let we consider a equilateral triangle.

In a equilateral triangle each angle measures 60°<90°.

and also:

60+60+60=180°.

Hence, the greatest number of acute angles a triangle can contain are:

3 because you can have a 60 60 60 triangle

Biologists are treating a lake contaminated with bacteria. The level of contamination is changing at a rate of dN/dt=-1110/t² -230 bacteria percubic centimeter per day, where is the number of days since treatment began. Find a function N(t) to estimate the level of contamination if the
level after I day was 5380 bacteria per cubic centimeter.

Answers

Answer: the function N(t) to estimate the level of contamination in the lake is:

N(t) = -1110 ln(t) - 230t + 1110 ln(I) + 230I + 5380

Step-by-step explanation: ∫ dN/dt dt = ∫ (-1110/t² -230) dt

N(t) = -1110 ln(t) - 230t + C

N(I) = -1110 ln(I) - 230I + C = 5380

C = 1110 ln(I) + 230I + 5380

A quadrilateral has vertices (-5,0), (2,8), (4,-5) and (7,3). Which matrix is the coordinate matrix for the given quadrilateral?

Answers

Answer:

The matrix that is the coordinate matrix of the given quadrilateral is:

$A.\ \left[\begin{array}{cccc}-5&2&4&7\n0&8&-5&3\end{array}\right]$

Step-by-step explanation:

We know that the vertices of a quadrilateral are expressed in form of a matrix by placing the vertices along the column of a matrix.

i.e. the vertex A(-5,0) form the first column of a matrix and similarly the vertex B form the second column of the matrix ; C from the third column of the matrix and D form the third column of the matrix.

Hence, the answer is:

Matrix A

(-5, 2, 4, 7)
0 8 -5 3

The co-ordinates are just rewritten in form of a column vector. This gives a matrix of order 2x4

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