Why can't you factor 2cosx^2+sinx-1=0 ?

Answers

Answer 1

Answer: $2cos^2x+sinx-1=0\n\n2(1-sin^2x)+sinx-1=0\n\n2-2sin^2x+sinx-1=0\n\n-2sin^2x+sinx+1=0\n\n-2sin^2x+2sinx-sinx+1=0\n\n-2sinx(sinx-1)-1(sinx-1)=0\n\n(sinx-1)(-2sinx-1)=0\iff sinx-1=0\ or\ -2sinx-1=0\n\nsinx=1\ or\ -2sinx=1\n\nsinx=1\ or\ sinx=-(1)/(2)\n\nx=(\pi)/(2)+2k\pi\ or\ x=-(\pi)/(6)+2k\pi\ or\ x=(7\pi)/(6)+2k\pi\ where\ k\in\mathbb{Z}$

Answer 2

Answer: $2cosx^2+sinx-1=2(1-sin^2x)+snx-1=\n\n=2(1-sinx)(1+sinx)-(1-sinx)=(1-sinx)[2(1+sinx)-1]=\n\n=(1-sinx)(2+2sinx-1)=(1-sinx)(1+2sinx)\n\n2cosx^2+sinx-1=0\ \ \ \Leftrightarrow\ \ \ (1-sinx)(1+2sinx)=0\n\n1-sinx=0\ \ \ \ \ or\ \ \ \ \ 1+2sinx=0\n\n1)\ \ \ 1-sinx=0\ \ \ \Rightarrow\ \ \ sinx=1\ \ \ \Rightarrow\ \ \ x= ( \pi )/(2) +2k \pi ,\ \ \ k\in I\n\n$

$2)\ \ \ 1+2sinx=0\ \ \ \ \ \ \Rightarrow\ \ \ sinx=- (1)/(2)\n\n \Rightarrow\ \ \ x_1=( \pi + ( \pi )/(6) )+2k \pi ,\ \ \ \ \ \ x_2=( - ( \pi )/(6) )+2k \pi,\ \ \ \ \ \ k\in I\n\n.\ \ \ \ \ \ x_1=(7 \pi )/(6) +2k \pi ,\ \ \ \ \ \ \ \ \ \ \ \ x_2=-( \pi )/(6) +2k \pi,\ \ \ \ \ \ \ \ \ k\in I\n\nAns.\ x=-( \pi )/(6) +2k \pi\ \ \ or\ \ \ x= ( \pi )/(2) +2k \pi\ \ \ or\ \ \ x=(7 \pi )/(6) +2k \pi,\ \ \ k\in I$

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The image of a parabolic mirror is sketched on a graph. The image can be represented using the function y = x2 + 2, where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis. How far away from the maximum depth is a point on the mirror that is inches in depth? 3 inches 4 inches 5 inches 6 inch

Answers

The equation of the parabola is
y = x2 + 2
where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis

We are asked to solve for the distance from the center of the parabola or simply the value of y given a value of x of 2 inches.

Substituting:
y = 2^2 + 2
y = 6 inches

its not 6 i put that and got it wrong

Which size container of cold farm ice cream is the better deal for Sheldon?

Answers

what are the sizes and what do they cost? I need to know all the info.

The midpoint of a segment is (−6,−5) and one endpoint is (1,3). Find the coordinates of the other endpoint.A. (8, 11)
B. (8, -13)
C. (-13, -13)
D. (-13, 11)

Answers

Answer: C. (-13, -13)

Step-by-step explanation:

The midpoint (x,y) of a line segment having two end points (a,b) and (c,d) is given by :-

$x=(a+c)/(2)\ ;\ y=(b+d)/(2)$

Given : The midpoint of a segment is (-6,-5) and one endpoint is (1,3).

Let the coordinates of other end point be (a,b) then , we have

$-6=(a+1)/(2)\ ;\ -5=(b+3)/(2)\n\n\Rightarrow\ a+1=2*-6\ ;\ b+3=2*-5\n\n\Rightharrow\ a+1=-12\ ;\ b+3=-10\n\n\Rightarrow\ a=-12-1\ ;\ b=-10-3\n\n\Rightarrow\ a=-13,\ ;\ b=-13$

Hence, the coordinates of the other endpoint = (-13,-13)

C. (-13,-13)
You take the x of the midpoint and equal it to the formula of the midpoint so it will be -6 = 1+x/2 so 1st you times 2 by 6 because you wanna get rid of 2 so it will -12 Then when you move 1 so x is alone it will be -1 so -12-1= -13
Same thing for y

For a button to fit through its buttonhole, the hole needs to be the size of the button's diameter. What size buttonhole is needed for a button with a circumference of 7.38 centimeters? (Use the value of 3.14 to represent pi, and the formula for circumference = 2*pi*r)

Answers

A button with a circumference of 7.38 cm will need a buttonhole with the size of 2.35 cm.

Since the circumference is equivalent to 7.38 cm, the formula can be displayed as follows:
7.38 cm = 2πr
r = 7.38cm/2π
r= 1.1751592 cm
diameter = 2r
= 2.3503184 cm or approximately 2.35 cm

Find the perimeter of the figure. Answer exactly or round to at least 2 decimal places.-width is 5 and height is 5

Answers

all you have to do is add up the angles total will equal up to 32.85

That's a square and a semicircle so we should calculate the perimeter for each one and then add them together.

Let's start with the easy one: the square
The perimeter of a square = 4x where x = one side of the square
Since the width of the shape is 5, that means the other three sides of the square should also be five so:

perimeter of square = 4(5)
perimeter of square = 20 units

Now let's find the perimeter of the semicircle.
That equation is this:

perimeter of semicircle = 1/2(π x diameter) + diameter

We know that the width is 5 which means the diameter is 5.
Let's plug that in!

perimeter of semicircle = 1/2(π x 5) + 5

Multiplying pi by 5 and dividing it in half will give us a decimal, so we have to round that to the second place:

perimeter of semicircle = 1/2(5π) +5
perimeter of semicircle ≈ 7.85 + 5
perimeter of semicircle ≈ 12.85 units

Like we said at the beginning, this is two shapes in one so we have to add the perimeter of the square to the perimeter of the semicircle

perimeter of square = 20 units
perimeter of semicircle ≈ 12.85 units

20 + 12.85 = 32.85 units

So the perimeter of the shape = 32.85 units

If three times a number minus 2 equals 13, what is the number?

Answers

Change the messy words into numerals
3 times a number minus 2    equals    13
3 × n - 2 = 13

3n - 2 = 13
take 2 to the other side
3n - 2 + (2) = 13 + (2)
3n = 15

Divide by 3 on either sides to isolate n
$(3n)/(3)$ = $(15)/(3)$
3 and 3 cancels out

n = 5

check:
3 times 5 minus 2 equals 13
3   × 5 - 2 = 13
15 - 2 = 13
13 =    13

The number is 5

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