All categories

3 years ago

Solve 2cos^2x+3cosx-2=0

1 answer:

8 0

$\bf 2cos^2(x)+3cos(x)-2=0\impliedby \textit{so, notice is just a quadratic}
\\\\\\\
[2cos(x)~~-~~1][cos(x)~~+~~2]=0\\\\
-------------------------------\\\\
2cos(x)-1=0\implies 2cos(x)=1\implies cos(x)=\cfrac{1}{2}
\\\\\\
\measuredangle x=cos^{-1}\left( \frac{1}{2} \right)\implies \measuredangle x=
\begin{cases}
\frac{\pi }{3}\\\\
\frac{5\pi }{3}
\end{cases}\\\\
-------------------------------\\\\
cos(x)+2=0\implies cos(x)=-2$

now, for the second case, recall that the cosine is always a value between -1 and 1, so a -2 is just a way to say, such angle doesn't exist.

You might be interested in

Brett writes a number that is the same distance from O as TO 6on a number line, but in the opposite direction. Whatnumber did Br

Gennadij [26K]

since the number is going on the opposite it must be a negative integrer.

and since the number was 6 units away from 0, it should be the half point between the points.

number = 3

since it is going in the oppsoite direction it should be -3

4 0

1 year ago

What is 55% of 75<br> Pls show the work !<br> I really need help

Ahat [919]

75 (your whole) / .55 (percentage) =41.25

4 0

3 years ago

What is a translation (math)

Vikentia [17]

Answer:

Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. In a translation, every point of the object must be moved in the same direction and for the same distance.

Step-by-step explanation:

Hope that helped :)

5 0

3 years ago

Read 2 more answers

**GIVING OUT BRAINLIEST PLS HELP**<br> Which inequality represents the graph below?

BartSMP [9]

Answer:

r≥2.5

it can't be < because the green dot is filled in

r is larger than 2.5 because the arrow goes to the right

7 0

3 years ago

Read 2 more answers

Part A

masya89 [10]

Answer:

Part A) The area of triangle i is $3\ cm^{2}$

Part B) The total area of triangles i and ii is $6\ cm^{2}$

Part C) The area of rectangle i is $20\ cm^{2}$

Part D) The area of rectangle ii is $32\ cm^{2}$

Part E) The total area of rectangles i and iii is $40\ cm^{2}$

Part F) The total area of all the rectangles is $72\ cm^{2}$

Part G) To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) The surface area of the prism is $78\ cm^{2}$

Part I) The statement is false

Part J) The statement is true

Step-by-step explanation:

Part A) What is the area of triangle i?

we know that

The area of a triangle is equal to

$A=\frac{1}{2} (b)(h)$

we have

$b=4\ cm$

$h=1.5\ cm$

substitute

$A=\frac{1}{2} (4)(1.5)$

$Ai=3\ cm^{2}$

Part B) Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii?

we know that

If Triangles i and ii are congruent

then

Their areas are equal

$Aii=Ai$

The area of triangle ii is equal to

$Aii=3\ cm^{2}$

The total area of triangles i and ii is equal to

$A=Ai+Aii$

substitute the values

$A=3+3=6\ cm^{2}$

Part C) What is the area of rectangle i?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=2.5\ cm$

$h=8\ cm$

substitute

$Ai=(2.5)(8)$

$Ai=20\ cm^{2}$

Part D) What is the area of rectangle ii?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=4\ cm$

$h=8\ cm$

substitute

$Aii=(4)(8)$

$Aii=32\ cm^{2}$

Part E) Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii?

we know that

Rectangles i and iii are congruent (have the same size and shape)

If rectangles i and iii are congruent

then

Their areas are equal

$Aiii=Ai$

The area of rectangle iii is equal to

$Aiii=20\ cm^{2}$

The total area of rectangles i and iii is equal to

$A=Ai+Aiii$

substitute the values

$A=20+20=40\ cm^{2}$

Part F) What is the total area of all the rectangles?

we know that

The total area of all the rectangles is

$At=Ai+Aii+Aiii$

substitute the values

$At=20+32+20=72\ cm^{2}$

Part G) What areas do you need to know to find the surface area of the prism?

To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) What is the surface area of the prism? Show your calculation

we know that

The surface area of the prism is equal to the area of all the faces of the prism

The surface area of the prism is two times the area of triangle i plus two times the area of rectangle i plus the area of rectangle ii

$SA=2(3)+2(20)+32=78\ cm^{2}$

Part I) Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?

The statement is false

Because, the three rectangles are not congruent

The total area of the rectangles is $72\ cm^{2}$ and if you multiply the area of one rectangle by 3 you will get $20*3=60\ cm^{2}$

$72\ cm^{2}\neq 60\ cm^{2}$

Part J) Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?

The statement is true

Because, the triangles are congruent

8 0

4 years ago