1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Goshia [24]
1 year ago
6

The expression cosine of pi over 2 times cosine of pi over 3 plus sine of pi over 2 times sine of pi over 3 can be rewritten as

which of the following?

Mathematics
1 answer:
9966 [12]1 year ago
6 0

Solution:

Given;

\cos\frac{\pi}{2}\cos\frac{\pi}{3}+\sin\frac{\pi}{2}\sin\frac{\pi}{3}

Using the identities;

Thus;

\begin{gathered} \cos\frac{\pi}{2}\cos\frac{\pi}{3}+\sin\frac{\pi}{2}\sin\frac{\pi}{3}=\cos(\frac{\pi}{2}-\frac{\pi}{3}) \\  \\ \cos\frac{\pi}{2}\cos\frac{\pi}{3}+\sin\frac{\pi}{2}\sin\frac{\pi}{3}=\cos(\frac{\pi}{6}) \end{gathered}

CORRECT OPTION: A

You might be interested in
What is the result when the number 87 is increased by 3.9%?
RoseWind [281]

Answer:

90.393

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
.Mariam went to the store to buy some apples. The price per pound of the apples is $6 per pound and she has a coupon for $2.25 o
8_murik_8 [283]

Answer:

$15.75

$6p-$2.25

4 0
3 years ago
a walking path across a park is represented by the equation y=-2x-7. A new path will be built perpendicular to this path.The pat
jonny [76]

Answer:

The equation that represents the new path is y=(1/2)x-2

Step-by-step explanation:

step 1

Find the slope of the give line

we have

y=-2x-7

so

the slope m is equal to

m=-2

step 2

Find the slope of the perpendicular line to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal of each other

so

we have

m=-2 -----> slope of the given line

therefore

The slope of the perpendicular line is equal to

m=1/2

step 3

With m=1/2 and the point (-2,-3) find the equation of the line

y-y1=m(x-x1)

substitute

y+3=(1/2)(x+2)

y=(1/2)x+1-3

y=(1/2)x-2 -----> equation that represent the new path

8 0
3 years ago
Read 2 more answers
Consider the three points ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 ) . Let ¯ x be the average x-coordinate of these points, and let ¯ y
loris [4]

Answer:

m=\dfrac{3}{2}

Step-by-step explanation:

Given points are: ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 )

The average of x-coordinate will be:

\overline{x} = \dfrac{x_1+x_2+x_3}{\text{number of points}}

<u>1) Finding (\overline{x},\overline{y})</u>

  • Average of the x coordinates:

\overline{x} = \dfrac{1+2+3}{3}

\overline{x} = 2

  • Average of the y coordinates:

similarly for y

\overline{y} = \dfrac{3+3+6}{3}

\overline{y} = 4

<u>2) Finding the line through (\overline{x},\overline{y}) with slope m.</u>

Given a point and a slope, the equation of a line can be found using:

(y-y_1)=m(x-x_1)

in our case this will be

(y-\overline{y})=m(x-\overline{x})

(y-4)=m(x-2)

y=mx-2m+4

this is our equation of the line!

<u>3) Find the squared vertical distances between this line and the three points.</u>

So what we up till now is a line, and three points. We need to find how much further away (only in the y direction) each point is from the line.  

  • Distance from point (1,3)

We know that when x=1, y=3 for the point. But we need to find what does y equal when x=1 for the line?

we'll go back to our equation of the line and use x=1.

y=m(1)-2m+4

y=-m+4

now we know the two points at x=1: (1,3) and (1,-m+4)

to find the vertical distance we'll subtract the y-coordinates of each point.

d_1=3-(-m+4)

d_1=m-1

finally, as asked, we'll square the distance

(d_1)^2=(m-1)^2

  • Distance from point (2,3)

we'll do the same as above here:

y=m(2)-2m+4

y=4

vertical distance between the two points: (2,3) and (2,4)

d_2=3-4

d_2=-1

squaring:

(d_2)^2=1

  • Distance from point (3,6)

y=m(3)-2m+4

y=m+4

vertical distance between the two points: (3,6) and (3,m+4)

d_3=6-(m+4)

d_3=2-m

squaring:

(d_3)^2=(2-m)^2

3) Add up all the squared distances, we'll call this value R.

R=(d_1)^2+(d_2)^2+(d_3)^2

R=(m-1)^2+4+(2-m)^2

<u>4) Find the value of m that makes R minimum.</u>

Looking at the equation above, we can tell that R is a function of m:

R(m)=(m-1)^2+4+(2-m)^2

you can simplify this if you want to. What we're most concerned with is to find the minimum value of R at some value of m. To do that we'll need to derivate R with respect to m. (this is similar to finding the stationary point of a curve)

\dfrac{d}{dm}\left(R(m)\right)=\dfrac{d}{dm}\left((m-1)^2+4+(2-m)^2\right)

\dfrac{dR}{dm}=2(m-1)+0+2(2-m)(-1)

now to find the minimum value we'll just use a condition that \dfrac{dR}{dm}=0

0=2(m-1)+2(2-m)(-1)

now solve for m:

0=2m-2-4+2m

m=\dfrac{3}{2}

This is the value of m for which the sum of the squared vertical distances from the points and the line is small as possible!

5 0
3 years ago
Two numbers that differ by 46
Reil [10]

the complete question is

Find two numbers whose difference is 46 and whose product is a minimum


Let

x------->larger number

y-------> smaller number

P-------> product of the two numbers


we know that

x-y=46\\ y=x-46-----> equation 1

P=x*y-----> equation 2


substitute equation 1 in equation 2

P=x*[x-46]\\ P=x^{2} -46x


using a graph tool

see the attached figure


Find the value of x for that the product P is a minimum

the vertex is the point (23,-529)

that means, for x=23

the product is a minimum P=-529


find the value of y

y=x-46\\ y=23-46\\ y=-23


therefore


the answer is

the numbers are 23 and -23

7 0
3 years ago
Read 2 more answers
Other questions:
  • 10^6+10^6 is equal to what.?
    9·1 answer
  • If cotθ = 2, then the value of the expression cot2 θ+ cosec2θ is
    5·1 answer
  • 2/3x = -12 how do you solve this​
    13·2 answers
  • Given y=-3/4x-2. What is the equation of the line that is perpendicular and has the point (-4,1)? Write answer in slope intercep
    6·1 answer
  • Suppose that 30% of all houses need a paint job. Also, 15% of all houses need both a paint job and a new roof. Further, 7% of al
    9·1 answer
  • helpp meeeeeeeeee (08.06 MC)Consider the following dot plot. Of the following statements, which two characteristics of this dot
    10·2 answers
  • I just want a joke im board please help me.
    7·2 answers
  • _ % of 4 is 7 someone pls help me
    9·1 answer
  • Answer the photo below thanks
    10·1 answer
  • Solve for X (step by step please)<br>3 (x - 2) = 4x + 2 <br>[?]x - [ ] = 4x + 2​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!