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2 years ago

Find the exact value for cos π 12 applying sum and difference formulas involving π 3 and π 4 .

1 answer:

8 0

First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, π/12 can be split into π/3−π/4.

cos(π/3−π/4)

Use the difference formula for cosine to simplify the expression. The formula states that cos(A−B)=cos(A)cos(B)+sin(A)sin(B)

cos(π/3)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/3) is 12, so:

(12)⋅cos(π/4)+sin(π/3)⋅sin(π/4)

The exact value of cos(π/4) is √22.

(12)⋅(√22)+sin(π/3)⋅sin(π/4)

The exact value of sin(π/3) is √32.

(12)⋅(√22)+(√32)⋅sin(π/4)

The exact value of sin(π/4) is √22.

(12)⋅(√22)+(√32)⋅(√22)

Simplify each term:

√24+√64

Combine the numerators over the common denominator.

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HURRYYY HELP! Triangle ABC is congruent to triangle FDE, and both triangles have the same orientation, as shown. What is the slo

muminat

We know that
point A(1,1) C(3,5)
point D(-2,-4) F(0,0)

step 1
find the slope FD
m=(y2-y1)/(x2-x1)------> m=(0+4)/(0+2)----> m=4/2----> m=2

step 2
find the slope AC
m=(y2-y1)/(x2-x1)------> m=(5-1)/(3-1)----> m=4/2-----> m=2

mAC=mFD

the answer is
the slope FD is 2

8 0

2 years ago

A freight carrier charges $0.57 for a package weighing up to one ounce plus and additional $0.32 for each additional ounce or fr

kherson [118]

We have to write an equation that uses this info so we can find the cost to ship that package. However, the package weight is given to us in grams and we need it in ounces. So first thing we are going to do is convert that 224 g to ounces. Use the fact that 1 g = .035274 ounces to convert. $224g*\frac{.035274oz}{1g}$ . Do the multiplication and cancel out the label of grams and we have 7.901376 ounces. Ok. We know that it costs .57 to mail the package for the first ounce. We have almost 8 ounces. So no matter what, we are paying .57. For each additional ounce we are paying .32. The number of .32's we have to spend depends upon how much the package goes over the first ounce. For the first ounce we pay .57, then for the remaining 6.901376 ounces we pay .32 per ounce. Our equation looks like this: C(x) = .32(6.901376) + .57 and we need to solve for the cost, C(x). Doing the multiplication we find that it would cost $2.78 to ship that package.

3 0

2 years ago

Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be model

ohaa [14]

Answer:

(2, 11/2)

Step-by-step explanation:

This is a vertical parabola; we know that because x is squared here, while y is not. The standard equation of a vertical parabola with vertex (h,k) is

4p(y-k) = (x-h)^2, where p is the distance between the vertex and the focus. Comparing

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

10(y-3) = (x-2)^2, we see that 4p = 10. Therefore, p = 10/4 = 5/2, which is the vertical distance between the focus and the vertex.

Since the coordinates of the vertex are easily read from the given equation

(x-2)^2=10(y-3): (h,k) = (2, 3)

all we need to do is to add p (5/2) to the y-coordinate (3);

The focus is at (2, 3 + 5/2), or (2, 11/2).

3 0

2 years ago

Sal was tired of waiting for Amir to show up at their meeting place, so he started running at an average speed of 4.5 mph withou

skelet666 [1.2K]

Let s and a represent the position of Sal and Amir respectively.

s=.75+4.5t and a=-.25+6.7t

When Sal catches Amir, s=a so we can say.

-.25+6.7t=.75+4.5t subtract 4.5t from both sides

-.25+2.2t=.75 add .25 to both sides

2.2t=1 divide both sides by 2.2

t=5/11 hours

t≈0.45 hours (to nearest hundredth of an hour)

3 0

2 years ago

Read 2 more answers

The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents th

Novay_Z [31]

Answer:

Step-by-step explanation:

I use 84+ CE

stat edit, then fill in the #s

then

vars 5

then

2'nd stat plot, on

then, click stat

Click arrow 1 time to the left to get to Calc

then click (4)(LinReg(ax+b))

then click enter 5 times

(y=-25.31428571x+1000.285714

y=-25.3x+1000.3

now, lets use computer:

y=-25.31(543)+1000.3

y=-12743.03

round to the biggest whole number )

this doesn't really work, so I will put 1999, 2000, 2001, 2002, 2003, 2004 instead of 0, 1, 2, 3, 4, 5 and do the same thing

now I get

y=-25.31428571x+51603.54286

y=-25.3x+51603.5

now, lets use computer:

y=-25.3(543)+51603.5

y=37865.6

round to the biggest whole number:

y=37866

so, year 37866

7 0

2 years ago