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dimulka [17.4K]
3 years ago
6

Find the exact value of sin(11pi/12)cos(pi/6)-cos(11pi/12)sin(pi/6)

Mathematics
1 answer:
krek1111 [17]3 years ago
6 0
We use the identity  sin (A - B) = sin A cos B - cos B sin A

so the above  = sin (11pi/12 -  pi/6) = sin 3pi/4 =  1 / sqrt2 answer
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Need help on this!!!!
Alexxandr [17]

Answer:

  • (a)  area = 3y^2 +14y +16
  • (b)  perimeter = 8y +20

Step-by-step explanation:

Part of the point of Algebra is that you can work with things that stand for numbers (almost) as easily as working with numbers themselves. Here, you are given values that stand for the length and width of the rectangle.

(a) You know the area of a rectangle is found by multiplying its length by its width. The same is true when length and width are algebraic expressions that stand for those numbers.

  <u>Given:</u> length = 3y+8, width = y+2

  <u>Find:</u> area = length × width

  <u>Solution:</u>

     area = (3y+8) × (y+2)

Using the distributive property, we can perform this multiplication in essentially the same way we would for the numbers 38 and 12.

     area = 3y(y +2) +8(y +2)           equivalent to 30(12) +8(12)

     = 3y^2 +6y +8y +16                  equivalent to 30·10 +30·2 +8·10 +8·2

     area = 3y^2 +14y +16              equivalent to 3·10^2 +14·10 +16

(Of course, with numbers, there are relationships between units and tens and hundreds that let us further combine terms. When variables are involved, we can combine terms with the same power of the variable, but we cannot combine "y" terms with "y^2" terms the way we can with numbers.)

___

(b) The perimeter is the sum of the lengths of the four sides of the rectangle. Since two of those sides are "length" and two are "width", we can write ...

  perimeter = 2(length + width)

Making the substitution for length and width as defined above, we have

  perimeter = 2((3y+8) + (y+2))

  = 2(3y+y + 8+2) = 2(4y +10)

  perimeter = 8y +20

5 0
3 years ago
Solve -np-80&lt;60 for n. Show your work.<br><br> Solve 2a-5d=30 for d. Show your work.
xz_007 [3.2K]

-np-80 < 60\qquad\text{change the signs}\\\\np+80

------------------------------------------------------

2a-5d=30\qquad\text{subtract 2a from both sides}\\\\-5d=-2a+30\qquad\text{change the signs}\\\\5d=2a-30\qquad\text{divide both sides by 5}\\\\d=0.4a-6

8 0
3 years ago
Please answer asap I really need it til 2.00 p.m, A sporting good store manager was selling a ski set for a certain price. The m
coldgirl [10]

Answer:

the ski original price is 641

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What is 250/363 in its simplest form
zaharov [31]
You find the GCF of 250 and 363 by factoring. 250 = 5^4 * 2. 363 = 3 * 11^2, and they have no common factors, so 250/363 is already in its simplest form!
8 0
3 years ago
What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
Maksim231197 [3]
Hello,
 the first step should be to distribue:
-4(3-5x)= -12+20x

Teh resolution may be:

-4(3-5x)>=-6x+9
==>-12+20x>=-6x+9
==>20x+6x>=9+12
==>26x>21
==>x>=21/26

But an other way may be used:

-4(3-5x)>=-6x+9
==>3-5x<= -6x/(-4)+9/(-4)
==>-5x-3/2 x<=-9/4 -3

==>-13/2 x <=-21/4

==>x>= -21/4 *(-2/13)
==>x>=21/(2*13)
==>x>=21/26

5 0
3 years ago
Read 2 more answers
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