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Reptile [31]
2 years ago
13

Find sin(a+B)

Mathematics
1 answer:
diamong [38]2 years ago
6 0

Answer:

Cos A=5/13

we have

Cos² A=1-Sin ²A

25/169=1-Sin²A

sin²A=1-25/169

sin²A=144/169

Sin A=\sqrt{144/169}=12/13

again

Tan B=4/3

P/b=4/3

p=4

b=3

h=\sqrt{3²+4²}=5

Now

Sin B=p/h=4/5

in IV quadrant sin angle is negative so

Sin B=-4/5

CosB=b/h=3/5

Now

<u>S</u><u>i</u><u>n</u><u>(</u><u>A</u><u>+</u><u>B</u><u>)</u><u>:</u><u>s</u><u>i</u><u>n</u><u>A</u><u>c</u><u>o</u><u>s</u><u>B</u><u>+</u><u>C</u><u>o</u><u>s</u><u>A</u><u>s</u><u>i</u><u>n</u><u>B</u>

<u>n</u><u>o</u><u>w</u><u> </u>

<u>substitute</u><u> </u><u>value</u>

<u>Sin(A+B):</u>12/13*3/5+5/13*(-4/5)=36/65-4/13

<u>=</u><u>1</u><u>6</u><u>/</u><u>6</u><u>5</u><u> </u><u>i</u><u>s</u><u> </u><u>a</u><u> </u><u>required</u><u> </u><u>answer</u>

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For what values of a is the sum of the fractions 2a−1/4 and a−1/3 positive?
Elenna [48]

\left(2a-\dfrac{1}{4}\right)+\left(a-\dfrac{1}{3}\right) > 0\\\\(2a+a)-\dfrac{1}{4}-\dfrac{1}{3} > 0\\\\3a-\dfrac{1}{4}-\dfrac{1}{3} > 0\qquad|\cdot12\\\\12(3a)-12\left(\dfrac{1}{4}\right)-12\left(\dfrac{1}{3}\right) > 0\\\\36a-3-4 > 0\\\\36a-7 > 0\qquad|+7\\\\36a > 7\qquad|:36\\\\a > \dfrac{7}{36}

3 0
3 years ago
Y’all I really need help with this, please help !!
gogolik [260]
2. The chord is bisected by the segment from the center, so you have a right triangle with legs 4 and 6. The hypotenuse is the radius of the circle, x.
   x = √(4^2 +6^2) = √(16+36) = √52
   x = 2√13

4. By the rules for secants, the product of the lengths of the parts of the chord is the same in each case.
   3*7 = 2*x
   x = 21/2
   x = 10.5

6. The measure of angle "a" is the average of the two intercepted arcs.
   a = (165° + 55°)/2
   a = 110°
Of course, b is its supplement.
   b = 180° - 110°
   b = 70°

8. Secant rules again. The products of the near and far lengths are the same in each case. When the segment is a tangent, the near and far lengths are the same, so it is the square of the tangent length.
   x² = 4(4+12) = 64
   x = 8

10. This works the same way as problem 2. Here, it looks like you have a triangle with hypotenuse 6 and side length 3. The other side length is
   half-chord = √(6² -3²) = √(36 -9) = √27 = 3√3
   AB = 2*(half-chord) = 2*3√3
   AB = 6√3

12. The equation of a circle of radius r and center (h, k) is
   (x-h)² + (y-k)² = r²
Of course, the "passes through" point must satisfy the equation, so you have
   (x-3)² + (y-0)² = r² = (-2-3)² + (-4-0)² = 25+16
   (x-3)² + y² = 41

14. Same as 12. Radius is 4.
   (x+5)² + (y-2)² = 16

16. Radius 2, center (0, -1).
   x² + (y+1)² = 4

18. The angle bisectors for the axes are the lines
   y = x
   y = -x
Here's a plot.

5 0
3 years ago
Math Help Help Fast Alot of points
MrMuchimi

Here mark the angles

  • m<FHG=75
  • m<FGH=55
  • m<GHI=59°
  • m<GIH=63°

By using angle sum property

  • m<IGH=180-122=58

So

  • m<FGH < m<IGH <m<GHI <m<GIH <m <FHG

So

  • FH<IH<GI<GH<FG
8 0
2 years ago
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Is 1/4 greater than 3/4
Eduardwww [97]
No because 3/4 is closer to one so 3/4 is greater
8 0
3 years ago
HELP
alina1380 [7]

Answer:

D

Step-by-step explanation:

72+21-11=82

82-67=15

3 0
2 years ago
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