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marishachu [46]
3 years ago
8

Solving polynomial equations

Mathematics
1 answer:
Yuliya22 [10]3 years ago
5 0

Answer:

x= 1 or x= 1.56 (3 s.f.) or x= -2.56 (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

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If 2tanA=3tanB then prove that,<br>tan(A+B)= 5sin2B/5cos2B-1​
Fed [463]

By definition of tangent,

tan(A + B) = sin(A + B) / cos(A + B)

Using the angle sum identities for sine and cosine,

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

yields

tan(A + B) = (sin(A) cos(B) + cos(A) sin(B)) / (cos(A) cos(B) - sin(A) sin(B))

Multiplying the right side by 1/(cos(A) cos(B)) uniformly gives

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) tan(B))

Since 2 tan(A) = 3 tan(B), it follows that

tan(A + B) = (3/2 tan(B) + tan(B)) / (1 - 3/2 tan²(B))

… = 5 tan(B) / (2 - 3 tan²(B))

Putting everything back in terms of sin and cos gives

tan(A + B) = (5 sin(B)/cos(B)) / (2 - 3 sin²(B)/cos²(B))

Multiplying uniformly by cos²(B) gives

tan(A + B) = 5 sin(B) cos(B) / (2 cos²(B) - 3 sin²(B))

Recall the double angle identities for sin and cos:

sin(2x) = 2 sin(x) cos(x)

cos(2x) = cos²(x) - sin²(x)

and multiplying uniformly by 2, we find that

tan(A + B) = 10 sin(B) cos(B) / (4 cos²(B) - 6 sin²(B))

… = 10 sin(B) cos(B) / (4 (cos²(B) - sin²(B)) - 2 sin²(B))

… = 5 sin(2B) / (4 cos(2B) - 2 sin²(B))

The Pythagorean identity,

cos²(x) + sin²(x) = 1

lets us rewrite the double angle identity for cos as

cos(2x) = 1 - 2 sin²(x)

so it follows that

tan(A + B) = 5 sin(2B) / (4 cos(2B) + 1 - 2 sin²(B) - 1)

… = 5 sin(2B) / (4 cos(2B) + cos(2B) - 1)

… = 5 sin(2B) / (4 cos(2B) - 1)

as required.

5 0
2 years ago
Write an extended response that analyzes the effectiveness of John F Kennedy's Inaugural Address, January 20, 1961, based on you
ioda

Answer:

huhhh  i dont understand fully

Step-by-step explanation:

6 0
3 years ago
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0
horsena [70]
X=-1
-1x2 + 5x-1 +7 = 0
-7+7 =0
0=0
6 0
3 years ago
40 POINTS NEED HELP ASAP
sesenic [268]
Use slope formula: y2-y1/x2-x1

XZ: -5/9
YZ: 2/7
XY: -7/2

XYZ is a right triangle because two of these slopes have a product of -1.

(YZ and XY does).  We are all busy these days.
7 0
3 years ago
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Which expression can be used to check the answer to 56 ÷ (-14) = n?
kozerog [31]
A. Multiplication is the ONLY function that reverses what division did. If you did 56/-14 = n, then n x -14 should equal 56.
6 0
3 years ago
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