<img src="https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B4%7D%20-x%5E%7B3%7D%20-7x%5E%7B2%7D%20%2B10%2B5x" id="TexFormula1" title="f(

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3 years ago

x)=x^{4} -x^{3} -7x^{2} +10+5x" alt="f(x)=x^{4} -x^{3} -7x^{2} +10+5x" align="absmiddle" class="latex-formula">
1. write in standard form
2. use Descartes rule of sign
3. possible roots
4. first synthetic division
5. reconsider possible roots
6. second synthetic division
7. quadratic equation
8. solution set

Mathematics

1 answer:

Slav-nsk [51]3 years ago

7 0

Nice hfiebeiciysbwjwkdkcoc

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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

Divide: 2/3 4/5<br> plz help me

HACTEHA [7]

Answer:

5/6

Step-by-step explanation:

brainliest please

8 0

2 years ago

A train takes 1.5 hours to travel 525 km. Calculate the speed of the train in kilometers per hour.

kow [346]

Answer:

1.5 hours to 525 km

Speed in km/h=

$525 \div 1.5 = 350 \: kmph$

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Colton is going to invest $76,000 and leave it in an account for 15 years. Assuming the interest is compounded daily, what inter

olga2289 [7]

Answer: 4.75%

Step-by-step explanation:

4 0

3 years ago

Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the inter

hoa [83]

Answer:

0.20 and 0.36

Step-by-step explanation:

y(t) = 2 sin (4π t) + 5 cos (4π t)

We wish to convert this to:

y = A sin(ωt + φ)

We know that ω = 4π. We also know the following:

5 = A sin φ

2 = A cos φ

Divide the first equation by the second equation:

5/2 = tan φ

φ = tan⁻¹(5/2)

Now, square the two equations and add them together.

5² + 2² = (A sin φ)² + (A cos φ)²

29 = A²

A = √29

The equation of the wave is therefore:

y = √29 sin(4π t + tan⁻¹(5/2))

The maximum negative position is -√29. And half of that is -½√29.

-½√29 = √29 sin(4π t + tan⁻¹(5/2))

-½ = sin(4π t + tan⁻¹(5/2))

7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)

7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π

t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24

Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.

t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24

t ≈ 0.20 or 0.36

5 0

3 years ago