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Galina-37 [17]
2 years ago
7

How do I factor this? cos^4x - sin^4x

Mathematics
2 answers:
padilas [110]2 years ago
6 0

Answer: https://socratic.org/questions/how-do-you-simplify-cos-4x-sin-4x#618537

IgorLugansk [536]2 years ago
4 0

Answer:

Step-by-step explanation:

FYI,

a² - b² = (a + b)(a - b)

f(x) = cos^{4} x - sin^{4} x = (cos²x + sin²x)(cos²x - sin²x) =

= <em>(cos²x + sin²x)(cos x + sin x)(cos x - sin x)</em>

If you need to simplify, then

f(x) = 1 × (cos²x - sin²x) = <em>cos(2x)</em>

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Find the vertex form of: y=2x^2-5x+13
Ket [755]
The vertex form of a quadratic function is:

 f(x) = a(x - h)² + k

The coordinate (h, k) represents a parabola's vertex.

In order to convert a quadratic function in standard form to the vertex form, we can complete the square.

y = 2x² - 5x + 13

Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.

y - 13 = 2x² - 5x

Factor out 2 on the right side of the equation.

y - 13 = 2(x² - 2.5x)

Add (b/2)² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2)² by 2 again on the left side.

y - 13 + 2(2.5/2)² = 2(x² - 2.5x + (2.5/2)²)

y - 13 + 3.125 = 2(x² - 2.5x + 1.5625)

Add the constants on the left and factor the expression on the right to a perfect square.

y - 9.875 = 2(x - 1.25)²

Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.

y = 2(x - 1.25)² + 9.875

Vertex: (1.25, 9.875)

Solution: y = 2(x - 1.25)² + 9.875

Or if you prefer fractions

y = 2(x - 5/4)² + 79/8
7 0
3 years ago
A 5-meter ladder is leaning against the side of a house. The foot of the ladder is pulled away from the house at a rate of 0.4 m
Flura [38]
<h2>The top of the ladder is descending at 0.3 m/s.</h2>

Step-by-step explanation:

By Pythagoras theorem we know that

              Hypotenuse² = Base² + Perpendicular²

                   h² = b² + p²

We have for ladder

                        h = 5 m

                        b = 3 m

                        5² = 3² + p²

                        p = 4 m

                        \frac{db}{dt}=0.4m/s\\\\\frac{dh}{dt}=0

Differentiating h² = b² + p² with respect to time

                    2h\times \frac{dh}{dt}=2b\times \frac{db}{dt}+2p\times \frac{dp}{dt}\\\\5\times 0=3\times 0.4+4\times \frac{dp}{dt}\\\\\frac{dp}{dt}=-0.3m/s

The top of the ladder is descending at 0.3 m/s.

3 0
3 years ago
What is the slope of the line? 7x+2y=57x+2y=5
skad [1K]

Answer:

Step-by-step explanation:

6 0
3 years ago
Evaluate the function k(x)=5 for the given value of x. Simplify your answer.
coldgirl [10]

Answer:

5

Step-by-step explanation:

k(x)=5 says I'm 5 no matter the value of x...

So therefore

k(-4)=5

k(56)=5

k(66378)=5

k(whatever)=5

k(x) is constantly 5 for whatever input x.

4 0
2 years ago
today a boat valued at $45,000.Thebvalue is expected to decrease at a rate of 8.5% each year.What is the value of the boat expec
Stels [109]

Current value of the boat = $45000

Rate at which the value decrease = 8.5%

Value decreased after 1 year = \frac{8.5}{100}\times45000=3825

Hence, value becomes = 45000-3825=41175

Value decreased after 2nd year =

\frac{8.5}{100}\times41175=3499.875

Hence, value becomes = 41175-3499.875=37675.125

Value decreased after 3 year =

\frac{8.5}{100}\times37675.125=3202.385

Hence, value becomes = 37675.125-3202.385=34472.74

So, value of the boat after 3 years becomes $34472.74

3 0
3 years ago
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