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NISA [10]
3 years ago
7

How do you simplify 2 sin (4theta) cos (4theta), using a double-angle formula?

Mathematics
1 answer:
VikaD [51]3 years ago
3 0
<span>sin(4θ)=sin(2⋅2θ)</span><span> You would use the double angle formula twice here. hope this helps :D</span>
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Write a polynomial of least degree with rational coefficients, a leading coefficient of 1, and zeros at 3 and sqr root 7. Expand
Tresset [83]

Answer:

(x-3)(x^2-7) = x^3 -3x^2 -7x + 21

just change the sign of the root and put x in front of it, then multiply the factors all together

(x-3)(x-sqr7)(x+sqr7)    roots come in conjugate pairs to eliminate irrational coefficients

(x-sqr7)(x+sqr7) = x^2-7.  similar to (a-b)(a+b) = a^2-b^2

Step-by-step explanation:

6 0
3 years ago
A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o
Drupady [299]

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

W - 120 = 0

W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

6000ft² = L × W

L = 6000/W

L = 6000/120

L = 50 feet

The dimensions of the land, correct to the nearest foot is 50ft by 120ft

3 0
3 years ago
Allen is given three lengths of rope: 4 feet, 8 feet, and 15 feet. Can Allen form a triangle with side lengths of 4 feet, 8 feet
Nady [450]

B) No, set of side lengths does not satisfy Triangle Inequality Theorem

5 0
3 years ago
Read 2 more answers
Refer to the rectangle below. The length of the rectangle is x + 12. The width of the rectangle is x + 3.
Elis [28]

Answer:

x^2+15x+36

Step-by-step explanation:

The complete question is shown in the attachment.

The length of the rectangle is x + 12. The width of the rectangle is x + 3.

Recall that area of a rectangle is Length \times Width

In terms of x, the area is (x+12)(x+3)

Recall the distributive property of real numbers: (a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get:

(x+12)(x+3)=x(x+3)+12(x+3)

We expand again to get:

(x+12)(x+3)=x^2+3x+12x+36

We now simplify to obtain:

(x+12)(x+3)=x^2+15x+36

The area of the rectangle is x^2+15x+36

4 0
3 years ago
Please is urgent!!! ​
Sophie [7]

Answer:

70.6x 10-⁵ is answer of first

4 0
3 years ago
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