Answer:
sin(2A) = (2√2 + √3) / 6
Step-by-step explanation:
2A = (A+B) + (A−B)
sin(2A) = sin((A+B) + (A−B))
Angle sum formula:
sin(2A) = sin(A+B) cos(A−B) + sin(A−B) cos(A+B)
sin(2A) = 1/2 cos(A−B) + 1/3 cos(A+B)
Pythagorean identity:
sin(2A) = 1/2 √[1 − sin²(A−B)] + 1/3 √[1 − sin²(A+B)]
sin(2A) = 1/2 √(1 − 1/9) + 1/3 √(1 − 1/4)
sin(2A) = 1/2 √(8/9) + 1/3 √(3/4)
sin(2A) = 1/3 √2 + 1/6 √3
sin(2A) = (2√2 + √3) / 6
We take the distance from points which indicates the location of the park and the mall.
For distance through north and east, we have positive values and negative for west and south.
Mall: (-3, -4)
Park: (3, 5)
The distance is calculate through the equation,
d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)
Substituting,
d = sqrt ((-4 - 5)² + (-3 - 3)²
d = sqrt 117 = 10.82
Thus, the distance between the mall and the park is approximately 10.82 miles.
It’s probably 10 given proof
Answer:
Third option is correct: 1 / (t+4)^2
Step-by-step explanation:
This equation can be written as the following:
(t+3)/(t+4)*(1/t^2+7t+12)
We know this because of the division of fractions. For example:
(1/y)/(1/x) = (1/y)*(x/1)
Now that we know this, we can advance.
Now we have to try to factor (t^2+7t+12)
We can make this into (t+3)(t+4)
Ah! Perfect! There is a t+3 in the denominator of the first fraction!
We can now cancel these out.
Now our equation looks like this:
(1 / t+4) * (1 / t+4)
This can also be written as 1^2 / (t+4)^2 = 1 / (t+4) ^2
So the correct option is the third one.
Answer:
24442 square inches of decorative paper
Step-by-step explanation:
To solve for the above question, we have to find the Surface Area of the box. The box is shaped as a Rectangular Prism.
Hence, the formula is given as:
A = 2(wl + hl+ hw)
Where:
Length (l) = 99 inches
Width (w) = 55 inches
Height (h) = 44 inches
=2 × (55×99 + 44×99 + 44×55)
=24442 square inches
Therefore, the minimum amount of decorative paper needed to cover the box is 24442 square inches of decorative paper.
