Answer:
388.5yd²
Step-by-step explanation:
We have Triangle TUV
In the question, we are given already
Angle U = 32°
Angle T = 38°
Angle V = ???
Side t = 31yd
Side u = ?
Side v = ?
Area of the triangle= ?
Step 1
We find the third angle = Angle V
Sum of angles in a triangle = 180°
Third angle = Angle V = 180° - (32 + 38)°
= 180° - 70°
Angle V = 110°
Step 2
Find the sides u and v
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle TUV
t/ sin T = u/ sin U = v/ sin V
We have the following values
Angle T = 38°
Angle U = 32°
Angle V = 110°
We are given side t = 31y
Finding side u
u/ sin U= t/ sin T
u/sin 32 = 31/sin 38
Cross Multiply
sin 32 × 31 = u × sin 38
u = sin 32 × 31/sin 38
u = 26.68268yd
u = 26.68yd
Finding side x
v / sin V= t/ sin T
v/ sin 110 = 31/sin 38
Cross Multiply
sin 110 × 31 = v × sin 38
v = sin 110 × 31/sin 38
v = 47.31573yd
v = 47.32yd
To find the area of triangle TUV
We use heron formula
= √s(s - t) (s - u) (s - v)
Where S = t + u + v/ 2
s = (31 + 26.68 + 47.32)/2
s = 52.5
Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)
Area of the triangle = √150967.6032
Area of the triangle = 388.5454973359yd²
Approximately to the nearest tenth =388.5yd²
Finding gradient:
m = y2 - y1
x2 - x1
= -1 - 6
1 - 3
= -7 / (-2)
= 7/2
y = m(x - x1) + y1
y = 7(x - 3) + 6
2
2y = 7x - 21 + 12
2y = 7x - 9
Answer:
Step-by-step explanation:
Step 1:-
using logarithmic formula
so given
now simplify
=
<u>Answer:</u>-
Answer:
<em>f(x) = x² (2+i)x-15-3i</em>
Step-by-step explanation:
Since the zeros of the equation are -3 and 5+i, hence the factors of the polynomial in x is (x+3) and (x-(5+i))
Multiplying both factors
f(x) = (x+3)(x-(5+i))
f(x) = (x²-(5+i)x+3x -3(5+i))
f(x) = x² - (5+i- 3)x -15-3i
f(x) = x² (2+i)x-15-3i
<em>hence the required polynomial function in x is f(x) = x² (2+i)x-15-3i</em>
<span>Binomial is the sum of two monomials.
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