∑ ( from n = 1 to n =5 ) 3 · ( -2 ) ^( n -1 )
a 1 = 3 · ( -2 ) ^0 = 3
a 2 = 3 · ( - 2 ) = - 6
a 3 = 3 · 4 = 12
a 4 = 3 · ( - 8 ) = - 24
a 5 = 3 · 16 = 48
3 - 6 + 12 - 24 + 48 = 33
Answer: C ) 33
Step-by-step explanation:
Use Pythagorean theorem here. To find the height, find the difference of the 2 y's. To find the length, find the difference between the 2 x's.
Length = x2 - x1
Height = y2 - y1
√length^2 + height^2 = distance
√5^2 + 5^2 = √50 = 7.07
Expression is: 2.2 × 10⁴ / 8.8 × 10⁹
= 1 × 10⁴ / 4 × 10⁹
= 0.25 × 10⁴⁻⁹
= 0.25 × 10⁻⁵
= 2.5 × 10⁻⁶
In short, Your Answer would be: Option D
Hope this helps!
Answer:
The longest side length b is approximately 13.172 cm
Step-by-step explanation:
The given parameters are;
The area of the triangle = 22.4 cm²
The given angles of the triangle = ∠97°
The given side of the triangle = 3.7 cm
The formula for the area of a triangle, A = 1/2 × a × b × sin(C)
Where;
a, and b are the side legs forming the angle C
Therefore, we have;
A = 22.4 = 1/2 × 3.7 × a × sin(97°)
a = 22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199
a ≈ 12.199 cm
Therefore, by cosine rule, we have;
b² = a² + c² - 2 × a × c × Cos(B)
Substituting the values, gives;
b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)
b² ≈ 173.507
∴ b ≈ √173.507 ≈ 13.172
b ≈ 13.172 cm
