This problem can be solved by making use of the Cosine Law. In general form, it is:
b2 = a2 + c2 - 2ac cos B
The given values are:
a = 8.75 cm
c = 4.26 cm
B = 87<span>°
Plugging in the values:
b2 = 8.75^2 + 4.26^2 - 2(8.75)(4.26) cos 87
b = 9.53 cm
So, the answer is:</span>
C. 9.53 centimeters
Answer:
339.29 m³
Step-by-step explanation:
π · r² · h
π · 3² · 12
π · 9 · 12
π · 108
<span>The third side of triangle ABC is AB. Using the Pythagorean Theorem, its length is 12.
12² + 16² = 20²
∠F is congruent to ∠C and so the sin(∠F) = sin(∠C)
The sin(∠C) = opposite/hypotenuse
= |AB| / |AC|
= 12/20
= 3/5
= 0.6
So the answer is 0.6.</span>
<span>∫c F · dr
= ∫∫s curl F · dS, by Stokes' Theorem
= ∫∫ <2, 0, -x> · <-z_x, -z_y, 1> dA
= ∫∫ <2, 0, -x> · <1, 0, 1> dA, since z = 2 - x
= ∫∫ (2 - x) dA.
Since the region of integration is inside x^2 + y^2 = 9, convert to polar coordinates:
∫(r = 0 to 3) ∫(θ = 0 to 2π) (2 - r cos θ) * (r dθ dr)
= ∫(r = 0 to 3) (2 * 2π - 0) * r dr
= 2πr^2 {for r = 0 to 3}
= 18π.
</span>