Answer:
c
Step-by-step explanation:
If the dot product of the vectors is zero then they are perpendicular
(5, - 1) • (- 3, 6)
= (5 × - 3) + (- 1 × 6) = - 15 + (- 6) = - 15 - 6 = - 21 ≠ 0
Since product is not zero vectors are not perpendicular
The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
You can make 6 different towers. If red was at the bottom, there'd be two different possibilities for that: red, yellow, blue, and red, blue, yellow. Same for if blue was at the bottom: blue, red, yellow, and blue, yellow, red. Yellow also applies: yellow, red, blue, and yellow, blue, red. 3*2=6, so 6 possible towers.
13. 1
14. 1
15. any number and 0 will have a quotient of 0.
for example 7/0=0 . 8/0=0 . 9/0=0
if you try and check your work using multiplication 7*0=0 . 8*0=0 . 9*0=0
then you will realize the rule is right
Answer:
195 cubic inches
Step-by-step explanation:
A fishing tackle box is 13 inches long, 6 inches wide, and inches high. What is the volume of the tackle box? SOLUTION: The volume of the tackle box is 195 cubic inches.
