9514 1404 393
Answer:
3) 74°
4) 260°
Step-by-step explanation:
3) Angle CAE is vertical to angle FAB, which is shown as 121°. Vertical angles are congruent. So, we have ...
∠DAE +∠DAC = ∠EAC
∠DAE + 47° = 121° . . . . . . . fill in known values
∠DAE = 121° -47° . . . . . . . . subtract 47°
∠DAE = 74°
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4) arc MJL is the long arc that completes the circle along with short arc MJ. Short arc MJ has the same measure as its central angle, 100°. Then long arc MJL is 360° -100° = 260°.
arc MJL = 260°
Answer:
the answer is b
Step-by-step explanation:
answers is pictured
Answer:
building: 51.4 ft
flagpole: 5.3 ft
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
If we let b and p represent the heights of the building and flagpole, respectively, then we can write two equations using the tangent relation:
tan(79°) = b/10
tan(80°) = (b +p)/10
Multiplying these equations by 10 gives the values we're interested in.
b = 10·tan(79°) ≈ 51.4 . . . feet
b +p = 10·tan(80°) ≈ 56.7 . . . feet
Then the height of the flagpole is ...
p = (b+p) -b = (56.7 ft) -(51.4 ft) = 5.3 ft
The building is 51.4 ft tall.
The flagpole is 5.3 ft tall.
Simplifying
12x + -8x = 12
Combine like terms: 12x + -8x = 4x
4x = 12
Solving
4x = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '4'.
x = 3
Simplifying
x = 3
Yes, your answers are correct.
The volume of a cone is given by V = 1/3πr²h. Since the diameter of the first cone is 4, the radius is 2; therefore the volume is
V = 1/3π(2²)(8) = 32π/3
We divide the volume of the sink, 2000π/3, by the volume of the cone:
2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.
The diameter of the second conical cup is 8, so the radius is 4. The volume then is:
V = 1/3π(4²)(8) = 128π/3
Dividing the volume of the sink, 2000π/3, by 128π/3:
2000π/3 ÷ 128π/3 = 2000π/3 × 3/128π = 6000π/384π = 15.625 ≈ 16
