9514 1404 393
Answer:
(a) 42.3°
Step-by-step explanation:
Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.
a² = b² +c² -2bc·cos(A)
cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050
A = arccos(777/1050) ≈ 42.3°
The measure of angle A is about 42.3°.
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<u><em>Additional comment</em></u>
The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.
X=7
Explanation:
A triangle equals 180°, and they gave us one length already, and it says the one arm of the triangle is equal to the other so we know that the third angle is going to be the same as the second angle.
180=90+(6x+3)+(6x+3)
Combine like terms
180=96+12x
Subtract 96 from both sides
84=12x
Divide 12 by both sides
7=x
Now check it,
90+(6*7+3)+(6*7+3)
90+(45)+(45) =180
Answer:
-x¹⁴ / 5040
-½ < x < ½
Step-by-step explanation:
f(x) = e^(-x²)
The Taylor series for eˣ centered at 0 is:
eˣ = ∑ (1/n!) xⁿ
Substitute -x²:
e^(-x²) = ∑ (1/n!) (-x²)ⁿ
e^(-x²) = ∑ (1/n!) (-1)ⁿ x²ⁿ
The 14th degree term occurs at n=7.
(1/7!) (-1)⁷ x¹⁴
-x¹⁴ / 5040
ln(1 + x) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ xⁿ / n
If we substitute 4x²:
ln(1 + 4x²) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ (4x²)ⁿ / n
Using ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺² (4x²)ⁿ⁺¹ / (n+1)] / [(-1)ⁿ⁺¹ (4x²)ⁿ / n]│< 1
lim(n→∞)│-1 (4x²) n / (n+1)│< 1
4x² < 1
x² < ¼
-½ < x < ½
Answer:
20 days
Step-by-step explanation:
t = time required by one worker to complete the job alone
(t+8) = time required by the other worker
So:
7.5/ t + 7.5/ (t + 8) = 1
Solve for t.
...
t = 12 days, the first guy working alone
The other worker would finish the job in 20 days.
Step-by-step explanation:
756 = 2² * 3³ * 7.
For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.
How to get from 2² to 2³: Multiply by 2.
3³ has already a power that is a multiple of 3.
How to get from 7 to 7³: Multiply by 7².
Hence n = 2 * 7² = 98.
