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34kurt
3 years ago
8

Last one, ​please :)

Mathematics
1 answer:
KengaRu [80]3 years ago
5 0

Answer:

m∠X = 29°

m∠V = 61°

m∠W == 90°⇒given

Step-by-step explanation:

∵ ΔXWV is right angle at W

∴ m∠W = 90°

∴ m∠X + m∠V = 180° - 90° = 90°

∵ m∠X = 2x + 5 and m∠V = 4x +13

∴ 2x + 5 +4x + 13 = 90

∴ 6x + 18 = 90

∴ 6x = 90 - 18 =72

∴ x = 72/6 = 12

∴ m∠X = 2(12) + 5 = 29°

∴ m∠V = 4(12) + 13 = 61°

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what is the first term of a geometric sequence in which the second term is 6 and the fourth term is 54
IRISSAK [1]
For a geometric sequence:
U_{n} = a * r^{n - 1}
U_{n} = the nth term, i.e. U₂ is the second term, U₃ is the third term, etc.
a = first term (U₁)
r = multiplier
n = number corresponding to the postion of the nth term in the sequence, e.g. for U₂, n = 2, for U₃, n = 3

According to the information:
U₂ = 6
U₄ = 54
So:
U_{2} = a * r^{(2) - 1} = 6 \\\\ a * r^{1} = 6 \\\\ ar = 6 \\
U_{4} = a * r^{(4) - 1} = 54 \\\\ a * r^{3} = 54 \\\\ ar^{3} = 54
Now, we have two equations in terms of a and r;
We can work out a by first working out r;
If we let the U₂ eq'n be [1] and the U₄ eq'n be [2];
Then, we do [2] ÷ [1] to cancel out the a and get an equation with only r that we are able to solve and then just solve it, like so:
\frac{ar^{3}}{ar} =  \frac{54}{6} \\\\ r^{2} = 9 \\\\ r = 3
Note: r has to be 3, and not -3, as the two given terms of the sequence tell us that the terms of the sequence will get bigger from each term to the next so r has to be above 1.

Now that we know r, we can sub it back into either [1] or [2] and solve for a, Its quicker and easier to sub it into [1] as we have no powers greater than 1 and we have smaller numbers to deal with (but you would get the same value of a either way), so:
U₂ = ar = 6
a(3) = 6
a = 6/3
a = 2
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