3/5 = 6/10
to get to tenths, multiply by 2/2
Answer:
Step-by-step explanation:
<u>This is an AP with:</u>
- The first term a₁ = 12
- Common difference d = 3
- Number of terms n = 40
<u>Number of the seats:</u>
- Sₙ = 1/2*n(a₁ + aₙ) = 1/2n(2a₁ + (n - 1)d)
- S₄₀ = 1/2*40(12*2 + 39*3) = 2820 seats
<u>Formula of nth term:</u>
- aₙ = a₁ + (n - 1)d
- aₙ = 12 + (n - 1)*3 = 12 + 3n - 3 = 3n + 9
- aₙ = 3n + 9
Answer:
x = 3
y = 15
Step-by-step explanation:
If △XPS ≅△DNF, their corresponding sides would be congruent. This implies that:
XP ≅ DN
PS ≅ NF
XS ≅ DF
Given that:
XP = 4y - 3
DN = 57
NF = 51
XS = 17x + 3
DF = 54
Therefore:
XP = DN
4y - 3 = 57 (Substitution)
Add 3 to both sides
4y = 57 + 3
4y = 60
Divide both sides by 4
y = 60/4
y = 15
Also,
XS = DF
17x + 3 = 54 (substitution)
Subtract 3 from each side
17x = 54 - 3
17x = 51
Divide both sides by 17
x = 51/17
x = 3
Draw a diagram:
from the top of the hill draw a line 18° above the horizontal to the top of the 30 ft pole.
From the top of the hill we draw a line 14° below horizontal to the bottom of the 30 ft pole.
We now have 2 right triangles sharing a common horizontal line,x, to the pole.
Let y=part of pole above horizontal line
30-y=part of pole below horizontal line.
We shall have the following equations:
y/x=tan 18
30-y/x=tan14
x=y/tan 18
x=(30-y)/tan 14
y/tan 18=(30-y)/tan 14
y tan 14=tan 18(30-y)
ytan 14=30tan 18-ytan18
y tan 14+y tan 18=30tan 18
y(tan 14+tan 18)=30*tan 18
y=(30*tan 18)/(tan 14+tan 18)
x=y/tan 18=30/(tan 14+tan10)=52.2423 ft
thus her distance x from the pole=52.2 ft
