Step-by-step explanation:
let T be the top of the ladder
let F be the foot of the ladder
let B be the base of the wall
you need to find the distance between the foot of the ladder and the base of the wall, in other words the distance of the 'ground' ( refer to the diagram).
you are given that the hypotenuse - H is 3 m and that the opposite - O ( wall ) is 2.8 m.
i) find the angle
given
H, O → use SOH, sin.
sin x = opp. /hyp.
sin x = 2.8 / 3
x = sin-1 ( 2.8/ 3)
x = 68.960...
x = 70.0 ° ( 3 s.f)
ii) use either tan or cos to find the adjacent (wall)
using TOA, tan:
tan ( 68.96) = 2.8/ adj.
2.8 / adj. = tan (68.96)
adj. × tan (68.96) = 2.8
adj = 2.8/ tan (68.96)
adj = 1.0770...
adj. = 1.08 ( 3 sf)
base = 1.08 m
or you could rather simply work this out using Pythagoras Theorem:
where hyp. is c², the base is b² and height is a²;
c² = a² + b²
b² = c² - a²
b² = (3)² - (2.8)²
b² = 1.16
b = √1.16
b = 1.0770
b = 1. 08 m ( 3sf)
you can give your answer to 3 sf or 2 sf.
hope this helps you!
-s.
Given:
The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).
To find:
The equation of the quadratic function.
Solution:
A quadratic function is defined as:
...(i)
It is passes through the point (0,11). So, substitute
in (i).
![11=a(0)^2+b(0)+c](https://tex.z-dn.net/?f=11%3Da%280%29%5E2%2Bb%280%29%2Bc)
![11=c](https://tex.z-dn.net/?f=11%3Dc)
Putting
in (i), we get
...(ii)
The quadratic function passes through the point (5,31). So, substitute
in (ii).
![20=25a+5b](https://tex.z-dn.net/?f=20%3D25a%2B5b)
Divide both sides by 5.
...(iii)
The quadratic function passes through the point (3,11). So, substitute
in (ii).
Divide both sides by 3.
...(iv)
Subtracting (iv) from (iii), we get
![4-0=5a+b-3a-b](https://tex.z-dn.net/?f=4-0%3D5a%2Bb-3a-b)
![4=2a](https://tex.z-dn.net/?f=4%3D2a)
![\dfrac{4}{2}=a](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B2%7D%3Da)
![2=a](https://tex.z-dn.net/?f=2%3Da)
Putting
in (iv), we get
![0=3(2)+b](https://tex.z-dn.net/?f=0%3D3%282%29%2Bb)
![0=6+b](https://tex.z-dn.net/?f=0%3D6%2Bb)
![-6=b](https://tex.z-dn.net/?f=-6%3Db)
Putting
in (ii), we get
Therefore, the required quadratic equation is
.
Answer:
6,265 votes
Step-by-step explanation:
The residents of a city voted on whether to raise property taxes. The ratios of yes votes to no votes was 5 to 7. If there were 10,740 total votes, how many no votes were there?
Given that :
Ratio of yes votes to no votes = 5 to 7
Yes votes : no votes = 5 : 7
Total votes = 10,740
The actual number of yes votes and no votes can be obtained thus :
Sum of ratio = (5 + 7) = 12
(ratio of vote / sum of ratio) * total votes
Number of no votes :
(Ratio of no votes / total ratio) * total votes
(7 / 12) * 10,740
0.5833333 * 10,740
= 6,265 votes
Number of no votes = 6,265 votes.
Answer:
25
Step-by-step explanation:
High = 77
Low = 52
Subtract to find difference
High - Low
77 - 52
25
Answer:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
Step-by-step explanation:
3 times n