The height of broken part of tree from ground is 5.569m.
Justification:
Let BD is a tree of height 12 m.
<u>Suppose it got bent at a point C and let the part CD take the position CA, meeting the ground at A</u>.
i.e., CD = AC = h m
<u>Broken part makes 60° angle from ground</u>
So, ∠BAC = 60°
<u>Now, height of remaining part of tree</u> = (12 – h)m.
In right angled ∆ABC,
sin 60° = BC/AC
⇒ √3/2 = (12 - h)/h
⇒ √3h = 2(12 – h)
⇒ √3h = 24 – 2h
⇒ √3h + 2h = 24
⇒ h(√3 + 2) = 24
⇒ h(1.732 + 2) = 24
⇒ h(3.732) = 24
⇒ h = 24/3.732 = 6.4308 m
<u>Hence, height of broken tree from ground</u>
⇒ BC = 12 – h
⇒ 12 – 6.4308 = 5.569m
<u>Hence, tree is broken 5.569 m from ground</u>.
<u>Note</u>: See attached picture.
Answer:
648
Step-by-step explanation:
Running this in Python, with the code as follows,
import math
cur_numbers = [0] * 3
num = 0
for i in range(100, 1000):
cur_numbers[2] = i % 10
i = math.floor(i/10)
cur_numbers[1] = i % 10
i = math.floor(i/10)
cur_numbers[0] = i % 10
if(len(set(cur_numbers)) == 3):
num += 1
print(cur_numbers)
print(num), we get 648 as our answer.
Another way to solve this is as follows:
There are 9 possibilities for the hundreds digit (1-9). Then, there are 10 possibilities for the tens digit, but we subtract 1 because it can't be the 1 same digit as the hundreds digit. For the ones digit, there are 10 possibilities, but we subtract 1 because it can't be the same as the hundreds digit and another 1 because it can't be the same as the tens digit. Multiplying these out, we have
9 possibilities for the hundreds digit x 9 possibilities for the tens digit x 8 possibilities for the ones digit = 648
Answer: The oil tank can take up to 1200 litres of oil. There are already 450 litres of oil in the tank. The price of oil is 81.5p per litre. As a loyal customer, Mr Leonard gets a 7.5% discount on the price of the oil.
Step-by-step explanation:
Answer:
part a and b only i was actually looking for c
Step-by-step explanation:
for part b
Area of DEF= 1/2× base × height = 1/2× 2 × 1 = 1
Area of FGD= 1/2× base × height = 1/2× 2.24 × 1.34 =1.50
Area of GBD= 1/2× base × height = 1/2× 2 × 1 = 1
Area of ABG= 1/2× base × height = 1/2× 4.12 × 0.49 =1.01
Area of BCD= 1/2× base × height = 1/2× 1.41 × 2.12 =1.49
The approximate area of the original polygon is 6 square units
Simplify both sides of the equation.
−3f=6
Divide both sides by -3.
−3f/−3 = 6/−3
f=−2
Answer:
f=−2
