Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.
Now, Pythagoras' Theorem is defined as follows:
c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:
c^2 = a^2 + b^2
24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)
b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)
b = √(24^2 - 8^2) (Take the square root of both sides)
b = √512 (Evaluate 24^2 - 8^2)
b = 16√2 (Simplify √512)
= 22.627 (to three decimal places)
I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.
can be changed into this equation:
The 32 and 8 have a common factor of 8 and can be simplified to become this equation:
Now multiply across to get
which then simplifies to
which as a decimal is 41.333 (repeating 3s). Nearest whole number is 41.
Your answer is
41
5 pounds of banana = 5 x $0.8 = $4
5 pounds of apple = 5 x $ 1.4 = $7
total cost = $4 + $7 = $11
Answer:
(-√2 + 3)/7
Step-by-step explanation:
To rationalize the denominator, we need to multiply by the conjugate:
1/(3 + √2)*(3 - √2)/(3 - √2)
(3 - √2)/(9 - √4)
(3 - √2)/(9 - 2)
(-√2 + 3)/7
