restrict the domains of quadratic functions and absolute value functions, because these functions are
functions. For instance, the quadratic function f(x) = x^2 pairs both −2 and 2 with 4, and the absolute value function f(x) = |x| pairs both −2 and 2 with 2.
Linear functions (excluding constant functions) and exponential functions are
functions, so their domains
to be restricted.
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An absolute value function, without domain restriction, has an inverse that is NOT a function.
In order to guarantee that the inverse must also be a function, we need to restrict the domain of the absolute value function to make it a one-to-one function.
Answer:
243cm^3
Step-by-step explanation:
By Pythagoras' Theorem,
height of the prism ^2 + 5.4^2 = 7.8^2
height of the prism = ±√(7.8^2 -5.4^2) = ±5.6285cm (5s.f.) (rej. - 5.6285 since height > 0cm)
volume of the prism = 1/2 x 5.4 x 5.6285 x 16 = 243cm^3 (3s.f.)
This is a question on mensuration. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Answer:
0.083
Step-by-step explanation:
To solve the above question, we use the combination method.
C(n, r) = nCr = n!/r!(n - r)!
Probability of answering (all 5 correctly)
= Probability of answering ( 5 out of 7 correctly)/ Probability of answering (5 out of 10 problems)
Probability of answering ( 5 out of 7 correctly) = 7C5
nCr = n!/r!(n - r)!
= 7!/5! (7 - 5)!
= 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (2 × 1)
= 21 ways
Probability of answering (5 out of 10 problems) = 10C5
nCr = n!/r!(n - r)!
= 10!/5! (10 - 5)!
= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (5 × 4 × 3 × 2 × 1)
= 252 ways
Probability of answering (all 5 correctly)
= 21/252
= 0.0833333333
Approximately = 0.083
