Answer:
a) £10.50
b) £5.40
Step-by-step explanation:
In this context, "of" means "times".
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<h3>a)</h3>
1/4 × £42 = £(42/4) = £10.50
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<h3>b)</h3>
2/5 × £13.50 = £(2·13.50/5) = £(27/5) = £5.40
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<em>Additional comment</em>
The symbol "£" is a currency symbol identifying the units of the associated number. For algebraic purposes, any symbol representing units can be treated as though it were a variable.
If we know your Pythagorean Triples we can immediately recognize that the last choice is a right triangle:
8² + 15² = 17²
If you don't know your Pythagorean Triples, it's worth learning the first few off the list because teachers use them in problems all the time. But for now let's just exhaustively check the Pythagorean Theorem for each triangle. We don't have to multiply everything out; we can analyze the common factors. If two have a common factor that the third one doesn't have, there's no way for the Pythagorean Theorem to add up.
Clearly 5²+15² is a multiple of 5 but 18² isn't so that one isn't a right triangle.
6²+12² is a multiple of 6, 16² isn't a multiple of 6, not an RT.
15²-5² is a multiple of 5, 13² isn't, no joy.
8²+15² = 64 + 225 = 289 = 17² -- that's a real right triangle, a valid Pythagorean Triple.
Funny, this looks like a complex graph, until you realize that the numerator can be written like (x+3)(x-9).
So really, this is a straight line f(x) = x-9.
But wait, there's a catch. x≠3, because that would divide by zero. So in your straight line, you have to draw a "hole" at (3,6)
Answer: 3/4 is the answer.
Step-by-step explanation:
(2/3)/(8/9)
(doing reciprocal)
2/3 * 9/8
= 18/24
= 6/8
= 3/4
Answer: Diameter is increasing as centimeter per hour.
Step-by-step explanation:
Alright, lets get started.
The formula for volume of sphere is given as V :
The volume of a sphere is increasing at a rate of cubic centimeters per hour.
It means :
Taking derivative with respect to t
at the instant the radius of the sphere is 3 centimeters, means
As
Hence diameter is increasing as centimeter per hour. : Answer
Hope it will help :)