maths revision sheet help + rep to all

[BowTies1]

solve 15x-8(3x-7)> 4-6(5-3x)

write in standard form (scientific notation) (I)0.00678 (II) 345000

9 : on the sea front at troon the beach slopes down at a constant angole of 9
to the horizontal murdo is 1.7 m tall how far can he walk out to sea before the water jsut reaches the top of his head

10:) sarah rides 300 up a hill and finds she has gained 200m in altitude
Calculate the angle the hill makes with the horizontal.

[H]

solve 15x-8(3x-7)> 4-6(5-3x)

to hard to explain but i work it out as this:

15x + 24x - 56 > 4 - 30 - 18x (ive multiplied out of the brackets)

57x - 56 > 4 - 30 (ive moved the 18x to the left plus it)

57x - 56 > - 26

57x > 30

x > 57/30. not sure if correct.

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write in standard form (scientific notation) (I)0.00678 (II) 345000

so you want something that looks like this: 1.23 x 10 to the power of 3

rule 1: the first number is always less then 10.
so take the first one (I) because there are zeros before any numbers then you count foward till you make a number less than 10: 6.78 yeah?
it cant be 67.8 cos this is greater then 10.

so the begining is going to look like this: 6.78 x 10
not to work out what the power of 10 is, you coun from 6 back to the decimal point in the first question: 0.00678 so:

pretend its lik this 0 (1st dp) 0 0 6 . 7 8
from the . to the (1st dp) it jumps 3 places from the numbers.
therefore its going to be:
6.78 x 10 to the power of -3. (minus cos you count back)

(II) 345000 (you count forward so the power wont be negative)

has to be less then 10 so: 3.45 x 10
the power will be the point in between the 3 & 4 right till the end of the last 0 in the number 345000 so its 5 jumpes.

= 3.45 x 10 to the power of 5

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9 : on the sea front at troon the beach slopes down at a constant angole of 9
to the horizontal murdo is 1.7 m tall how far can he walk out to sea before the water jsut reaches the top of his head

l
l
X l (image a slope like a triangle)
l thats 9.
l
l_____________
1.7m

you need to find x so what you is backwards hypotenuse. FORMULA for hypotenuse formula is: a squared + b squares = then quare root answer
so you have a = x b = 1.7 hypo = 9

so you work backwards. you square the 9 cos it was square rooted making it 81.
then you square 1.7 = 2.89
so you do 81 - 2.89 = 78.11
square root 78.11 = 8.837...... so this is how far he can walk, 8.84m.
to check this all you do is put the numbers into the formula
8.837 squared + 1.7 squared = 81 square root of 81 = 9

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10:) sarah rides 300 up a hill and finds she has gained 200m in altitude
Calculate the angle the hill makes with the horizontal.

cba to do 10 :)

[sierk1]

10:) sarah rides 300 up a hill and finds she has gained 200m in altitude
Calculate the angle the hill makes with the horizontal.

This suggests a rectangular triangle with hypothenusa (diagonal side) of length 300, and vertical side of length 200. If we call the angle that is asked for x, we know from geometry that sinus(x)=200/300=2/3. Hence the angle x=inverse sinus (2/3).