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Artemon [7]
3 years ago
5

Factorise Please with full method

Mathematics
2 answers:
tino4ka555 [31]3 years ago
6 0

Answer:

Step-by-step explanation:

Remember:\\\\\boxed{x^3-y^3=(x-y)(x^2+xy+y^2)}\\\\64a^3-(b-c)^3\\\\=(4a)^3-(b-c)^3\\\\=(4a-(b-c))(16a^2+4a(b-c)+(b-c)^2)\\\\=(4a-b+c)(16a^2+4ab-4ac+b^2-2bc+c^2)\\

cestrela7 [59]3 years ago
5 0

\boxed{\sf (a-b)^3=a^3-3a^2b+3ab^2-b^3}

\\ \sf\longmapsto 64a^3-(b-c)^3

\\ \sf\longmapsto 64a^3-(b^3-3b^2c+3bc^2-c^3)

\\ \sf\longmapsto 64a^3-b^3+3b^2c-3bc^2+c^3

\\ \sf\longmapsto 64a^3-b^3+c^3+3b^2c-3bc^2

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Two trains are 210 miles apart, and their speeds differ by 17 mph. Find the speed of each train if they are traveling toward eac
Marizza181 [45]
V1 - velocity first train
v2 - velocity second train
v2 > v1

v2 - v1 = 17 mph

We know, that: 
s_1+s_2=210 \ [miles] \\ \\ t_1=t_2=2h

So:

v_1=\dfrac{s_1}{t_1}=\dfrac{s_1}{2} \\ \\ v_2=\dfrac{s_2}{t_2}=\dfrac{s_2}{2} \\ \\ \\ v_1+v_2= \dfrac{s_1}{2}+\dfrac{s_2}{2} \\ \\ v_1+v_2= \dfrac{s_1+s_2}{2} \\ \\  v_1+v_2= \dfrac{210}{2}=105

NOw we've got simple system of equations:

+\begin{cases} v_2-v_1=17 \\ v_2+v_1=105\end{cases} \\ \\ 2v_2=122 \qquad /:2 \\ \\ v_2=61 \qquad [mph] \\ \\ v_2-v_1=17 \\ \\ 61-v_1=17 \\ \\ v_1=44

Velocities of these trains are  61mph  and 44mph

3 0
3 years ago
Read 2 more answers
This is what I need to know
I am Lyosha [343]
\bf \begin{array}{ccllll}
\$&minutes\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
920,000&46,000,000\\
x&1
\end{array}\implies \cfrac{920,000}{1}=\cfrac{46,000,000}{x}
so solve for "x", to see how much is the company paying for the purchase of 1 minute

now, they're plan to sell the minute for 8cents, how much is the profit?
that is, the difference from their cost of the cents to the planned selling price.

bear in mind, is 46,000,000 minutes, so whatever value you get for 1minute,
you need to multiply it for 46,000,000 to get the actual cost.

and the revenue from the sell of 8cents per minute, is of course, 8 * 46,000,000

profit = revenue - cost
7 0
4 years ago
To make purple plum paint, the paint store mixes blue and red paint in a ration of 8:5 if a customer needs 65 gallon of paint ho
Olegator [25]

Answer:

Number of gallons of blue paint = 40 gallons

Number of gallons of red paint = 25 gallons

Step-by-step explanation:

We are given the ratio:

Blue paint : Red paint =

8 : 5

Sum of proportion = 8 + 5 = 13

If the customer need 65 gallons of paint,

a) Number of gallons of blue paint needed =

8/13 × 65 gallons = 40 gallons

b) Number of gallons of red paint needed =

5/13 × 65 gallons = 25 gallons

Therefore:

Number of gallons of blue paint = 40 gallons

Number of gallons of red paint = 25 gallons

3 0
3 years ago
why is it not usually realistic to measure the distance between two points on a map as a straight line? explain.
aksik [14]
The map is a flat schematic of some actual distance, on a map, the distance form point A to point B may well be 10 units say, however, in actuality, if you go and walk from point A to point B, you'd notice that, first off is not a straight line most of the time, and also it may have a slanted or sloped section, and the map is not including that slope or hill, whilst you do have to walk it.

so, adding all the twists and curves along the way and any bumps or slopes, is really not exactly 10 units from A to B.
3 0
4 years ago
Read 2 more answers
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Alexeev081 [22]
36.36 is thirty-six and thirty-six hundredths.
36.63 is thirty-six and sixty-three hundredths.

The whole parts are the same. They are both 36.
The decimal parts are 0.63 and 0.36.
Sixty-three hundredths is greater than thirty-six hundredths.
Since 0.63 is greater than 0.36, 36.63 is greater.
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