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natali 33 [55]
3 years ago
15

A tank is being filled with water using an old

Mathematics
1 answer:
ElenaW [278]3 years ago
6 0
<span>Found a similar problem with the given table. 

Elapsed time (Minutes)   0    10   20   30    40    50   60   70   80   90
Rate (gallons / minute)   42   40  38   35    35    32   28    20   19   10

Because the interval is every 10 minutes, we will use 10 and multiply it to each rate and get the sum total.

42*10 + 40*10 + 38*10 + 35*10 + 35*10 + 32*10 + 28*10 + 20*10 + 19*10 + 10*10
420 + 400 + 380 + 350 + 350 + 320 + 280 + 200 + 190 + 100
2,990

There will be a total of 2,990 gallons in the tank after 90 minutes. </span>
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What is the exact value of <img src="https://tex.z-dn.net/?f=tan%5Cfrac%7B11%5Cpi%20%7D%7B12%7D" id="TexFormula1" title="tan\fra
AnnyKZ [126]

Notice that

11/12 = 1/6 + 3/4

so that

tan(11π/12) = tan(π/6 + 3π/4)

Then recalling that

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

⇒   tan(x + y) = (tan(x) + tan(y))/(1 - tan(x) tan(y))

it follows that

tan(11π/12) = (tan(π/6) + tan(3π/4))/(1 - tan(π/6) tan(3π/4))

tan(11π/12) = (1/√3 - 1)/(1 + 1/√3)

tan(11π/12) = (1 - √3)/(√3 + 1)

tan(11π/12) = - (√3 - 1)²/((√3 + 1) (√3 - 1))

tan(11π/12) = - (4 - 2√3)/2

tan(11π/12) = - (2 - √3) … … … [A]

8 0
1 year ago
What’s the answer to f(a)
S_A_V [24]

Answer:

The answer to this is fa

Step-by-step explanation:

This is because you as the solver doesn't know what the variables f or a is so you put them together as multiplication until you do understand what f and a are so you can multiply them.

If you were to graph this it would be a horizontal line going infinite in both directions. That means no slope or y axis.

6 0
3 years ago
The scale of a map is 1cm:12 km. find the actual distance for 12cm
anzhelika [568]
This is simply a question about ratios. This ratio means that for every 1 cm on the map, there are 12 km in actuality. You can set this problem up in fractions:

1 cm           12 cm
--------   =   ----------
12 km             x

To solve for x, we cross-multiply, for the moment ignoring units. Remember, your answer will be in km.

1*x=12*12

x=144

If x=144, then for 12 cm, there are 144 km.


6 0
3 years ago
((PLEASE HELP ASAP!! D:)) Natasha bought a tennis racket that was marked down in price, p, by 20%. Write an expression with TWO
kumpel [21]

Answer: p - 0.2p

Step-by-step explanation:

Given the following :

Original Price of tennis racket = p

Mark down or discount on original price = 20% of original price = (20/100) × p = 0.2p

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Amount after discount = p - 0.2p

Amount paid by Natasha = p - 0.2p

7 0
3 years ago
A cricket weighs 7/6 gram. A grasshopper weighs 0.76 gram. Which insect weighs more?
Anit [1.1K]
Just divide 7 by 6 to convert the fraction to decimal form and then compare the two
5 0
3 years ago
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