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3 years ago

1) An ice cream factory makes 320 quarts of ice cream in 10 hours.

2 answers:

8 0

320 qts/10 hrs = 32 qts/1 hr

They can make 384 quarts in 12 hours.

They can make 768 quarts per day (24 hours) if they open 24 hours.

Vesna [10]3 years ago

5 0

In 12 hours the factory would make 320 quarts of ice cream. the rate per day would be 768 quarts.

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For which values of P and Q does the following equation have infinitely many solutions ?

solmaris [256]

Answer:

(P, Q) = (-75, 57)

Step-by-step explanation:

The equation will have infinitely many solutions when it is a tautology.

Subtract the right side from the equation:

Px +57 -(-75x +Q) = 0

x(P+75) +(57 -Q) = 0

This will be a tautology (0=0) when ...

P+75 = 0

P = -75

and

57-Q = 0

57 = Q

_____

These values in the original equation make it ...

-75x +57 = -75x +57 . . . . . a tautology, always true

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2 years ago

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Can a triangle be formed with sides 18, 20, 2? If so, classify it by angles..

Nady [450]

Answer:

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2 years ago

Sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0

andreev551 [17]

Recall the angle sum identity for cosine:

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

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

==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0

sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2

sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ

… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π

… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5

sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ

… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π

… … … … … ==> x = nπ or x = (2n + 1)π/2

cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ

… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ

… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ

(where n is any integer)

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2 years ago

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Bumek [7]

$\bf \cfrac{x}{x-2}+\cfrac{x-1}{x+1}=-1\impliedby LCD\to (x-2)(x+1)\\\\
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\cfrac{x(x+1)+(x-1)(x-2)}{(x-2)(x+1)}=-1
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\begin{cases}
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\end{cases}$

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2 years ago