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3 years ago

!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

7 0

ANSWER

A. (x+4)

EXPLANATION

The given binomial is

${x}^{2} + 12x + 32$

Split the middle term:

${x}^{2} + 8x + 4x + 32$

Factor;

$x(x + 8) + 4( x + 8)$

Factor further;

$(x + 8)(x + 4)$

Therefore

$(x + 4)$

is a factor.

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Assume that it costs Apple approximately E(x) 25,600 + 100x + 0.012 dollars to manufacture x 32GB iPods in a day. (a) The averag

uranmaximum [27]

Answer:

(a) $C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)x=1600, Minimum Average Cost Per iPod=$132

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

Step-by-step explanation:

Given that it costs Apple approximately $ C(x) to manufacture x 32GB iPods in a day, where:

$C(x)=25,600+100x+0.01x^2$

(a)The average cost per iPod when they manufacture x iPods in a day is given by:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}$

The average cost per iPod is therefore:

$C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)To minimize average cost of x iPods per day, we set the average cost per iPod=0 and solve for x.

$C'(x)=\dfrac{x^2-2560000}{x^2}=0\\x^2-2560000=0\\x^2=2560000\\x=\sqrt{2560000}=1600$

The resulting minimum average cost (at x=1600) is given as:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}\\\dfrac{25,600+100(1600)+0.01(1600)^2}{1600}\\=\$132$

<u>Second derivative test</u>

(c)The answer above is a critical point for the average cost function. To show it is a minimum, we calculate the second derivative of the average cost function.

$C''(x)=\dfrac{5120000}{x^3}$

At the critical point, x=1600

$C''(1600)=\dfrac{5120000}{1600^3}=0.00125$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

3 0

3 years ago

HURRY I'LL PICK A BRAINLIEST PERSON!!!

Rzqust [24]

Answer:

The only options which are having same solution as the given equation is A, B and D.

Explanation:

Given the equation: $\frac{3}{5}x+ \frac{2}{3} +x =\frac{1}{2}- \frac{1}{5}x$ ......[1]

Like terms are terms whose variables are the same.

In the given equation [1],

Combine like terms of variable x on LHS; we have

$\frac{3x+5x}{5}+ \frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$

Simplify:

$\frac{8x}{5}+\frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$

or we can write this as;

$\frac{8}{5}x +\frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$ .

LCM(Least Common Multiple) to change each fraction to make their denominators the same as the least common denominator.

Taking LCM to both sides of an equation [1] as;

LCM of 3, 5 on LHS is 15 and LCM of 2 , 5 on RHS is 10;

$\frac{9x+10+15x}{15} = \frac{5-2x}{10}$

By cross multiplication we get;

$10 \cdot (9x+10+15x) = 15 \cdot (5-2x)$

Divide both side by 5 we get;

$2 \cdot (9x+10+15x) = 3 \cdot (5-2x)$

Using distributive property on both sides of an equation (i.e, $a\cdot (b+c) =a\cdot b+a\cdot c$ )

we have;

$18x+20+30x = 15-6x$ ......[2]

Additive Property of Equality states that allows one to add the same quantity to both sides of an equation.

Using additive property of equality:

Add 6x to both sides of an equation in [2];

$18x+20+30x+6x = 15-6x+6x$

Simplify;

$18x+20+30x+6x = 15$

Combine 18x and 6x we get;

$24x+20+30x= 15$ ......[3]

Subtraction Property of Equality states that allows one to subtract the same quantity to both sides of an equation.

Subtract 20 from both sides of an equation in [3] we get;

$24x+20+30x-20= 15-20$

Simplify:

$24x+30x= -5$

Therefore, from the given options only A, B and D have the same solution as $\frac{3}{5}x+ \frac{2}{3} +x =\frac{1}{2}- \frac{1}{5}x$

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3 years ago

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago

Using the figure bellow find m<_6 if m<_8=110 degrees. What will m<_6=? (show your work if possible)

damaskus [11]

Answer:

angle 6= 110°

Step-by-step explanation:

complimentary angles are congruent

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3 years ago