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3 years ago

Simplify and solve for x.

Mathematics

1 answer:

I am Lyosha [343]3 years ago

4 0

Answer:

x = 35

Step-by-step explanation:

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4 years ago

(1 pt) A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the

mrs_skeptik [129]

Answer:

Rate at which volume of the snowball decreasing = 90.48 cm³/min

Step-by-step explanation:

$\texttt{Volume of sphere, V =}\frac{4}{3}\pi r^3=\frac{4}{3}\pi \left (\frac{D}{2} \right )^3=\frac{1}{6}\pi D^3$

Differentiating with respect to time,

$\frac{dV}{dt}=\frac{d}{dt}\left (\frac{1}{6}\pi D^3 \right )=\frac{1}{6}\pi \times 3D^2\frac{dD}{dt}\\\\\frac{dV}{dt}=\frac{1}{2}\pi D^2\frac{dD}{dt}$

Substituting

D = 12 cm and rate of change of diameter = 0.4 cm/min.

$\frac{dV}{dt}=\frac{1}{2}\pi D^2\frac{dD}{dt}\\\\\frac{dV}{dt}=\frac{1}{2}\pi \times 12^2\times 0.4=90.48cm^3/min$

Rate at which volume of the snowball decreasing = 90.48 cm³/min

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3 years ago

You have a wire that is 74 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

liq [111]

Answer:

32.55 cm

Step-by-step explanation:

Let x = the length of wire that becomes a circle.

Then 74 - x = the length of wire that becomes a square

Circumference of circle + perimeter of square = 74

1. Expression for the side of the square

P = 4s = 74 - x

s = ¼(74 - x)

2. Expression for the radius of the circle

C = 2πr = x

r = x/(2π)

3. Expression for the total area

$\begin{array}{rcl}\text{Total area} & = &\text{area of circle+ area of square}\\A & = & \pi r^{2} + s^{2}\\& = &\pi \left(\dfrac{x}{2 \pi}\right)^{2} + \left (\dfrac{1}{4}(74 - x)\right)^{2}\\\\ & = & \dfrac{x^{2}}{4 \pi} + \dfrac{1}{16}(5476 - 148x + x^{2})\\\\ & = & 0.07958x^{2} + 342.25 - 9.25x + 0.0625x^{2}\\A & = & 0.1421x^{2} -9.25x + 342.25 \\ \end{array}$

This is the equation of a parabola.

In standard form,

ƒ(x) = 0.1421x² -9.25x + 342.24

a = 0.1421; b = -9.25; c = 342.24

The parabola opens upwards, because a > 0. Therefore, the vertex is a minimum.

The vertex of a parabola occurs at

x = -b/(2a) = 9.25/(2 × 0.1421) = 9.25/(0.2842) = 32.55

The circumference of the circle is 32.55 cm.

The graph below shows that the area of the circle is a minimum when x = 32.55 cm

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3 years ago

What is the expanded form of the number below?

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It is the first one

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3 years ago