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Ostrovityanka [42]
3 years ago
14

The Unisphere is the world's largest man-made globe. It was built as the symbol of the 1964-1965 New York World's Fair. A sphere

with the same diameter as the Unisphere globe would have a surface area of 45,239 square feet. What is the diameter of the Unisphere?
Mathematics
1 answer:
Xelga [282]3 years ago
5 0
\bf \textit{surface area of a sphere}\\\\
A=4\pi r^2\qquad 
\begin{cases}
r=radius=\frac{diameter}{2}\\
diameter=2r\\
----------\\
A=45,239
\end{cases}\implies 45,239=4\pi r^2

solve for "r", to see what the radius is

keep in mind that, the diameter is just "2r"
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A. The point-slope form of the equation of a line is y ? y1 = m(x ? x1), where m is the slope and (x1, y1) is a point on the lin
Rudiy27

Answer:

A.

y - 5 = -2(x-6)

Negative reciprocal gives you the perpendicular slope so negative reciprocal of 1/2 is -2.

Then apply point-slope form.

B. The answer is x = 6.

The midpoint of JK is

\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{8+ 4}{2}, \frac{4 + 4}{2} \right) = \left(6,4\right)

The line that goes through JK is just a horizontal line y = 4 because the y-coordinate does not change. So its perpendicular bisector is the vertical line that goes through the x-coordinate of the midpoint, that is, x = 6.

8 0
2 years ago
Which statement describes the effect on the parabola f(x)=2x•x-5x+3 when changed to f (x)= 2x•2-5x+1
o-na [289]

Answer:

The parabola is translated down 2 units.

Step-by-step explanation:

You have the parabola f(x) = 2x² – 5x + 3

To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:

f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1  <u><em>Expresion A</em></u>

The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.

  • If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
  • If p> 0 and q <0, the parabola shifts p units to the right and q units down.
  • If p <0 and q> 0, the parabola shifts p units to the left and q units up.
  • If p <0 and q <0, the parabola shifts p units to the left and q units down.

In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.

This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.

In conclusion, <u><em>the parabola is translated down 2 units.</em></u>

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Hope this helped and I’ve shown my work and the answer! :)

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