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KiRa [710]
3 years ago
6

An artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants

the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and height of 6 inches. What should be the height of the cone in the artists sculpture?
Mathematics
1 answer:
brilliants [131]3 years ago
8 0

Answer:

115.2 inches

Step-by-step explanation:

What we must do is calculate the ratio between the real version and the version to be imitated, in this case the ice cream cone.

To calculate the ratio, we will do it through the diameter:

48 / 2.5 = 19.2

So the ratio is 19.2: 1

Which means that one inch of the ice cream cone represents 19.2 inches in the real version.

Therefore, in the case of height it would be:

6 * 19.2 = 115.2

Therefore, the height should be 115.2 inches.

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If g(x)=4x^2-16 we’re shifted 9 united to the right and 1 down, what would the new equation be?
Inessa05 [86]

Shown in the graph

<h2>Explanation:</h2>

Using graph tools we can graph the function:

g(x)=4x^2-16

which is the red graph shown below. As you can see, this is a parabola. The rule for vertical and horizontal shifts is as follows:

Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:

\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)

Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it h(x)) will be:

h(x)=4\left(x-9\right)^{2}-16-1 \\ \\ Simplifying: \\ \\ h(x)=4\left(x-9\right)^{2}-17

This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:

(0,-16)

By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:

New \ vertex: \\ \\ (0+9,-16-1) \\ \\ (9,-17)

<h2>Learn more:</h2>

Cubic function: brainly.com/question/13773618#

#LearnWithBrainly

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