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loris [4]
2 years ago
11

Please help!! TYSM!! What do a cylinder and a cone have in common? How are they different? (Hint: Look up the formula for the vo

lume of a cone.)
Mathematics
1 answer:
geniusboy [140]2 years ago
3 0

Similarities:

Similarities are that these figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base.

Differences:

A cone is a 3-dimensional solid object that has a circular base and a single vertex. ... Cylinder : A cylinder is a 3-dimensional solid object that has two parallel circular base connected by a curved surface.

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Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).
Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

  1. <u>Shifting</u>: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the <em><u>y-coordinate</u></em> is<em> </em>added or subtract and the x-coordinate is unchanged, there is a <em><u>vertical</u></em> <u><em>shift</em></u>. If it is the <em><u>x-coordinate</u></em> which changes and y-coordinate is kept the same, the shift is a <em><u>horizontal</u></em> <u><em>shift</em></u>;
  2. <u>Scaling</u>: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the <em>y-coordinate</em> is multiplied or divided by a constant but x-coordinate is the same, it is a <em>vertical scaling</em>. If the <em>x-coordinate</em> is changed by a constant and y-coordinate is not, it is a <em>horizontal</em> <em>scaling</em>;
  3. <u>Reflecting</u>: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0)  (0,6)  (5,-4)  (8,0)

And the points for g(x) are:

(-5,-3)  (0,-9)   (5,1)   (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a <u>Vertical</u> <u>Shift</u>.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a <u>Reflection</u>.

<u>Range</u> <u>of</u> <u>a</u> <u>function</u> is all the values y can assume after substituting the x-values.

<u>Domain</u> <u>of</u> <u>a</u> <u>function</u> is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph            translation            domain      range

f(x)                       none                 [-5,8]          [-4,6]

g(x)                vertical shift           [-5,8]          [-9,1]

<u>In conclusion, this transformation (or translation) will affect the range of g(x)</u>

5 0
2 years ago
Which expression shows how to find the quotient of 4.8÷2?
xenn [34]

Answer:

[A] (4 ÷ 2)+(0.8 ÷ 2)

Step-by-step explanation:

Divide the 2 into each digit, which must be in the same spot it was before:

Knowing that 8 in 4.8 ⇒ 0.8

Thus, you can infer that [B] is wrong

You also infer that [D]  and [C] is wrong because 4 is a whole number.

Thus, that left us with [A] 4 ÷ 2+0.8 ÷ 2 which shows the quotient of 4.8 ÷ 2

Hence, [A] 4 ÷ 2+0.8 ÷ 2 is the answer.

<em>~Learn with Lenvy~</em>

5 0
2 years ago
Read 2 more answers
Given the equation: 2y+8x=20. Rearrange the equation into slope-intercept form.
zhannawk [14.2K]

Answer:

y = - 4x + 20 ... slope=-4   y intercept:20

Step-by-step explanation:

2y+8x=20

2y=-8x+20

y = - 4x + 20 ... slope=-4   y intercept:20

(y = mx + b)

8 0
2 years ago
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If a rectangle JKLM, JK is equal to 12 feet, and LN is equal to 6.5 feet, find KM
Rus_ich [418]
12.5 feet is the answer.


8 0
3 years ago
Read 2 more answers
P is inversely proportional to V.<br> When V = 8, P = 5<br> Find a formula for Pin terms of V.
AveGali [126]

Answer:

P = \frac{40}{V}

Step-by-step explanation:

given P is inversely proportional to V then the equation relating them is

P = \frac{k}{V}

to find k use the condition when V = 8 , P = 5 , then

5 = \frac{k}{8} ( multiply both sides by 8 to clear the fraction )

40 = k

P = \frac{40}{V} ← equation of proportion

6 0
2 years ago
Read 2 more answers
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