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3 years ago

How do transformations preserve distance and angle?

Mathematics

1 answer:

katen-ka-za [31]3 years ago

8 0

Answer:

When a transformation doesn't change the side lengths and angle measurements

of a shape, we call this preserving length and angle measurement. These are rigid

transformations . Translations, rotations, and reflections are all rigid

transformations .

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The base of a solid is the region enclosed by the graphs of y=e^x, y=0, x=0, and x = 1. If each cross-section perpendicular to t

yanalaym [24]

Answer:

Step-by-step explanation:

The base of a solid in the region enclosed by the graphs of y = eˣ, y = 0, x = 0, and x = 1. Each cross-section perpendicular to the x-axis is an equilateral triangle. We want to find the volume of the solid.

Please refer to the graph below. We are concerned with the red region.

In order to find the volume, we essentially sum up the area of the figure at each x value. So, we integrate from x = 0 to x = 1.

The area for an equilateral triangle is given by:

$\displaystyle A=\frac{\sqrt{3}}{4}s^2$

Where s is the side length of the triangle.

Since the triangle lies perpendicular on the region, the side length of the triangle at x is simply y, which is eˣ.

Therefore, our volume is:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(y)^2\, dx$

Substitute:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(e^x)^2\, dx$

Evaluate the integral. Simplify:

$\displaystyle V=\frac{\sqrt3}{4}\int_0^1e^{2x}\, dx$

Integrate using u-substitution:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2x}\Big|_0^1\right)$

Evaluate:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2(1)}-e^{2(0)} \right)$

Therefore, the volume of the solid is:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^2-1\right)$

Our answer is A.

3 0

3 years ago

Read 2 more answers

Find the slope of the line passing through the points (3,9) and (3,-5)

rjkz [21]

Answer:

u do y2-y1 and x2-x1 then add ur answer

Step-by-step explanation:

7 0

4 years ago

The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula M=2/3log(E/10^11.8). Fin

laiz [17]

Just substitute M=4.2 in the given equation. Make the whole log term the subject.

 $\log(\frac{E}{10^{11.8}})=\frac{3M}{2}$

Then, remove the log,:

$\frac{E}{10^{11.8}}=10^{\frac{3M}{2}}

E=10^{11.8}\times10^{\frac{3\times4.2}{2}}=10^{11.8+6.3}=10^{18.1}=1,258,925,411,794,167,210$

4 0

4 years ago

Read 2 more answers

1.)how many boxes of tissues can you buy with $46.06 if one box costs $6.58?

GenaCL600 [577]

1. It is already given in the question that one box of tissues cost $6.58. Need to find the number of boxes that can be bought with $46.06.
So
$6.58 is required to buy = 1 box
Then
With $46.06 one can buy = (46.06/6.58) boxes
= 7
So with $46.06 a person can buy 7 boxes of tissue paper.
2. In this question it is given that Castle had spent $4.83 for buying a box of envelope. It is required to find the number of boxes of envelope Castle can buy with $38.64
Now
$4.83 is required to buy = 1 box of envelope
then with $38.64 Castle can buy = (38.64/4.83) boxes of envelope
= 8
So Castle can buy 8 boxes of envelope with $38.64

5 0

3 years ago

Read 2 more answers

How many times greater is 2.94 x 10^-8 and 6.22 10^-7?

Serga [27]

(2.94x10^-8)/(6.22x10^-7)=112.5 Times larger

6 0

3 years ago