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3 years ago

PLEASE HELP I NEED THIS

Mathematics

2 answers:

Reptile [31]3 years ago

8 0

Answer:

Step-by-step explanation:

The Pythagorean Theorem is c^2=a^2+b^2. This can be applied to right triangles

h^2=x^2+y^2

Meaning the hypotenuse is equal to the square root of the sum of its squared sides.

In this case:

14^2=3^2+x^2

x^2=14^2-3^2

x^2=196-9

x^2=187

x=(187)^(1/2)

x=13.7 rounded to nearest tenth

Vesna [10]3 years ago

5 0

Answer:

I think it would be 11cm

Step-by-step explanation:

I think you would subtract the 3 by the 14

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Answer:

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Step-by-step explanation:

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4 years ago

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anygoal [31]

Answer:

B: $c(3c^2-4)$

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3 years ago

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.

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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:

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

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

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:

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

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Kitty [74]

A^2 + b^2 = c^2
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