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2 years ago

(03.05 LC)

Mathematics

2 answers:

vlabodo [156]2 years ago

8 0

3.14 * 3 * 6 = 56.52 cubic inches. Hope this helps. :)

Rama09 [41]2 years ago

8 0

V = 1/3 * a_base * height, a_base = pi * r^2

V = 1/3* pi * 3^2*6 = 56.54 cubic inch,

so ... Third one!!

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Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t ==> dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

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2 years ago

Find the surface area of the triangular prism

melomori [17]

Answer:

608 ft²

Step-by-step explanation:

1) Find the area of the bases

$A=\frac{1}{2} bh$ where b is the base length and h is the height

Plug in b and h

$A=\frac{1}{2} (12)(8)\\A=48$

Multiply the answer by 2 (because there are 2 bases)

A=96

Therefore, the area of the two bases is 96 ft².

2) Find the area of the two sides facing up

$A=lw$ where l is the length and w is the width

Plug in l and w

$A=10*16\\A=160$

Multiply the answer by 2 (because there are 2 sides)

A=320

Therefore, the area of these two sides is 320 ft².

3) Find the area of the bottom side

$A=lw$ where l is the length and w is the width

Plug in l and w

$A=12*16\\A=192$

Therefore, the area of this side is 192 ft².

4) Add all the areas together

96 ft² + 320 ft² + 192 ft²

= 608 ft²

Therefore, the surface area of the triangular prism is 608 ft².

I hope this helps!

5 0

2 years ago

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A rectangle garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet

Lana71 [14]

Width = 4ft

Length = 6ft

Explanation:

Let length = l ,

So, width = 2l-8

Perimeter of rectangle = 2x(length + width)

According to the question,

$20ft = 2X(l + 2l-8)\\20ft = 2X(3l -8)\\ 10ft = 3l-8\\18ft = 3l \\ l = 6ft$

Hence,

Width = 4ft

Length = 6ft

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3 years ago

What are 5 different equation that have x=5 as a solution.

777dan777 [17]

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Keith_Richards [23]

Answer:

0 answer is yes.........

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2 years ago