The base of a triangle is 3 feet shorter than twice its height. if the area is 27 ft, find the dimensions of the triangle

A student uses a piece of string to measure the approximate distance between New York and Los Angeles on a globe she finds that

andre [41]

The answer is 250 miles per inch. Hope I helped!

3 0

3 years ago

Read 2 more answers

Find the area of the helicoid (or spiral ramp) with vector equation r(u, v) = ucos(v) i + usin(v) j + v k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π

Natasha2012 [34]

Let $H$ denote the helicoid parameterized by

$\mathbb r(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+v\,\mathbf k$

for $0\le u\le1$ and $0\le v\le9\pi$ . The surface area is given by the surface integral,

$\displaystyle\iint_H\mathrm dS=\iint_H\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$

We have

$\mathbf r_u=\dfrac{\partial\mathbf r(u,v)}{\partial u}=\cos v\,\mathbf i+\sin v\,\mathbf j$
$\mathbf r_v=\dfrac{\partial\mathbf r(u,v)}{\partial v}=-u\sin v\,\mathbf i+u\cos v\,\mathbf j+\mathbf k$
$\implies\mathbf r_u\times\mathbf r_v=\sin v\,\mathbf i-\cos v\,\mathbf j+u\,\mathbf k$
$\implies\|\mathbf r_u\times\mathbf r_v\|=\sqrt{1+u^2}$

So the area of $H$ is

$\displaystyle\iint_H\mathrm dS=\int_{v=0}^{v=9\pi}\int_{u=0}^{u=1}\sqrt{1+u^2}\,\mathrm du\,\mathrm dv$
$=\dfrac{9(\sqrt2+\sinh^{-1}(1))\pi}2$

5 0

3 years ago

Find the slope of the line. On a coordinate plane, a line goes through (0, negative 6) and (2, 0). a. Negative one-third c. 3 b.

statuscvo [17]

The slope of the line that passes through between (0, -6) and (2, 0) is: C. 3.

<h3>What is the Slope of a Line?</h3>

The slope of a line can be defined as the measure of the ratio of the vertical distance to the horizontal distance that exists between two points on a coordinate plane.

<h3>How to Find the Slope of a Line?</h3>

If we are given two points on a line, (x1, y1) and (x2, y2), the slope (m) is the rise/run = change in y / change in x = (y2 - y1)/(x2 - x1).

Given the following coordinates of two points as follows, (0, -6) and (2, 0), let:

(0, -6) = (x1, y1)

(2, 0) = (x2, y2)

Plug in the values into the slope formula to find the slope:

Slope (m) = (0 - (-6)) / (2 - 0)

Slope (m) = (0 + 6) / (2 - 0) [minus multiplied by minus is plus]

Slope (m) = (6) / (2)

Slope (m) = 3

Thus, the slope of the line that passes through between (0, negative 6) and (2, 0) is calculated as: C. 3.

Learn more about slope on:

brainly.com/question/3493733

#SPJ1

5 0

2 years ago

The bases of an isosceles trapezoid are represented by 4x and 2x.. The height of the trapezoid is represented by (x − 6). Which

rusak2 [61]

The formula for solving the area of a trapezoid is shown below:
Area = ((a+b)/2 ) * h
where "a" and "b" for the base and "h" for the height
a = 4x
b = 2x
c = (x-6)

The solution for the polynomial expression is shown below:
Area = (4x + 2x)/2 * (x-6)
Area = 6x/2 * (X-6)
Area = 3X * (X-6)
Area = 3X² - 18X

The answer is 3X² - 18X.

8 0

3 years ago

They’re 3 questions

ZanzabumX [31]

1A: Cylinder 1B: Sphere 2: Circle 3: Rectangle

7 0

3 years ago