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fgiga [73]
3 years ago
7

A ramp rises 2.9 ft vertically and extends 58 At horizontally. Find the slope of the ramp.​

Mathematics
2 answers:
Ymorist [56]3 years ago
8 0

Answer:

0.05

Step-by-step explanation:

The formula for slope is rise/run.

So, in this case it would be 2.9ft/58ft = 0.05

Tcecarenko [31]3 years ago
6 0

Answer:

The slope of the ramp is 2.86 degrees to the nearest hundredth.

Step-by-step explanation:

tan x = 2.9 / 58 = 0.05    where x is the angle of the slope.

x = 2.86 degrees to the nearest hundredth.

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Step-by-step explanation:

Given

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Using the formula

f(x) - g(x) =  3x² + x - 3 - ( x² - 5x + 1)

              = 3x² + x - 3 - x² + 5x - 1

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Therefore, the value of f(x) - g(x) is:

f(x) - g(x) =  2x² + 6x - 4

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3 years ago
(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
valentinak56 [21]

Find the intersection of the two planes. Do this by solving for <em>z</em> in terms of <em>x</em> and <em>y </em>; then solve for <em>y</em> in terms of <em>x</em> ; then again for <em>z</em> but only in terms of <em>x</em>.

-4<em>x</em> + 2<em>y</em> - <em>z</em> = 1   ==>   <em>z</em> = -4<em>x</em> + 2<em>y</em> - 1

3<em>x</em> - 2<em>y</em> + 2<em>z</em> = 1   ==>   <em>z</em> = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -4<em>x</em> + 2<em>y</em> - 1 = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -8<em>x</em> + 4<em>y</em> - 2 = 1 - 3<em>x</em> + 2<em>y</em>

==>   -5<em>x</em> + 2<em>y</em> = 3

==>   <em>y</em> = (3 + 5<em>x</em>)/2

==>   <em>z</em> = -4<em>x</em> + 2 (3 + 5<em>x</em>)/2 - 1 = <em>x</em> + 2

So if we take <em>x</em> = <em>t</em>, the line of intersection is parameterized by

<em>r</em><em>(t)</em> = ⟨<em>t</em>, (3 + 5<em>t</em> )/2, 2 + <em>t</em>⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

(a) The tangent vector to <em>r</em><em>(t)</em> is parallel to this line, so you can use

<em>v</em> = d<em>r</em>/d<em>t</em> = d/d<em>t</em> ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in <em>x</em> = -1, <em>y</em> = 1, and <em>z</em> = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

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