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SCORPION-xisa [38]
3 years ago
5

What is one fourth of a number decreased by 10,is -50 ​

Mathematics
2 answers:
Andru [333]3 years ago
6 0

Answer:

x=-160

Step-by-step explanation:

One-fourth of a number decreased by 10 is -50. Find the number.

\frac{1}{4}x-10=-50

First, add 10 to both sides:

\frac{1}{4}x-10+10=-50+10\\\\\frac{1}{4}x=-40

Then, divide each side by \frac{1}{4}:

\frac{1}{4}x\div{\frac{1}{4}}=-40\div{\frac{1}{4}}\\\\x=-40\times{\frac{4}{1}}\\\\x=-160

Rashid [163]3 years ago
5 0

1/4x - 10 = -50

1/4x = one forth of a number

-10 is decreased by 10

= -50 means is -50

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QUESTION 1
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It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is

<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)

The cosine of the angle between the vectors can be obtained from the dot product identity,

<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>)   ==>   cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)

so that

<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)

For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is

<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   <em>W</em> ≈ 5.12 J

(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).

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