Alright, lets get started.
Sophie has 5 pieces of string that are 4 yards each.
1 yards = 3 feet,
So, 4 yards = feet
Total number of string she has = 5 piece
So, total length she has = feet
It means she had 60 feet string in starting.
Now, She uses 3 pieces that are each 3 feet long, means
She uses = feet
So, remaining string length will be = feet
Means 51 feet string does Sophie have. : Answer
Hope it will help :)
I would recommend "Introduction to Linear Algebra," by Gilbert Strang. It is a compact but very helpful textbook reference written by a well-known MIT professor. There is a corresponding online MIT course that is free, so that's a bonus. I am currently using it to study linear algebra with no class or previous experience, and I think it does a solid job of explaining things. Each section in the book has a set of questions for you to work through, and answers to selected questions appear in an appendix at the end of the book.
Hope this helps!
Step-by-step explanation:
<em>cotx-</em><em> </em><em>tanx</em><em>=</em><em> </em><em>2cot2x</em>
<em>L.H.S</em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>cosx</em><em>/</em><em>sinx-</em><em> </em><em>sinx</em><em>/</em><em>cosx</em><em> </em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>(</em><em>cos</em><em>²</em><em>x-</em><em> </em><em>sin</em><em>²</em><em>x</em><em>)</em><em>/</em><em> </em><em>sinxcosx</em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>[</em><em> </em><em>cos</em><em>²</em><em>x-</em><em>(</em><em>1</em><em>-cos</em><em>²</em><em>x</em><em>)</em><em>]</em><em>/</em><em>sinxcosx</em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>(</em><em> </em><em>2cos</em><em>²</em><em>x-1</em><em>)</em><em>/</em><em>sinxcosx</em>
<em> </em><em> </em><em> </em><em>2cosx</em><em>/</em><em> </em><em>2sinxcosx</em>
<em> </em><em> </em><em> </em><em>2cot2x</em>
Answer:
112 people
Step-by-step explanation:
= write the proportion where x is the number of people with a missplaced time
50x = 5600 cross multipy
x = 112 divide both sides by 50
3(1)+4<span>≥ 13
7</span><span>≥ 13
No
3(2.5)+4</span><span>≥ 13
11.5</span><span>≥ 13
No
3(3)+4</span><span>≥ 13
13</span><span>≥ 13
Yes
{3, 4.5, 5}</span>