The circumference of a circle is10π feet what is the radius
1 answer:
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Answer:
The answers are:
- 2u = <10,2>
- -3u = <-18,-6>
- u+v = <11,3>
- 3u-4v = <-9,-5>
Step-by-step explanation:
Given vectors are:
u = <5,1>
v = <6,2>
The vectors are given in the form of ordered pairs, the operations can be applied on the coordinates of ordered pairs
Now,
Now we have to add two vectors
In order to add two vectors, their respective coordinates are added:
So,
And
Hence,
The answers are:
- 2u = <10,2>
- -3u = <-18,-6>
- u+v = <11,3>
- 3u-4v = <-9,-5>
Answer:
(24) 3 - 4b = 10c + 10
(25) 4(3c+5) = 8
(26) - 6
(27) 4
Step-by-step explanation:
These questions require that words are translated into equations and then may be solved.
<u>(</u>24) Three minus four times a number is equal to ten times a number plus ten.
let the first number be b.
<em>(a)Three minus four times a number ... </em>can be represented as:
3 - (4 x b) = 3 - 4b
<em>(b) </em>...<em>ten times a number plus 10</em>
let the other number be c. Therefore we have;
(10 x c) + 10 = 10c + 10
Now, <em>three minus four times a number</em><em> is equal to </em><em>ten times a number plus ten </em>means that expressions in (a) and (b) above are equal. i.e
3 - 4b = 10c + 10
<u>(</u>25<u>)</u> Four times the quantity of three times c plus 5 is equal to 8.
<u>(</u>a) <em>four times the quantity of three times c plus 5</em> can be represented as
4 x (3 x c + 5) = 4(3c + 5)
(b) ... <em>is equal to 8. </em>This means that the expression in (a) is equal to 8.
4(3c + 5) = 8
(26) Six less than two thirds of a number is negative ten. Find the number.
(a) <em>six less than </em>can be represented as:
- 6
<em>(b) two thirds of a number </em> can be represented as
()x [where x is the number]
(c) <em>six less than two thirds of a number</em> can thus be written as;
()x - 6
(d) <em>... is negative 10 </em>means that the expression is (c) above is equal to -10. i.e
()x - 6 = -10
(e) Find the number.
The number can be found by solving for x in the expression in (d) above.
()x - 6 = -10 [multiply through by 3]
2x - 18 = -30 [collect like terms]
2x = -30 + 18
2x = -12 [divide both sides by 2]
x = - 6
Therefore, the number is -6
(27) Twenty-nine is thirteen added to four times a number. What is the number.
(a) <em>... thirteen added to four times a number</em> can be written as:
13 + 4b [where the number is b]
(b) <em>Twenty-nine is thirteen added to four times a number </em>means that the 29 is equal to the expression in (a) above. i.e
29 = 13 + 4b
(c) Find the number.
The number can be found by solving for b in the expression in (b) above. i.e
29 = 13 + 4b [collect like terms]
4b = 29 - 13
4b = 16 [divide both sides by 4]
b = 4
Therefore, the number is 4.