The width of the rug is 3 inches
Step-by-step explanation:
A knitter wants to make a rug for a dollhouse
- The length of the rug will be 2 inches more than it’s width
- The total area of the rug ( in square inches) based on the width w of the rug (in inches ) is given by A(w) = w (2 + w)
- The desired area of the rug is 15 square inches
We need to find the width of the rug
∵ The area of the rug is A(w) = w(2 + w)
- Simplify the right hand side
∴ A(w) = 2w + w²
∵ The desired area of the rug is 15 square inches
- Equate A(w) by 15
∴ 2w + w² = 15
- Subtract 15 from both sides
∴ 2w + w² - 15 = 0
- Its a quadratic equation arrange its terms from the greatest power of x
∴ w² + 2w - 15 = 0
Factorize it into two binomial factors
∵ w² = w × w
∵ 15 = 3 × 5
∵ 5w - 3w = 2w
∴ w² + 2w - 15 = (w -3)(w + 5)
∴ (w - 3)(w + 5) = 0
- Equate each factor by 0
∴ w - 3 = 0 OR w + 5 = 0
∵ w - 3 = 0
- Add 3 to both sides
∴ w = 3
∵ w + 5 = 0
- Subtract 5 from both sides
∴ w = -5 ⇒ rejected because no dimension with -ve value
∴ w = 3 only
The width of the rug is 3 inches
Learn more:
You can learn more about the quadratic equation in brainly.com/question/9328925
#LearnwithBrainly
1 -) ( 5 sin ø - 3 cos Ø )
________________
sin Ø + 2 cos Ø
← <u>SOLUTION</u><u>→</u>
( 5 sin ø - 3 cos Ø )
________________
sin Ø + 2 cos Ø
=> 5 - 3 cot ∅
( ___________ )
1 + 2 cot ∅
=>. 5 - 3 × 4
[ ____. ]
5
________________
1 + 2 x 4
__
5
= 25 - 12
________. (:. cot Ø = 4 / 5
5 + 8
= 13
___
13
= 1
2 - ) ( b sin Ø - a cos Ø)
_______________
b sin Ø+ a cos Ø
SOLUTION
( b sin Ø - a cos Ø)
_______________
b sin Ø+ a cos Ø
= ( b tan Ø - a )
____________
( b tan Ø+ a )
b
= b × ___ - a
a
__________. (:. tan Ø= b /a
b
b × ___. + a
a
= b ² - a ²
________
b² + a ²
Answer:
Ybdchbbdhcbhdbch
Step-by-step explanation:
Answer:
3.453125 or 3 29/64
Step-by-step explanation:
3 1/4 * 1 1/16 = 221/64
= 3 29/64
= 3.453125
Hope this helps :)