Answer:
<h2>MN = 9.1 cm</h2>
Step-by-step explanation:
If MN is tangent of a circle then the angle M is a right angle.
We have a dimeter of acircle d = 8 cm.
Therefore the radius CM = 8 cm : 2 = 4cm.
In a right triangle CMN use the Pythagorean theorem:
Substitute CM = 4cm and CN = 9.9 cm:
<em>subtract 16 from both sides</em>
Let
e = Gibson Explorer’s = 20
v = Gibson Flying V’s
So, our problem is
<u>Maximize</u>Money = 80e + 5v<span>
<u>Subject to</u>0 </span>≤ <span>e ≤ 20
</span>0 ≤ v ≤ 20
0 ≤ e + v ≤ 30
In order to solve this problem, we look at the graph (attached), and find the value of Money =80e + 5v at corner points to find the maximum value of money.
(e,v)=(0,0) >> Money = 80e+5v = 80*0+5*0 = 0
(e,v)=(0,20) >> Money = 80e+5v = 80*0+5*20 = 100
(e,v)=(20,0) >> Money = 80e+5v = 80*20+5*0 = 1600
(e,v)=(20,10) >> Money = 80e+5v = 80*20+5*10 = 1650 (maximum)
(e,v)=(10,20) >> Money = 80e+5v = 80*10+5*20 = 900
So Bob can make the
<u>most money = $1,650</u> when he makes and sell
e = <span>Gibson Explorer’s = 20
</span>v = Gibson Flying V’s = 10
1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.
For given question,
Let x be the quantity ( in liters ) of glycerin added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin,
Thus,
Quantity of glycerin in 12 liters + Quantity of glycerin in x
= Quantity of glycerin in resultant mixture.
⇒ 8% of 12 + 100% of x = 16% of (12 + x )
⇒ 0.08 × 12 + x = 0.16 × ( 12 + x )
⇒ 0.96 + x = 0.16 × 12 + 0.16x
⇒ 0.96 + x = 1.92 + 0.16x
⇒ x - 0.16x = 1.92 - 0.96
⇒ 0.84x = 0.96
⇒ x = 1.143 liters
Therefore, 1.143 liters of glycerin should be added to 12 liters of an 8% glycerin solution so that the resulting solution contains 16% glycerin.
Learn more about the resulting solution here:
brainly.com/question/12051765
#SPJ4
K is equal to 3. to find this i used the slope formula y2-y1/x2-x1. 4-k/-1-2
-1-2=-3 so that means that 4-k has to equal 1. 4-3=1
k=1
