What is the surface area of a sphere with a radius of 11 units?
2 answers:
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Answer:
D) y = -4/5x – 47/10
Step-by-step explanation:
Step 1. Find the <em>midpoint of the segmen</em>t.
The two end points are (-6, -4) and (-2, 1).
The midpoint is at the average of the coordinates.
(xₚ, yₚ) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
(xₚ, yₚ) = ((-6 - 2)/2, (-4 + 1)/2)
(xₚ, yₚ) = (-8/2, -3/2)
(xₚ, yₚ) = (-4, -3/2)
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Step 2. Find the <em>slope (m₁) of the segment</em>
m₁ = (y₂ - y₁)/(x₂ - x₁)
m₁ = (1 - (-4))/(-2 - (-6))
m₁ = (1 + 4)/(-2 + 6)
m₁ = 5/4
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Step 3. Find the <em>slope (m₂) of the perpendicular bisector </em>
m₂ = -1/m₁
m₂ = -4/5
====================
Step 4. Find the <em>intercept of the perpendicular bisector</em>
y = mx + b
y = -(4/5)x + b
The line passes through (-4, -3/2).
-3/2 = -(4/5)(-4) + b
-3/2 = 16/5 + b Multiply each side by 10
-15 = 32 + 10 b Subtract 32 from each side
-47 = 10b Divide each side by 10
b = -47/10
===============
Step 5. Write the <em>equation for the perpendicular bisector</em>
y = -4/5x – 47/10
The graph shows the midpoint of your segment at (-4, -3/2) and the perpendicular bisector passing through the midpoint and (0, -47/10).
Answer:
A's mixture is more acidic.
Step-by-step explanation:
Given:
Two friends mix water and citric acid.
One (Let A) add 3 cups of citric acid for every 16 cups of water and another (Let B)adds 2 cups of citric acid for every 12 cups of water.
Now, we have to find that whose mixture is more acidic means:-
Solution:
A add 3 cups of citric acid for every 16 cups of water, the ratio =
B adds 2 cups of citric acid for every 12 cups of water =
Now, to find that who mix more citric acid in the mixture, firstly we will equalize the denominator of both fraction by taking LCM so that can be compare easily.
LCM of 16 and 12:- <u>48</u>
16 - 16, 32, <u>48</u>, 64, 80, 96....
12 - 12, 24, 36, <u>48, </u>60, 72.......
For friend A -
For friend B -
<em>We found that in terms of 48 cups of water, friend A mixes 9 cups of acid while friend B mixes 8 cups of acid, means A is adding more acid than B and</em> hence friend A's mixture is more acidic.