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Dvinal [7]
3 years ago
5

AP calculus HW Need help on #61

Mathematics
1 answer:
Yuki888 [10]3 years ago
7 0
Expanding the limit, we get (x^2+2x∆x+∆x^2-2x-2∆x+1-x^2+2x-1)/<span>∆x

Crossing the 1s , the 2xs, and the x^2s out, we get

(2x</span>∆x+∆x^2-2∆x)/<span>∆x

Dividing the </span><span>∆x, we get 
2x+</span><span>∆x-2. 

Making the limit of </span><span>∆x=0, we get 2x-2.</span>
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In order for this ratio of volumes to be true, what measurements would have to be equal in all 3 solids?
Neporo4naja [7]

The measurements of the figures that should be equal in order for the ratio of volumes between the volumes of the cone, sphere, and cylinder of 1:2:3 to be true is; The radius and the height

<h3>What is a ratio?</h3>

A ratio is a comparison between the magnitudes or measurements of items, expressing the number of times one item in the ratio is contained within another item in the ratio.

The formula for the volume of a cone, V_p is, V_p = (1/3)·π·r₁²·h₁

The formula for the volume of a sphere, V_s, is V_s = (4/3)·π·r₂³

The formula for the volume of a cylinder, V_c, is V_c = π·r₃²·h₃

The ratio of the volumes in the question is 1:2:3

Therefore; The volume of the sphere is twice the volume of the cone, and the volume of the cylinder is three times the volume of the cone, which indicates;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁...(1)

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁...(2)

Equation (1) indicates that we have;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁

Where, h₁ = 2·r₂, we get;

(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·(2·r₂) = (4/3)·π·r₁²·r₂

Therefore; r₁ = r₂, and the diameter of the sphere is equal to the height of the cone

The radius of the cone is equal to the radius of the sphere

Equation (2) indicates;

π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁ = π·r₁²·h₁

Therefore;

r₃²·h₃ = r₁²·h₁

r₃ = r₁

h₃ = h₁

The radius of the cone = The radius of the cylinder

The height of the cone = The height of the cylinder

  • The ratio of the volumes, 1 : 2 : 3 is true when the measurements of the radius and the height are equal for all three solids.

Learn more about the volume of regular solids here:

brainly.com/question/15316195

#SPJ1

4 0
1 year ago
Write in slope intercept form . y+4=−12(x−2)
inna [77]

Answer:

20

Step-by-step explanation:

y+4=−12(x−2)

Step 1: Add -4 to both sides.

y+4+−4=−12x+24+−4

y=−12x+20

6 0
3 years ago
Read 2 more answers
Please help 15 points
Gwar [14]

Answer:

46/100

Step-by-step explanation:

The decimal reaches a point into the hundreths.

<em>kiniwih426</em>

5 0
2 years ago
Read 2 more answers
Mr Prothero places £3003 into a
mamaluj [8]

Answer:

£3,543.54

Step-by-step explanation:

Amount after 2 years = Principal + interest

Get the interest

Interest = PRT/100

Interest = 3003 * 9 * 2/100

Interest = 3003 * 18/100

Interest  = 30.03 * 18

Interest  = 540.54

Amount after 2 years = 3003 + 540.54

Amount after 2 years = £3,543.54

6 0
3 years ago
1/8 of a cup of cinnamon was sprinkle evenly over some pieces of toast. if 1/32 of a cup was sprinkled on each piece, how many p
Margaret [11]
C because C is the right answer
4 0
2 years ago
Read 2 more answers
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