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klio [65]
2 years ago
5

Please help with these question, giving brainliest :)

Mathematics
1 answer:
garri49 [273]2 years ago
3 0

Answer:

Step-by-step explanation:

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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
The height of a football during a punt is modeled by h=-16t^2+60t+3. If the football hits the ground, how long did it stay in th
weqwewe [10]

"how long..." is asking for time (t).  "The amount of time spent in the air" is the time from when the ball was kicked (0 seconds) to the time it landed on the ground.  Need to find the x-intercepts (one will be negative which will be invalid). You can do this by factoring ... <em>or by using the quadratic formula.</em> With the equation you provided, it is not factorable, so you must use the quadratic formula.

h = -16t² + 60t + 3

   a=-16   b=60  c=3

t = \frac{-b +/- \sqrt{b^{2}-4ac } }{2a}

t = \frac{-60 +/- \sqrt{60^{2}-4(-16)(3) } }{2(-16)}

t = \frac{-60 +/- \sqrt{3600 + 192} }{-32}

t = \frac{-60 +/- \sqrt{3792} }{-32}

t = \frac{-60 +/- 61.6}{-32}

t = \frac{-60 + 61.6}{-32}   or   t = \frac{-60 - 61.6}{-32}

t = \frac{1.6}{-32}        or     t = \frac{-121.6}{-32}

   t = -0.05            or     t = 3.8           <em>disregard the negative</em>

Answer: 3.8 seconds


     

8 0
3 years ago
For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?
Klio2033 [76]
When b=0
f(x)=ax^2+c

test each
A. with x^2-1, A is false
B. with -x^2-1, B is false
C. cannot find contradiction
D. the axis is actually x=0, 0 is nithere positive nor negative, false


answer is C

7 0
3 years ago
Read 2 more answers
Which of the following is the vertex of the equation \large x^2-2x=-5 ?
Lelu [443]
I think it’s C but I’m not too sure
8 0
3 years ago
What is the value of x in the equation x - 2/3 + 1/6 = 5/6?<br><br> 1) 4<br> 2) 6<br> 3) 8<br> 4) 11
Licemer1 [7]

Answer:

\large\boxed{x=\dfrac{4}{3}=1\dfrac{1}{3}}

Step-by-step explanation:

x-\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{5}{6}\qquad\text{multiply both sides by 6}\\\\6x-6\!\!\!\!\diagup^2\cdot\left(\dfrac{2}{3\!\!\!\!\diagup_1}\right)+6\!\!\!\!\diagup^1\cdot\left(\dfrac{1}{6\!\!\!\!\diagup_1}\right)=6\!\!\!\!\diagup^1\cdot\left(\dfrac{5}{6\!\!\!\!\diagup_1}\right)\\\\6x-(2)(2)+1=5\\\\6x-4+1=5\\\\6x-3=5\qquad\text{add 3 to both sides}\\\\6x=8\qquad\text{divide both sides by 6}\\\\x=\dfrac{8}{6}\\\\x=\dfrac{8:2}{6:2}\\\\x=\dfrac{4}{3}

3 0
3 years ago
Read 2 more answers
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