The formula for the volume of a cylinder is V = πr2h. The volume of a cylinder is three times the volume of a cone with the same radius and height. If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of cone R in terms of the radius of cylinder r is

Answers

Answer 1

Answer: Since both objects are assumed to have the same volume, matching the formulas we'll get:

π $r^(2)$ h = $(1)/(3)$ π $R^(2)$ h

Having both π and h at both sides of the equation, we can ignore them, so:

$r^(2)$ = $(1)/(3)$ $R^(2)$

And clearing R, according to the equation rules, we'll get:

$\sqrt[2]{3 r^(2) }$ = R

Answer 2

Answer:

Answer:

A on egde

Step-by-step explanation:

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the area under the graph line made with the x-axis represents the change in position of the object on a velocity versus time graph. true false

Answers

Answer:

True, because the integral of velocity is displacement.

Step-by-step explanation:

Katherine is three times older than Joel now. In twenty years Katherine will be six years older than Joel. How old is Katherine now?

Answers

She is currently 9 years old.

If Katherine is 9, and Joel is 3, 20 years later they'll be 29 and 23. Katherine is 6 years older than him.

k = 3*j;
k + 20 = 6 + (j + 20) => k = 6 + j; but k =3*j => 3*j = 6 + j => j = 3( Joel has 3 years) and k = 9 (Katherine has 9 years);

Max or min value y=3x^2+6x-5

Answers

$y = 3x^2+6x-5$

For a parabola $ax^2+bx+c$ the vertex's x equals:

$(-b)/(a)$

$a = 3, b =6$

$x = (-6)/(2*3)$

refine:

$x = -1$

Plug in x = -1 to find the y value :

$y=3(-1)^2+6(-1)-5$

refine :

$y = -8$

Therefore the parabola vertex is :

$(-1,-8)$

if a < 0 , then the vertex is a maximum value

if a > 0, then then vertex is a minimum value

a=3

Therefore $(-1,-8)$ minimum

hope this helps!

What is 30:12 simplified

Answers

30:12
The Highest common factor is 6;
Dividing both terms by 6
5:2

How do I expand
r(r-r2) the 2 is meant to be r squared

Answers

$r(r-r^2) \n =r^2-r^3$

$r(r-r^2) =\n r^2-r^3$

Factor completely 16x2 + 40x + 25

Answers

Equation at the end of step 1 : (24x2 + 40x) + 25 Step 2 :Trying to factor by splitting the middle term

2.1     Factoring  16x2+40x+25

The first term is,  16x2  its coefficient is  16 .
The middle term is,  +40x  its coefficient is  40 .
The last term, "the constant", is  +25

Step-1 : Multiply the coefficient of the first term by the constant   16 • 25 = 400

Step-2 : Find two factors of  400  whose sum equals the coefficient of the middle term, which is   40 .

-400 + -1 = -401 -200 + -2 = -202 -100 + -4 = -104 -80 + -5 = -85 -50 + -8 = -58 -40 + -10 = -50 -25 + -16 = -41 -20 + -20 = -40 -16 + -25 = -41 -10 + -40 = -50 -8 + -50 = -58 -5 + -80 = -85 -4 + -100 = -104 -2 + -200 = -202 -1 + -400 = -401 1 + 400 = 401 2 + 200 = 202 4 + 100 = 104 5 + 80 = 85 8 + 50 = 58 10 + 40 = 50 16 + 25 = 41 20 + 20 = 40 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  20  and  20
                     16x2 + 20x + 20x + 25

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4x • (4x+5)
              Add up the last 2 terms, pulling out common factors :
                    5 • (4x+5)
Step-5 : Add up the four terms of step 4 :
                    (4x+5)  •  (4x+5)
             Which is the desired factorization

Multiplying Exponential Expressions :

2.2    Multiply  (4x+5) by  (4x+5)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (4x+5) and the exponents are :
          1 , as  (4x+5) is the same number as  (4x+5)1
and   1 , as  (4x+5) is the same number as  (4x+5)1
The product is therefore,  (4x+5)(1+1) = (4x+5)2

Final result : (4x + 5)2

hope this helps hope i am brainliest i need it

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a fast food restaurant sells small soft drinks for .99, medium soft drinks for $1.09, and large drinks for $1.29. during the lunch time rush, mark sold 65 drinks for a total of $ 70.55. the number of small and large drinks combined were 5 fewer than the number of medium drinks. how many drinks of each size were sold