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3 years ago

the diameter of your bicycle wheel is 25 inched. how far will you move in two truns your wheel use 3 for pie

Mathematics

1 answer:

lianna [129]3 years ago

6 0

Answer:

150 inches

Step-by-step explanation:

Using 3 for pie, PIE x D= C

3 x 25= 75

for two roatations you multiply 75 times 2 and you get...

150

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A cone has a volume of 108 pi and a base diameter of 12. What is the height of the cone?

serious [3.7K]

Answer:

h = 9 units of length

Step-by-step explanation:

Volume of a circular right cone is:

V(c) = (1/3)*Area of the circular base * h

Where h is the height of the cone, then

V(c) = (1/3) * π * r² * h

And we have that V(c) = 108*π

Then:

108 * π = (1/3) * π * r² * h (1)

We know diameter of the circular base is 12 units, according to that

r = d/2 ⇒ r = 12/2 r = 6 units

Then:

108 * π [ cubic units ] = (1/3) * π * (6)² * h [square units] [ units of length]

When simplifying we have to take into account that in order to keep last equation h needs to have units of length

Therefore:

108 = (1/3) * 36 * h

h = ( 108* 3 )/ 36

h = 9 units of length

7 0

3 years ago

Show that y=cos(t)y=cos(t) is a solution to (dydt)2=1−y2(dydt)2=1−y2. Enter your answers below in terms of the independent varia

GrogVix [38]

Answer:

$(\frac{dy}{dt})^2=sin^2t$

Step-by-step explanation:

$y=cost$

DE : $(\frac{dy}{dt})^2=1-y^2$

If y is a solution of given DE then it satisfied the DE.

Differentiate w.r.t t

$\frac{dy}{dt}=-sint$

Using the formula

$\frac{d(cosx)}{dx}=-sinx$

LHS: $(\frac{dy}{dt})^2=(-sint)^2=sin^2t$

RHS

$1-y^2=1-cos^2t=sin^2t$

By using the formula

$sin^2t=1-cos^2t$

LHS=RHs

Hence, y is a solution of given DE

$(\frac{dy}{dt})^2=sin^2t$

7 0

3 years ago

How do you graph y=-1.5<img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20" id="TexFormula1" title=" x^{2} " alt=" x^{2} " align

lorasvet [3.4K]

$y=-1.5 x^{2} +6 \\ \\ x=-3 \Rightarrow y=-1.5*(-3)^2+6 =-1.5*9+6=-13.5+6=-7.5\\ \\x=-2 \Rightarrow y=-1.5*(-2)^2+6 =-1.5*4+6=-6+6=0\\ \\x=-1 \Rightarrow y=-1.5*(-1)^2+6 =-1.5*1+6=-1.5+6=-4.5\\ \\x=0 \Rightarrow y=-1.5*0^2+6 =6$

$x=1 \Rightarrow y=-1.5*(1)^2+6 =-1.5+6=-4.5\\ \\ x= 2 \Rightarrow y=-1.5*2^2+6 =-1.5*4+6=-6+6=0\\ \\x=3 \Rightarrow y=-1.5*3^2+6 =-1.5*9+6=-13.5+6=-7.5$

6 0

3 years ago

What is the square root of 32 over 4

castortr0y [4]

$\frac{\sqrt{32}}{4}$

Factor square root of 32: 2^5/2.

Factor 4: 2^2

$\frac{2^\frac{5}{2}}{2^{2}}$

Cancel 2 1/2= 2 1/2.

2 1/2= square root of 2.

Answer: $\sqrt{2}$

Hope this helps :)

4 0

3 years ago

Read 2 more answers

Create the equation of a quadratic function with a vertex of (5,6) and a y-intercept of -69

Elena L [17]

If the y-intercept is at -69, meaning the point is (0, -69), thus x = 0, y = -69

$\bf ~~~~~~\textit{parabola vertex form}
\\\\
\begin{array}{llll}
\boxed{y=a(x- h)^2+ k}\\\\
x=a(y- k)^2+ h
\end{array}
\qquad\qquad
vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\
-------------------------------\\\\
vertex~(5,6)\quad 
\begin{cases}
x=5\\
y=6
\end{cases}\implies y=a(x-5)^2+6
\\\\\\
\textit{we also know that }
\begin{cases}
x=0\\
y=-69
\end{cases}\implies -69=a(0-5)^2+6
\\\\\\
-75=25a\implies \cfrac{-75}{25}=a\implies a=-3
\\\\\\
therefore\qquad \boxed{y=-3(x-5)^2+6}$

3 0

2 years ago