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Sonbull [250]
3 years ago
12

A cylinder has a height of 9 centimeters and a radius of 13 centimeters. What is its volume? Use ​ ≈ 3.14 and round your answer

to the nearest hundredth.
Mathematics
1 answer:
mash [69]3 years ago
5 0

Step-by-step explanation:

as any other fully symmetric 3D object, the volume is

base area × height.

the area of a circle is

pi×r²

so, we have in our case

pi×13²×9 = 3.14×169×9 = 4,775.94 cm³

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Please help me I need it right now
Nana76 [90]

Answer:

X+y=180, Y=Z, X+Z=180

Step-by-step explanation:

Hope this helps. i remember doing this.

6 0
3 years ago
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients.
Anika [276]

Answer:

\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \  }

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})

Now we can substitute in the equation

x^2y''(x)+9xy'(x)-20y(x)=0\\ e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\ \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\ \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\

so the new equation is

y''(t)+ 8y'(t)-20y(t)=0

the auxiliary equation is

x^2+8x-20=0\\ x^2-2x+10x-20=0\\x(x-2)+10(x-2)=0\\(x+10)(x-2)=0\\ x=-10\text{ or }x=2

so the solutions of the new equation are

y(t)=ae^{2t}+be^{-10t}

with a and b real

as

x(t)=e^t\\ t(x)=ln(x)

y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}

hope this helps

do not hesitate if you have any questions

8 0
3 years ago
What is the solution of log3x − 5 16 = 2?
devlian [24]
<span> log3x − 5 16 = 2
+516            +516
log3x=518
x=(10^518)/3
the answer seems a bit crazy, you probably typed something wrong</span>
5 0
3 years ago
It cost $109 per night to rent a motel room in Hampton. There is a one time $30 non refundable deposit required. How much will i
Lelu [443]

Answer: $793

Step-by-step explanation:

You would take the $109 and multiply it by 7 ( the amount of days in a week) and add $30 non-refundable fee! hope this helps :)

8 0
4 years ago
There's supposed to be 2 ansers for x, by the way​
lorasvet [3.4K]

Answer:

  • x = 143° and x = 323°

Step-by-step explanation:

<u>Solving</u>

  • 3tanx = -4
  • tanx = -4/3
  • tan values are negative in the 2nd and 4th quadrant
  • The base value is x = 53°

In <u>Quadrant II</u>,

  • 90° + 53°
  • ⇒ <u>x = 143°</u>

In <u>Quadrant IV</u>,

  • 270° + 53°
  • ⇒ <u>x = 323°</u>
3 0
2 years ago
Read 2 more answers
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