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Sliva [168]
3 years ago
14

Find the value of x the triangle shown below

Mathematics
2 answers:
Novay_Z [31]3 years ago
3 0

Answer:

82

Step-by-step explanation:

24+74+x=180

98+x=180

x=180-98

x=82

alexira [117]3 years ago
3 0

Answer:

x =82

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees

24+74+x = 180

Combine like terms

98+x = 180

Subtract 98 from each side

98+x-98= 180-98

x =82

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Step-by-step explanation:

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the volume of a cone of radius r and height h is given by v=1/3pir^2h. If the radius and height is both increasing at a constant
Tamiku [17]

Answer:

The rate of change of the volume \frac{dV}{dt} when the height is 9 centimeters and the radius is 6 centimeters is 24\pi \:\frac{cm^3}{s}

Step-by-step explanation:

This is a related rate problem because you know a rate and want to find another rate that is related to it. If 2 variables both vary with respect to time and have a relation between them, we can express the rate of change of one in terms of the other.

From the information given we know:

  • \frac{dr}{dt}=\frac{1}{2}\:\frac{cm}{s}
  • \frac{dh}{dt}=\frac{1}{2}\:\frac{cm}{s}
  • The volume of a cone of radius r and height h is given by V=\frac{1}{3} \pi r^2 h

We want to find the rate of change of the volume \frac{dV}{dt} when the height is 9 centimeters and the radius is 6 centimeters.

Applying implicit differentiation to the formula of the volume of a cone we get

\frac{dV}{dt}=\frac{1}{3}\pi [r^2\frac{dh}{dt}+2rh\frac{dr}{dt} ]

Substituting the values we know into the above formula:

\frac{dV}{dt}=\frac{1}{3}\pi [(6)^2\frac{1}{2}+2(6)(9)\frac{1}{2} ]\\\\\frac{dV}{dt}=\frac{1}{3}\pi[18+54]\\\\\frac{dV}{dt}=\frac{72\pi}{3}=24\pi \:\frac{cm^3}{s}

5 0
4 years ago
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