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lilavasa [31]
3 years ago
10

Two sides of a triangle are 8 m and 9 m in length and the angle between them is increasing at a rate of 0.06 rad/s. Find the rat

e at which the area of the triangle is increasing when the angle between the sides of fixed length isπ3rad.
Mathematics
1 answer:
Lelechka [254]3 years ago
4 0
<h2>Rate at which area is increasing is 1.08 m²/s.</h2>

Step-by-step explanation:

Area of triangle is with side a and b and angle C between them is given by

                             A = 0.5 ab SinC

Here we need to find how area changes with  a and b fixed and C is changing,

                       \frac{dA}{dt}=\frac{d}{dt}\left (0.5 absinC\right )\\\\\frac{dA}{dt}=0.5ab\frac{d}{dt}\left (sinC\right )\\\\\frac{dA}{dt}=0.5abcosC\frac{dC}{dt}

We have

                 a = 8 m

                 b = 9 m

                 C=\frac{\pi}{3}rad\\\\\frac{dC}{dt}=0.06rad/s

Substituting

                 \frac{dA}{dt}=0.5\times 8\times 9\times cos\left ( \frac{\pi}{3}\right )\times 0.06\\\\\frac{dA}{dt}=1.08m^2/s

Rate at which area is increasing is 1.08 m²/s.

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Find the distance between points P(3, 4) and Q(4, -6) If necessary round to the nearest hundredth.
Andrei [34K]

Answer:

10.05 units

Step-by-step explanation:

We can find the distance between these points using the distance formula. The distance formula is:

\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

We know that x1 is 3, x2 is 4, y1 is 4, and y2 is -6, so we can substitute inside the equation.

\sqrt{(4 - 3)^2 + (-6 - 4)^2} \\\\\sqrt{1^2 + -10^2} \\\\\sqrt{1 + 100} \\\\\sqrt{101} \\\\\approx10.05

Hope this helped!

7 0
3 years ago
38 = y/2. <br> What equals y?
yan [13]
<span>38 = y/2.
y = 38 * 2
y  = 76

answer
y = 76</span>
5 0
4 years ago
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PLEASE  HELP AND PLEASE HAVE THE CORRECT ANSWER !!!!!! THANK YOU
iragen [17]
1) p + 8 
Substitute 2 in for the variable. 
2 + 8 = \fbox {10}

2) 3p
Substitute 2 in for the variable.
3(2) = \fbox {6}

3) 16 - p
Substitute 2 in for the variable.
16 - 2 = \fbox {14}

4) -12 ÷ p
Substitute 2 in for the variable.
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7 0
3 years ago
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BARSIC [14]

A heptagon is a polygon.

It has 7 sides

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3 0
3 years ago
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Conference A and conference B each have 10 football teams. The table shows the number of football games that each team in the tw
babymother [125]

Answer with explanation:

1.Mean of a Data set

   =\frac{\text{Sum of all the observation}}{\text{total number of observation}}

=\frac{10+9+11+8+10+12+2+7+8+0+12+10+8+11+3+12+6+7+4+3}{20}\\\\=\frac{153}{20}\\\\=7.65

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=12

The mean number of wins for teams from the two conferences is 7.65.

The range in wins is  12.

3 0
3 years ago
Read 2 more answers
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