Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>
![\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdA%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bw%5Cell%5D)
By the Product Rule:
Since we know that dl/dt = 6 and that dw/dt = 5:
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
A) <span>Scale factor of the smaller pyramid to the larger pyramid in simplest form:
</span>6 m / 12 m = 1/2
b) <span>Ratio of the areas of the bases of the smaller pyramid to the larger pyramid:
</span><span>(1/2)^2 = 1/4 </span>
c) <span>Ratio of the volume of the smaller pyramid to the larger:
</span><span>(1/2)^3 = 1/8 </span>
d) <span>Volume of the smaller pyramid:
</span>(1/8) * 400 m^3 = 50 m^3
Multiply everything in the parenthesis by a.
ac + ab = d
Subtract ab from both sides.
ac = d - ab
Divide a on both sides.
c = d - ab / a
Hope this helps!
Answer: y=2x+4 for parallel and y=-1/2x+1 1/2
Step-by-step explanation: you need to do an equation using the slope which you can find by using y2-y1/x2-x1
from there you have to use y-y1=m(x-x1)
Dimensions of the room in cm = 2.54 x 12 by 15 x 2.54 by 2.54 x 8.5 = 30.48 by 38.1 by 21.59
Volume of the room in cubic cm = 30.48 x 38.1 x 21.59 cubic cm = 25,072.21 cubic cm
Given that the density of air at room temperature is
, thus the mass of air in the room = 25,072.21 x 0.00118 = 29.59 g = 0.0296 kg
Given that the lethal dose of HCN is approximately 300 mg HCN per kilogram of air when inhaled, thus the <span>amount of HCN that gives the lethal dose in the small laboratory room is given by 300 x 0.0296 =
8.88 mg.</span>
