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.
Answer:
The answer to your question is: 161x + 17y - 391 = 0
Step-by-step explanation:
Data
y-intercept = 23 Get the points (0, 23)
x- intercept = 4.75 (4.75, 0)
4.75 = 17/4 (17/4, 0)
slope
m = (y2 - y1) / (x2 - x1)
m = (0 - 23) / (17/4 - 0)
m = -23 / 17/4
m = - 161 / 17
equation
(y - y1) = m (x - x1)
( y - 23) = -161 / 17 (x - 0)
y - 23 = -161/17 x
17(y - 23) = -161x
17y - 391 = -161x
161x + 17y - 391 = 0
Answer:
Step-by-step explanation:
c
9514 1404 393
Answer:
5544 square units
Step-by-step explanation:
Translation does not change the dimensions of the figure. The two figures together tell you the right triangle has a base of 154 units and a height of 72 units.
The area of a triangle is given by ...
A = 1/2bh
A = 1/2(154 units)(72 units) = 5544 square units
The areas of each of the triangles are 5544 square units.
Following the principle of supplements angles, the angle next to the 101 is 79°. 79+38+c(call the third angle c) = 180
c = 180-117 =63° x is supplemental to c so 180 = x +c
180=x + 63
x =117
