The value of the scale factor is 3. Then the height and area of the triangle ΔABC will be 9 ft and 54 square ft.
<h3>What is dilation?</h3>
Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
The area of the triangle ΔDEF is 6 square ft. And the base length of the triangle ΔDEF is 4 ft.
The area of the triangle is given as
Then the height of the triangle ΔDEF will be
Then the scale factor will be
Then the height of the triangle ΔABC will be
Then the area of the dilated triangle ΔABC will be
More about the dilation link is given below.
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Answer: The answer is x=6, the final set of (x,y) values are (6,-4)
Step-by-step explanation:
You must move around the equation to get it to y= mx+b to find the (x,y) values
Since you know y=-4 since it is stated above, plug in -4 for all y values and solve.
1. 6x+ 7(-4) =4x +4(-4)
2. 6x -28= 4x -16
3. 2x-28=-16
4. 2x=12
5. x=6
Answer:
Step-by-step explanation:
We have volume of cone as
and for a cone always r/h = constant
Given that r' = rate of change of radius = -7 inches/sec
(Negative sign because decresing)
V' =- 948 in^3/sec
Radius = 99 inches and volume = 525 inches
Height at this instant = 
Let us differentiate the volume equation with respect to t using product rule
![V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%5C%5CV%27%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2rhr%27%2Br%5E2%20h%27%5D%5C%5C-948%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2%2899%29%28-7%29%28%5Cfrac%7B0.1607%7D%7B%5Cpi%7D%29%2B99%5E2%20h%27%5D%5C%5C)
![-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14 + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514](https://tex.z-dn.net/?f=-948%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%5B2%2899%29%28-7%29%28%5Cfrac%7B0.1607%7D%7B%5Cpi%7D%29%2B99%5E2%20h%27%5D%5C%5C-948%20%3D%2033%283.14%29%28-2.25%2F3.14%20%20%2B%2099%20h%27%29%5C%5C-9.149%3D-0.72%2B99h%27%5C%5C-8.429%20%3D%2099h%27%5C%5Ch%27%20%3D%200.08514)
Rate of change of height = 0.08514 in/sec
Answer:
The slope of a line parallel to the given line = 5
The slope of a line perpendicular to the given line = - 1/5
Step-by-step explanation:
