Answer:
This is an exponential decay
Because the base of the exponent is 1/4.4 which is less than 1
Step-by-step explanation:
What is exponential growth?
when the base of our exponential is bigger than 1, which means those numbers get bigger.
What is exponential decay?
when the base of our exponential is in between 1 and 0 and those numbers get smaller.
Answer:
1 = 144
2 = 80
3 = 192
4 = 1209.6 or 1209
5 = 375
Step-by-step explanation:
A triangular pyramid has 4 triangular faces. If all 4 have the same area, then one of them has area 1/4 of the surface area, 1836. That gives 459 sq ft as the area of one of the triangular faces.
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The original width would be 19 and the original length would be 32.
Let w be the width. Then 2w-6 would be the length. However, after cutting a 3-inch square from each corner, both the width and length left over to fold into a box would be 6 inches smaller; thus the dimensions would be w-6 and 2w-6-6 or 2w-12.
Since the section cut out is 3 inches long, 3 will be the height of the box.
Volume is found by multiplying the length, width and height of the box; thus we have:
1014=(w-6)(2w-12)(3)
We multiply the binomials and have:
1014 = [w*2w-12*w-6*2w-6(-12)](3)
1014 = (2w²-12w-12w+72)(3)
1014 = (2w²-24w+72)(3)
1014 = 6w² - 72w + 216
When solving a quadratic equation, we want it set equal to 0. Subtract 1014 from each side:
1014-1014 = 6w² - 72w + 216 - 1014
0 = 6w² - 72w - 798
We will use the quadratic formula to solve this:

Since we cannot have a negative number for a measurement, 19 has to be the width; then 2(19)-6 = 32 would be the length.