The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the pop
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Answer:
x= 3 inch should be turned up on each side
Step-by-step explanation:
Let the height of trough be x.
Width of trough be 12 - 2x.
and length of trough = 120 inch
Volume of trough, V = L×W×H = 120 × (12-2x) × x = 120x(12 - 2x)
For maximum volume, we find V' = 0
i.e 1440 -480x = 0
or x =
or x= 3
Hence x= 3 inch should be turned up on each side
Based on the calculations, the depth of tent is equal to 12 feet.
<h3>How to calculate the depth of the tent?</h3>Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):
- Triangle ABC is an isosceles triangle (AB = AC).
- The front and back of the triangle are identical triangles.
- Side AD is perpendicular side BC.
- CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.
Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:
AC² = AD² + DC²
AD² = AC² - DC²
AD² = 5² - 3²
AD² = 25 - 9
AD² = 16
AD = √16
AD = 4 feet.
Also, we would determine the area of the triangle (ABC):
Area = 1/2 × b × h
<u>Where:</u>
- b is the base area.
- h is the height.
Substituting the given parameters into the formula, we have;
Area = 1/2 × 6 × 4
Area = 12 feet².
Depth of tent = 3 × height of ADC
Depth of tent = 3 × 4
Depth of tent = 12 feet.
Read more on area of triangle here: brainly.com/question/21917592
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