2^2x=5^x−1
Take the log pf both sides:
ln(2^2x) = ln(5^x-1)
Expand the logs by pulling the exponents out:
2xln(2) = (x-1)ln(5)
Simpligy the right side:
2xln(2) = ln(5)x - ln(5)
Now solve for x:
Subtract ln(5)x from both sides:
2xln(2) - ln(5)x = -ln(5)
Factor x out of 2xln(2)-ln(5)x
x(2ln(2) - ln(5)) = -ln(5)
Divide both sides by (2ln(2) - ln(5))
X = - ln(5) / (2ln(2) - ln(5))
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>
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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Answer:
It should be obtuse.
Step-by-step explanation: if i'm not mistaken it has to be obtuse. sorry i'm still learning i'm a beginner but, i'm volunteering to help everyone anyways because i'm a very nice person.