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Naddika [18.5K]
3 years ago
10

Select the correct answer.

Mathematics
1 answer:
77julia77 [94]3 years ago
4 0
I’m pretty
Shore it’s b
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A newborn baby weighs 2900 grams. How many pounds does this baby weigh? Also how many pounds, how many ounces
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6.39 pounds, 102.29 ounces.

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After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.5 6/ (t+4)3 feet per year, where
kipiarov [429]

Answer:

<h2>a) 0.5367feet</h2><h2>b) 0.5223feet</h2><h2>c) 0.7292feet</h2>

Step-by-step explanation:

Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).

The amount of growth can be gotten by integrating the given rate equation as shown;

\int\limits {0.5 + \frac{6}{(t+4)^{3} }  } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} }  } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \  where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C

a)  The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from  t =1 to t = 2

\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} }  } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\   = 0.9167 - 0.5 + 0.12\\= 0.5367feet

b)  The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from  t =2 to t = 3

\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} }  } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\  = 1.439 - 0.9167\\= 0.5223feet

c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown

\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} }  } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\   = 0.9167 - 0.1875\\= 0.7292feet

8 0
3 years ago
Find a polynomial function of degree 7 with -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 1 as a zero
trapecia [35]

The polynomial function is P(x) = x^3(x + 1)^3(x -1)

<h3>How to determine the polynomial function?</h3>

The zeros of the polynomial and the multiplicities are given as:

  • -1 as a zero of multiplicity 3,
  • 0 as a zero of multiplicity 3,
  • 1 as a zero of multiplicity 1

The degree is given as

Degree = 7

The polynomial is represented as:

P(x) = (x - zero)^multiplicity

Using the above format, we have

P(x) = (x + 1)^3(x - 0)^3(x -1)

This gives

P(x) = x^3(x + 1)^3(x -1)

Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)

Read more about polynomial function at

brainly.com/question/2833285

#SPJ1

7 0
2 years ago
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