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irga5000 [103]
3 years ago
11

PLEASE HELP ME!!!!!!!!!!!!!!!!!!! ASAP :)

Mathematics
1 answer:
Mashcka [7]3 years ago
4 0

Answer:

c) The growth factor per days is 1.08

e) The growth factor per hour is 1.08^{1/24}

Step-by-step explanation:

Given the following data;

P(d) = 10 * 1.08^{d} in thousands.

a. To find the number of insects on day 1;

Day, d = 1

P(d) = 10 * 1.08^{d} ......equation 1

Substituting into the formula, we have;

P(1) = 10 * 1.08^{1}

P(1) = 10 * 1.08

P(1) = 10.08

Therefore, option (a) and (b) are incorrect.

c. To find the growth factor per day;

An exponential function is given by the formula;

y = mg^{x} .....equation 2

Where;

g is the growth factor of a population.

Comparing eqn 2 with eqn 1;

g = 1.08

Therefore, option (c) is correct.

e. To find growth factor per hour;

From equation 1 above;

P(1) = 10 * 1.08^{\frac {1}{2}}

Therefore, option e is correct.

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Answer:

Population variance 579

Population standard deviation 24

Step-by-step explanation:

The average estimated hours a person in the United States spent playing video games per year from 2002 to 2012 were 71, 80, 82, 78, 80, 91, 107, 121, 125, 131, and 142.

The population variance is given by:

\sigma^2=\frac{\sum(x-\mu)^2}{n}

\mu=\frac{71+80+82+78+80+91+107+121+125+131+142}{11}

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This implies that:

\sigma^2=\frac{(71-\frac{1108}{11})^2+(80-\frac{1108}{11})^2+(82-\frac{1108}{11})^2+(78-\frac{1108}{11})^2+(80-\frac{1108}{11})^2+...+(142-\frac{1108}{11})^2}{11}

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Answer:

a) t = 4

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Step-by-step explanation:

You have the following vector equation for the position of a particle:

r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}    (1)

(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.

For a height of 20 you have:

5t=20\\\\t=\frac{20}{5}=4

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v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}    (2)

and for t=4 (height = 20):

v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}

(c) The vector parametric equation of the tangent line is given by:

r_t(t)=r_o+vt      (3)

ro: position of the particle for t=4

r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}

Then you replace ro and v in the equation (3):

r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}

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Step-by-step explanation:

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