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3 years ago

a 175cm tall student casts a shadow that is 2.3cm long. at the same time, a tree casts a shadow that is 8.2m longest

Mathematics

1 answer:

Anika [276]3 years ago

8 0

Ok so I’m assuming the question is how the tall is we need to find the Angle of the sun so

Student : 175

Shadow: 2.3

Hypotenuse: 175.0151136

Using -cos(175/175.0151136) we find the

Suns angle: .753 Above him/her

Our tree’s shadow:8.2

Using the suns angle we use cos(x

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For the given angle 0, identify the reference angle, _

ankoles [38]

Answer:

π\6

Step-by-step explanation:

The reference angle is the smallest angle measured from the terminal side of the angle (where the angle ends) to the x axis. The reference angle is an acute angle (i.e less than 90° or π/2)

For O = 11π/6 = 1.833π

1.833π is in the fourth quadrant between 3π/2 radians and 2π radians. Since it is in the fourth quadrant, the reference angle is given as:

reference angle = 2π - 11π/6 = π\6

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3 years ago

Uninhibited growth can be modeled by exponential functions other than A(t) =Upper A 0 e Superscript kt. For example, if an i

laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than $A(t)=A_{0}e^{kt}$ . for example, if an initial population P₀ requires n units of time to triple, then the function $P(t)=P_{0}(3)^{\frac{t}{n} }$ models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form $P(t)=P_{0}(3)^{\frac{t}{n} }$ that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form $A(t)=A_{0}e^{kt}$ .

Answer: a) $P(t)=50(3)^{\frac{t}{30} }$

b) P(t) = 280 insects

c) t = 74 days

d) $A(t)=50e^{0.037t}$

Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

$P(t)=50(3)^{\frac{t}{30} }$

b) In t = 47 days:

$P(t)=50(3)^{\frac{t}{30} }$

$P(47)=50(3)^{\frac{47}{30} }$

$P(47)=50(3)^{1.567}$

P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

$750=50(3)^{\frac{t}{30} }$

$\frac{750}{50}=(3)^{\frac{t}{30} }$

$(3)^{\frac{t}{n} }=15$

Using the property <u>Power</u> <u>Rule</u> of logarithm:

$log(3)^{\frac{t}{30} }=log15$

$\frac{t}{30}log(3)=log15$

$t=\frac{log15}{log3} .30$

t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

A(t) = 3A₀ and t = 30

$A(t)=A_{0}e^{kt}$

$3A_{0}=A_{0}e^{30k}$

$3=e^{30k}$

Use Power Rule again:

$ln3=ln(e^{30k})$

$ln3=30k$

$k=\frac{ln3}{30}$

k = 0.037

Equation for exponential growth will be:

$A(t)=50e^{0.037t}$

3 0

3 years ago

a dealer paid 10000 for a boat at an auction. at the dealership a sales person sold the boat for 30 percent more than the auctio

podryga [215]

Commission is 2500
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3 years ago

Which of the following equations represents a line that is parallel to the line that passes through the points below?

Pepsi [2]

Answer:

See below

Step-by-step explanation:

Two lines are parallel if they have the same slope but different y-intercepts. So the slope that can be formed given the points (-3,6) and (9,2) is (9-(-3))/(2-6)=12/-4=-3

With y=-3x+b, we need b, which can be found by plugging in either point:

2=-3(9)+b

2=-27+b

29=b

So the y-intercept therefore cannot be 29 but it can be any real number.

So the equation y=-3x+2 works, y=-3x+3, y=-3x+4, and so on....

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3 years ago

Use the graph of the polynomial function to find the factored form of the

elixir [45]

Answer:

I dont but want to.

Hope this helps! :) ;-;

Step-by-step explanation:

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2 years ago