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3 years ago

Helppppppppppppppppppppppppppp

Mathematics

1 answer:

Otrada [13]3 years ago

7 0

The equation is:
y = 10 sin(π/15 t) + 30
where 30 represents the initial height of the blade above the ground and π/15 represents the period as we are given that the blade completes two rotation every minute.Finally the 10 represents the length of the blades.

Hope this helps :)

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The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below:

iogann1982 [59]

Answer:

Step 2: 4(2) + 4(3x)

Step-by-step explanation:

By definition, the area of a rectangle is given by:

Area = Length × Width

In this case, we know that:

Area = 8 + 12x

Width = 4

Therefore:

Step 1: 8 + 12x

Step 2: 4(2) + (4)(3x)

Step 3: 4(2 + 3x)

Therefore, the dimensions of the rectangle are 4 and 2 + 3x.

The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be 4(2) + 4(3x). Which is the second option.

5 0

3 years ago

During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

2 years ago

50 POINTS!

photoshop1234 [79]

Answer:

9.4

Step-by-step explanation:

interpret and match The approximate

4 0

2 years ago

Can somebody pls show me how to solve this?

fomenos

Answer:

C. 52.5

Step-by-step explanation:

The total from W(-20) to Z(120) is 140.

You can add up all of the numbers in the ratio, 2:3:3, to get 8

Divide 140 by 8 to get 17.5

Multiply 17.5 times the number in the ratio for each segment, so the new ratio would be 35 : 52.5 : 52.5

Since you are trying to find segment XY, which was the 2nd number in the ratio, you would get your answer as 52.5

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3 years ago

Travis performs a dilation of 1/3 on a polygon. He then classifies the image and pre-image as being congruent. Is Travis correct

krok68 [10]

To polygons are <span>congruent when </span>their corresponding sides are equal in length and their corresponding angles are equal in measure.
so he's not true

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3 years ago