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FromTheMoon [43]
3 years ago
9

Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters

from the start line and the last hurdle is 15.5 meters from the finish line. Calculate how far apart the hurdles are from one another in decimal form?
Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
7 0

Answer: 32 meters

Step-by-step explanation:

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A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum
Ivan

Answer:

Differential equation

\frac{dy}{dt} =ky(1-y)

Solution

y=\frac{1}{1+4e^{-0.327t}}

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

\frac{dy}{dt} =ky(1-y)

Solving the differential equation

\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}

Initial conditions:

y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48

The rumor reaches 80% at 8.48 days.

8 0
3 years ago
The regular pentagon below is a scale drawing of an original pentagon that was made by using a scale factor of One-fourth. A hex
Lana71 [14]

Answer:

-The scale drawing represents a reduction

-each side of the original is 22 in long

-the scale drawing is proportional to the original

Step-by-step explanation:

8 0
3 years ago
7b) A recipe for salad dressing calls for 3 tablespoons of oil for every 2 tablespoons of
mixas84 [53]

Answer:

the meaning of 1, 1.5 is that 1.5 is the oil sad and the 1 is the vinegar.

Step-by-step explanation:

4 0
3 years ago
Solve and show your work for each question...
satela [25.4K]

0.\overline{36} = \dfrac{36-0}{99} = \dfrac{36}{99} = \dfrac{4}{11}\\\\\\0.3\overline{6}= \dfrac{36-3}{90} = \dfrac{33}{90} = \dfrac{11}{30}\\\\\\0.36 = \dfrac{36}{100} = \dfrac{9}{25}

4 0
2 years ago
The cone and cylinder above have the same radius, r, and height, h. The volume of the cone is 69 cubic centimeters. What is the
MatroZZZ [7]

Answer:

207 cubic centimeters

Step-by-step explanation:

Given

volume of cone  = 9 cubic centimeters

Since the cone and cylinder above have the same radius, r, and height, h, then r = h

volume of the cone = 1/3πr²h

69 =  1/3πr²h

πr²h = 69*3

πr²h = 207cubic cm

Since the volume of the cylinder =  πr²h

Hence volume of the cylinder is 207 cubic centimeters

8 0
3 years ago
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