MATHEMATICS COLLEGE

The base diameter and the height of a cone are both equal toX units.
Which expression represents the volume of the cone, in
cubic units?
Piex2
2piex3
o 1/3piex?
o 1/12piex

Answers

Answer 1
Answer:

Answer:

For this case we know that the diameter and height of a cone are both equal. That means:

h = D=x

With D =2r with r the radius. The volume of a cone is given by:

V =(1)/(3) \pi r^2 h

And for this case we know that h =x and x =2r so then r= (x)/(2)

And replacing we got:

V= (1)/(3) ((x)/(2))^2 (x)= (1)/(12) x^3

And the best option would be:

1/12pix^3

Step-by-step explanation:

For this case we know that the diameter and height of a cone are both equal. That means:

h = D=x

With D =2r with r the radius. The volume of a cone is given by:

V =(1)/(3) \pi r^2 h

And for this case we know that h =x and x =2r so then r= (x)/(2)

And replacing we got:

V= (1)/(3) ((x)/(2))^2 (x)= (1)/(12) x^3

And the best option would be:

1/12pix^3

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Answers

Answers:

(C)

step by step Explanation:

The answer for this question is going to be C the 2nd last one

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 assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor. a. Write the differential equation satisfied by y in terms of proportionality k.
b. Find k (in units of day−1, assuming that 10% of the population knows the rumor at time t=0 and 40% knows it at time t=2 days.
c. Using the assumptions in part (b), determine when 75% of the population will know the rumor.
d. Plot the direction field for the differential equation and draw the curve that fits the solution y(0)=0.1 and y(0)=0.5.

Answers

Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

a)

(dy)/(dt)\ \alpha\ y(1-y)

(dy)/(dt)=ky(1-y)

where k is the constant of proportionality, dy/dt =  rate at which the rumor spreads

b)

(dy)/(dt)=ky(1-y)\n(dy)/(y(1-y))=kdt\n\int\limits {(dy)/(y(1-y))} \, =\int\limit {kdt}\n\int\limits {(dy)/(y)} +\int\limits {(dy)/(1-y)} =\int\limit {kdt}\n\nln(y)-ln(1-y)=kt+c\nln((y)/(1-y)) =kt+c\ntaking \ exponential \ of\ both \ sides\n(y)/(1-y) =e^(kt+c)\n(y)/(1-y) =e^(kt)e^c\nlet\ A=e^c\n(y)/(1-y) =Ae^(kt)\ny=(1-y)Ae^(kt)\ny=(Ae^(kt))/(1+Ae^(kt)) \nat \ t=0,y=10\%\n0.1=(Ae^(k*0))/(1+Ae^(k*0)) \n0.1=(A)/(1+A) \nA=(1)/(9) \n

y=((1)/(9) e^(kt))/(1+(1)/(9) e^(kt))\ny=(1)/(1+9e^(-kt))

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

y=(1)/(1+9e^(-0.8959t))\n0.75=(1)/(1+9e^(-0.8959t))\nt=3.68\ days

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of five cars form this company have an average gas mileage of 25.2 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?

Answers

Answer with explanation:

Let \mu be the population mean.

Null hypothesis : H_0:\mu\geq26

Alternative hypothesis : H_1:\mu<26

Since the alternative hypothesis is left tailed, so the test is a left-tailed test.

Sample size : n=5 <30 , so we use t-test.

Test statistic: t=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}

t=(25.2-26)/((1)/(√(5)))\approx-1.79

Critical t-value for t=t_(n-1, \alpha)=t_(4,0.06)=1.9712

Since, the absolute value of t (1.79) is less than the critical t-value , so we fail to reject the null hypothesis.

Hence, we have sufficient evidence to support the company's claim.

Sarah hired a painter to paint her bedroom walls and ceiling. Each of the four bedroom walls is 18 ft. long and 8 ft. high. Two walls each have one door,and both doors measure 3 ft. by 7 ft. One wall has a window that is 3 ft. by 5 ft. The doors and window do not have to be painted
What is the area of the wall space that has to be painted?

Answers

Answer:

Step-by-step explanation:

519 I believe

ASAPP PLEASEESolve the following equation algebraically:
x2 = 20
a.4.47
b. -3.97, 3.97
c. -10, 10
d. -4.47, 4.47

Answers

Answer: if using the quadratic formula it is D :)

hope this helps

Step-by-step explanation:

Factor the trigonometric expression. 5sin^2x-8sinx-4

Answers

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