YOU! yes you... answer me

Suppose that 240 m of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle as the following figure

Figure: http://webwork.unbsj.ca/webwork2_files/tmp/Math100...

I hope you guys can see that

Let x be the width of the rectangle, and y be the height of the rectangle (both measured in meters), as shown in the diagram. Find the dimensions of the corral with maximum area.

x = ____m

y = ____m

Please help, I keep finding that x is 120, but the y is negative which doesn't make sense

Let me know answer and how you got to it!

Thank you!

Find the equation of a quartic polynomial ( a polynomial of degree four) whose graph is symmetric about the y-axis and has local maxima at (-2, -2) and (2, -2) and a y-intercept of -4.

Please let me know answer and how you got to it

Thank you!

Use interval notation to indicate where f(x) is concave up and concave down.

f(x)= (x^(1/3))((x+3)^(2/3))

Find all inflection points of f.

Please help me, I ve been at this question for hours! I keep getting

Up (-2.30278, 0)U( 1.30278, inf)

Down (-inf,-2.30278)U(0, 1.30278)

Inflection points: 1.30278, -2.30278

All of this is wrong. Let me know what you get on this, and if you get the same thing, do you think there is an other way to wright it then? Let me know what you get for this problem!

Consider the function f(x) = 2 x^3 - 6 x^2 - 48 x + 2 on the interval [ -5 , 8 ]. Find the average or mean slope of the function on this interval.

average or mean slope:_______

By the Mean Value Theorem, we know there exists at least one c in the open interval ( -5 , 8 ) such that f'( c) is equal to this mean slope.

Find all values of c that work and list them (separated by commas) in the box below. If there are no values of c that work, enter None.

List of numbers: _______

Please let me know answer and how you got to it!

Thank you!

Suppose f(x) is continuous on [4,5] and -4 (less than or equal to) f'(x) (less than or equal to) 5 for all x in (4,5). Use the Mean Value Theorem to estimate f(5)-f(4).

Answer:

_____ (less than or equal to) f(5)-f(4) (less than or equal to) _____

Please let me know answer and how you got to it!

Thank you!

By applying Rolle's theorem, check whether it is possible that the function f(x) = x^(9)+ x - 13 has two real roots.

Answer: _______(input possible or impossible )

Your reason is that if f(x) has two real roots then by Rolle's theorem:

f'(x) must be _______(input a number here)

at certain value of x between these two roots, but f'(x) is always ______(input negative , positive, or zero )

Please let me know answer and how you got to it!

Thank you!

Find the Critical numbers of h(t)=((t^2)-16)^(1/3) on [0,4] and [0,8].

Please let me know answer and how you got to it!

A police car traveling south toward Sioux Falls at 160km/h pursues a truck traveling east away from Sioux Falls, Iowa, at 140 km/h

At time t=0, the police car is 40 km north and the truck is 60 km east of Sioux Falls.

Calculate the rate at which the distance between the vehicles is changing 3 minutes later.

The rate is = _________ km/h.

(Use decimal notation. Give your answer to three decimal places.)

I got 777/sqrt13 aprox. equal to 215.501 but it says this is incorrect.

Please let me know answer and how you got to it!

Thank you!

One study suggests that from 1955 to 1970, the number of bachelor's degrees in mathematics awarded per year by Canadian universities grew exponentially, with growth constant k=0.096.

If 250 mathematics degrees were awarded in 1955, in which year did the number of degrees awarded reach 1500?

When cane sugar is dissolved in water, it converts to invert sugar over a period of several hours. The percentage f(t) of unconverted cane sugar at time t (in hours) satisfies f'=-0.5 f.

What percentage of cane sugar remains after 4 hours?

What percentage of cane sugar remains after 8 hours?

Please let me know answer and how you got to it!

Thank you!

Calculate y' and y'' at the point (1,1) on the curve 7x(y^2)+1 y-8 = 0.

for y', I got (-7y^2)/(14xy+1), once I put in the (1, 1), I got -7/15 which is correct.

as for y'' I tried it multiple times and usually get (98y^3)/196x^2y^2+28xy+1+98xy^2+14y, plug in the (1, 1) and I get 98/337 which is wrong. I know that y'' is the derivative of y' but obviously I messed up somewhere. I tried it multiple times and keep getting this one wrong.

Please let me know the correct answer and how to get to it,

Thank you!

Calculate y' and y'' at the point (1,1) on the curve 7x(y^2)+1 y-8 = 0.

for y', I got (-7y^2)/(14xy+1), once I put in the (1, 1), I got -7/15 which is correct.

as for y'' I tried it multiple times and usually get (98y^3)/196x^2y^2+28xy+1+98xy^2+14y, plug in the (1, 1) and I get 98/337 which is wrong. I know that y'' is the derivative of y' but obviously I messed up somewhere. I tried it multiple times and keep getting this one wrong.

Please let me know the correct answer and how to get to it,

Thank you!

Calculate the derivative of y with respect to x. ((x^3)y)+(3x(y^3))=x+y

dy/dx=_________

Please let me know final answer and how to get to it,

Thank you!

Calculate the derivative of y with respect to x. ((x^3)y)+(3x(y^3))=x+y

dy/dx=_________

I keep getting ((-3(x^2)y)-(3(y^3)))/((x^3)+(9x(y^2))-1) but this is wrong.

Please let me know what I am doing wrong and what I need to do to get it right.

Thank you!

The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber on a car) is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion of a point on such a spring is

s(t)=(8e^(-1.6t))(sin(2pi t)

where s is measured in centimeters and t is measured in seconds. Find the velocity of the point after t seconds.

Graph both the position and the velocity function for 0 (smaller or equal to) t (smaller or equal to) 8.

Please help me understand!

Thanks in advance!

Let F(x)= f(x^9) and G(x)=(f(x))^9 .

You also know that:

a^8=2

f(a)=2

f'(a)=4

and f'(a^9)=9.

Find F'(a) and G'(a)

Please help and explain each step, I've been at this question for hours. I appreciate your help!

Let F(x)= f(x^9) and G(x)=(f(x))^9 .

You also know that:

a^8=2

f(a)=2

f'(a)=4

and f'(a^9)=9.

Find F'(a) and G'(a)

Evaluate the limit.

Please help, also preferably without using l'Hopital's rule because I am not suppose to know it yet.

Answer is 2 but I don't know how they got there.

Thank you!

Find a formula for h'(x), where h(x)= |x-2|+|x-9|.

Hint: h(x) may not be differentiable at x=2 or x=9.

h'(x)= _____if x<2

_____if 2<x<9

_____if x>9

The answer for if x<2 is sgn(x-2)+sgn(x-9) but I don't know how they got there. I have no idea about the other two. Please help!

Use the limit definition to compute f'(a) and find an equation of the tangent line.

f(x)=1/(sqrt(225x)), a=4

a) f'(a)=______

b) y=______

Please help me understand!