1-Prove the identity.
cosh(x) + sinh(x) = ex
| cosh(x) + sinh(x) | = |
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2-Prove the identity.
sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y)
| sinh(x) cosh(y) + cosh(x) sinh(y) | = |
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3-Prove the identity.
sinh(2x) = 2 sinh(x) cosh(x)
| sinh(2x) | = | sinh
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| = | sinh(x) + cosh(x) sinh(x) | |||
| = | ||||
4-Prove the identity.
| 1 + tanh(x) |
| 1 − tanh(x) |
= e2x
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= |
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5-If
tanh(x) =
| 4 |
| 5 |
,
find the values of the other hyperbolic functions at x.
| sinh(x) | = | |
| cosh(x) | = | |
| coth(x) | = | |
| sech(x) | = | |
| csch(x) | = |
In: Math
1. Consider the region bounded by the graph of y^2 = r^2 −x^2
(a) When this region is rotated about the x-axis a sphere of radius r is generated. Use integration to find its volume V (b) Use integration to find the surface area of such a sphere
2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60] (
3. Consider the graph of y = x^3 . Compute the surface area of revolution about the x-axis over the interval [0, 2]
4. A spring whose equilibrium length of 15in. exerts a force of 50 lbs when it is stretched to 20in. Find the work required to stretch the spring from 22in. to 24in.
In: Math
Find the local maximum and minimum values and saddle point(s) of the function. If you have three dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter NONE in any unused answer blanks.) f(x, y) = x^3 – 27xy + 27y^3
In: Math
EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 + 1,t2 −1,t2 −2ti, 0 ≤ t ≤ 2. Hint: Check whether F is conservative. If so, the Fundamental Theorem for Line Integrals might be useful
In: Math
A piece of wire 28 m long is cut into two pieces. One piece is
bent into a square and the other is bent into an equilateral
triangle. (Give your answers correct to two decimal places.)
(a) How much wire should be used for the square in order to
maximize the total area?
(b) How much wire should be used for the square in order to
minimize the total area?
In: Math
Answer all the question below.
Table 2:
|
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 |
12.2373551424579 11.7708440253038 11.3114033194700 11.0981090241345 10.9917532871426 10.9633449623870 10.9328985186904 11.0609123182770 11.1447150124713 11.2994243413533 11.4699411879533 11.5862580969086 11.7887055678588 11.9277833926721 11.9332325617172 12.0027754228957 12.0455191817870 11.9895076044597 12.1161492247957 11.9142999902406 11.9523445384738 11.8444716643177 11.8325572681845 11.6394782554936 11.4409836766153 |
Need to solve this all question. Please Provide the proper solution. Thank you
In: Math
find the riemann sum f(x)=x^2 +3x over the interval [0,8] where x0 =o, x1=1 , x2=6, x4=8, and c1=1, c2=2, c3=4, c4=6
In: Math
An economy is based on three sectors, agriculture, manufacturing, and energy. Production of adollar’s worth of agriculture requires inputs of $0.30 from agriculture, $ 0.30 frommanufacturing, and $0.30 from energy. Production of a dollar’s worth of manufacturing requires inputs of $0.30 from agriculture, $0.20 from manufacturing, and $0.20 from energy. Production of a dollar’s worth of energy requires inputs of $0.20 from agriculture, $0.30 frommanufacturing, and $0.30 from energy.
Find the output for each sector that is needed to satisfy a final demand of $67 billion foragriculture, $34 billion formanufacturing, and $14 billion for energy.
1) The output of the agricultural sector is ___ billion dollars
2) The output of the manufacturing sector is __ billion dollars
3) The output of the energy sector is __ billion dollars
In: Math
Consider a region R bound by the coordinate axes and y = ( 9 + x 2 ) − 1 2 on 0 ≤ x ≤ 4.
a. Find the area of R.
b. Suppose R is revolved about the x-axis to form a solid. Find the volume of the solid.
c. Suppose R is revolved about the y-axis to form a solid. Find the volume of the solid.
In: Math
Is this true or false? The foci for the hyperbola ((x-2)^(2))/(36)-((y+1)^(2))/(64)=1 are (2, -1 +4\sqrt(7) and (2, -1 - 4\sqrt(7)
In: Math
The populations of termites and spiders in a certain house are growing exponentially. The house contains 110 termites the day you move in. After four days, the house contains 195 termites. Three days after moving in, there are two times as many termites as spiders. Eight days after moving in, there were four times as many termites as spiders.
How long (in days) does it take the population of spiders to triple? (Round your answer to one decimal place.)
In: Math
Define
Instructions:
After reading Chapter 4 of the textbook, define the following terms:
-System of linear equations
-Solution to a system of equations
-Consistent system of equations
-Inconsistent system of equations
Write a good paragraph with at least 5 sentences using a minimum of 75 words.
In: Math
Calculate an approximate value of the area of the place inside the curve. (So if you sketch it up (by using WolframAlpha or something else) then you will see that what is sought after is the calculated value of the area that is inside the curve
1 = (40+43)x^2y^2 + y^4 + (1+1)x^4
In: Math
American General offers a 8 -year annuity with a guaranteed rate of 6.73% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $600 annually over the 8 year period?
In: Math
5 + (3 * 4)^2 - 2 = 147
(5 + 3) * 4^2 - 2 = 126
(5 + 3 )* (4^2 – 2) = 112
5 + (3 * 4^2) - 2 = 51
In: Math