Evaluate the integral
(x^3+2x^2-4x+5)/(3x^2+x-10)dx
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What is the standard form of the equation of the parabola with the focus (−1,3) and the directrix x=9?
Select the correct answer below:
a) (x+1)2=−12(y−6)
b) (y−3)2=−20(x−4)
c) (x−9)2=8(y−1)
d)(y−3)2=20(x−4)
please show work and what is the correct answer? thanks
In: Math
what is the radius of convergence for
sum {0} to {infinity} x^3n / 27^n
In: Math
In: Math
(a) Find the vertices, foci and asymptotes of the hyperbola and sketch its graph 9y^2 − 4x^2 − 72y + 8x + 176 = 0. (b) Find the vertex, focus and directrix of the parabola and sketch its graph 6y^2 + x − 36y + 55 = 0.
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Evaluate the line integral, where C is the given curve. ∫CF(x,y,z)⋅dr where F(x,y,z)=xi+yj+ysin(z+1)k and C consists of the line segment from (2,4,-1) to (1,-1,3).
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Suppose f(1) = 2, g(1) = −1, f′(1) = 3, g′(1) = 2, f(2) = 1, and f′(2) = 0.2. Calculate the derivatives of the following functions at the provided point (be careful with using the correct values) 3 pts each:
(a) d/dx (e^xf(x)) when x=2
(b) d/dx (f(x)/g(x)) when x=1
(c) d/dx (ln(xf(x))) when x=1
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If the production function is
Q=450√L – 5L
Where Q denotes output and L denotes the size of the workforce,
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Find the equation of the tangent line to the curve y=5sec(x)−10cos(x) at the point (π/3,5). Write your answer in the form y=mx+b where m is the slope and b is the y-intercept.
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Water is flowing at the rate of 5 m3 /min into a tank in the form of a cone of altitude 20 m and a base radius of 10 m, with its vertex in the downward direction.
a) How fast is the water level rising when the water is 8m deep?
b) If the tank has a leak at the bottom and the water level is rising at 0.084 m/sec when the water is 8 m deep, how fast is the water leaking?
(Related rates)
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A primitive economy consists of a fishing industry and an oil industry. A unit of fishing industry output requires 0.30 unit of fishing industry input and 0.35 unit of oil industry input. A unit of oil industry output requires inputs of 0.04 unit of fishing products and 0.10 unit of oil products.
(a) Write the technology matrix for this primitive economy.
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(b) If surpluses of 10 units of fishing products and 545 units of
oil products are desired, find the gross production of each
industry.
| fishing | units |
| oil | units |
In: Math
Let the function c(v) model the gas consumption (in liters/km) of a car going at velocity v (in kilometers/hour). In other words, c(v) tells you how many liters of gas the car uses to go 1 km, if it is going at velocity v.
You find that (80) 0.04 and '(80) 0.0004
1. Let the function d(v) model the distance the same car goes on 1 L of gas at velocity v.
a. Express the relationship between c(v) and d(v) in an
equation. [4 pts]
b. Find d(80) and d’(80). (Hint: Find the general d’(v) first.) [4
pts]
c. Interpret your result for d’(80) in a sentence. (That is, “When
the car is travelling at 80 kph ….” ) [4 pts] (Even if you couldn’t
get part b, you can still tell me what d’(80) means about the car.)
[5 pts]
In: Math
Calculate both of the Taylor series of:
- tanx up to and including the x^7 term
- secx up to and including the x^6 term.
**Please answer in full. If you cannot complete because the "derivatives are getting too complicated" then please do not attempt this question. I need a FULL answer. I keep getting stuck, hence the reason why I need a FULL answer.
In: Math
A water trough is 8 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 20 cm deep?
In: Math
Find the equation of the tangent line at x=2 to the graph of
y= x^2-x-7
Write your answer as a simplified slope-intercept equation y=mx+b.
For example y=7x-8
In: Math