Coordinate system Questions and Answers

An organism's population has an initial biomass concentration of 200 mg/L, a maximum specific growth rate of 1/day, and respiration rate coefficient of 0.05/day. Assuming a logistic growth model, what is the difference in the predicted final biomass amounts (in units of mg/L) at t1 = 10 days and at t2 = 10,000 days? Assume the carrying capacity is reported to be 5,000 mg/L. A) 4990 B) Not applicable (error) - the model cannot be used. C) 1000 D) No significant difference in resulting biomasses.

Describe any phase shift and vertical shift in the graph. y = 3 cos (x + 1)-3

Let I be the line through the point Q-(-3,-1, 2) and direction vector -[-9, -6, 3]T. Find scalar equations of two perpendicular planes P1 and P2 intersecting in L. P1: P2:

Sketch the graph of the following function. f(x) = -2x³

Draw the graph of the function. y = -x² - 80x+1200

bisector of a Show that the perpendicular side of a regular pentagon is a line of symmetry. Would your proof be extendable to show that the perpendicular bisectors of the sides of any regular polygon are lines of symmetry?

2. Graph a polynomial function of degree 5 with at least two unique x-intercepts and passes through the point (0, -2). Be sure to number the axis. Determine the equation of the polynomial. Show all your work.

What is the angular closure for the following interior field angles of traverse ABCDEF, measured with equal precision? A. 87° 54' 14" B. 90° 32' 45" C. 102° 43' 31" D. 99° 24' 34" E. 156° 01' 55" F. 183° 23' 01"

The linear equation 5y - 3x - 4-0 can be written in the form y =mx + c. Find the value of m and c. A. m=-3,c=0.8 b. m=0.6,c=-4 c. m=-3,c=-4 d. m=0.6,c=0.8

Find the first fundamental form of polar coordinate of xy-plane.

consider the map given by F(x)=1-x² discuss the charactristics of the orbits starting at x=0

Rewrite the polar equation r = 3 cos (θ) as a Cartesian equation.

A curve with polar equation r =8/3 sin 019 cos 0 represents a line. This line has a Cartesian equation of the form y = mx +b,where m and b are constants. Give the formula for y in terms of x. For example, if the line had equation y = 2x + 3 then the answer would be 2 x + 3. y =

Known a cube ABCD.EFGH with the side length 3p. A point P,Q, and R on FB,FG,and AD so that BP=GQ=DR=p. Let beta is a slice through P,Q, and R. Find the ratio of the area that result of the proyeksion beta on ABCD with area ABCD A. 14/18 3. 9/18 C. 13/18 D. 11/18

Solve graphically (using the Cartesian Plane): f(x) = |x|-2>-x² +4.

What is the midpoint of a line segment with endpoints at (-1, 4) and (5,8)? Select one: O (4,12) O (6,12) O (2.6) O (3,6)

A soccer team has 10 players and needs to choose 2 captains. How many ways can the captains be selected? Select one: O 45 O 20 O 90 O 180

Which lines are perpendicular to each other? Select two lines. Choose all that apply: 3x + 2y = 1 3y=-2x +9 3x+y=6 x+3y= −1 x-3y = 5

The vertices of triangle ABC are A (-4,-2), B (3,0) and C (0,4). Which type of triangle is it? Select one: O isosceles Oright O obtuse O acute

What is the most specific name of the quadrilateral ABCD created by connecting A (-1,3), B(1,-1), C (-1,-2); and D(-3,2)? O square O rhombus O rectangle O parallelogram

What is the equation of the line that is perpendicular to x + 2y = 4 and passes through (1, 1) y=2x-1 y=-1/2 x +2/3 y=-1/2 x +3/2 y = 2x

A line passes through A (-2, -1) and B (2,5). What is an equation a line that is perpendicular to AB? Select all that apply. Choose all that apply: y = 3/2x+2 2x+3y=7 3y=-2x + 11 y=-x+8 y=x+4

Write the following numbers in the polar form e^iθ,0 ≤ θ < 2pi (a)1/9 r=____ θ=_______ (b) 6+ 6i r=____ θ=_______ c) - 9 + 9i r=____ θ=_______ Write your answer for r using either exact value or decimal accurate to at least one deciaml place. Write your answer for θ in radian and accurate to at least one decimal place.

6. For the pair of polynomials given, select all the points of intersection of their graphs. g(x) = (x+3)(x-7) h(x) = x - 7 a. (-8,-13) b. (-7,0) c. (-2,-9) d. (-5, -10) e. (7,0)

Find the coordinates of a point on a circle with radius 30 corresponding to an angle of 220° (x, y) = Round your answers to three decimal places.

Convert the polar coordinate (6,2pi/3)to Cartesian coordinates. Enter exact values. x= y=

Convert the Cartesian coordinate (3,1) to polar coordinates, r>0 and 0 <θ< 2pi r = Enter exact value. θ=

Find an angle with 0° <θ< 360° that has the same: Sine as 20:θ=_________degrees Cosine as 20:θ=_________degrees

Which of the following has a slant asymptote when graphed? Oy=2x³ +3/(x-1) Oy=2x/(x-1) Oy= 2x²/(x-1) Oy=3/(x-1)

Find the point at which the line intersects the given plane. x = 2 - 2t, y = 3t, z = 1+ t; x+2y-z = 7 (x, y, z)=

Determine on which line(s) the invariant point lies if the graph of y = f(x) is transformed into: a) y = -f(x) b) y = f(-x) c) y = √f(x)

Sketch the region bounded by the surfaces z = √√x² + y2 and x² + y2 = 1 for 1 ≤ z ≤ 7. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. (Write an equation for the inner trace at z = 7 using x and y.) (Write an equation for the outer trace at z = 7 using x and y.). (Write an equation for the inner trace at y = 0 using x and z.) (Write an equation for the outer trace at y = 0 using x and z.) (Write an equation for the inner trace at x = 0 using y and z.). (Write an equation for the outer trace at x = 0 using y and z.) (Write an equation for where the two surfaces meet using z.)

graph the given functions on the coordinate plane. f(x) = (3)^x

1. Given a line 2x - 3y = 6 in the plane, (i) find the slope-intercept equation of the line that passes through the point (2,-4) and is parallel to the given line; use exact values for all the numbers in your answer. (ii) find the slope-intercept equation of the line that passes through the point (-6, 3) and is perpendicular to the given line.