MATH MODULE 2

premopremo remo · 75問 · 2年前

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What is the distance between the line (x+1)/7=(y+1)/6=(z+1)/1 and the line (x-3)/1=(y-5)/-2=(z-7)/1 ?

82(sqrt. of 25)/25

Evaluate the integral of y^{\wedge}2dx+xdy=0 of the line segment from points (-5, - 3) and (0, 2).

5/6

What is ∫ (ydx + xydy) from points (0, 0) and (1,1)?

5/6

From past experience, it is known 90% of one-year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability at least 3 children do not recognize their mother's voice

0.323

Find the volume cut off from the sphere x^2+y^2+z^2=a^2 by the cylinder x^2+y^2=ay

2a^3(π-4/3)/3

Find a general solution to the differential equation y"-2y'+y=xe^2x

y = C1 e^x+C2 xe^x + xe^2x - 2e^2x

Find a general solution to the differential equation y" - 2y' + y = xe^x + 4 y(0)=1 y' (0) = 1

y = -3e^x + 4xe^x + (1/6)x^3 e^x + 4

An audience of 450 persons is seated in a row having the same number of persons in each row. If 3 more persons seat in each row, it would require 5 rows less to sear the audience. How many rows were there originally?

Find the parametric equations for the line through the point (1.7.2) that is parallel to the plane x+y+z=10 and perpendicular to the line x=3+t. y=-18-t z=5t

x = 6t + 1, y = -4t + 7, z = -2t + 2

Find the shortest distance between the lines x + 1= 2y = -12z and x = y + 2 = 6z - 6

The time X a student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends at least 6 hours learning the software package?

0.9082

The time X student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends between 6.5 and 8.5 hours learning the software package?

0.470

A tank initially holds 100 gal of salt solution in which 50 lbs of salt has been dissolved. A pipe fills the tank with brine at the rate of 3gpm containing 2 lbs. of dissolve salt per gallon. Assuming that the mixture is kept uniform by stirring a drain pipe draws out of the tank the mixture of 2gpm. Find the amount of salt in the tank at the end of 30 minutes.

124.11 lbs

Find the area of the polygon with vertices at 2+3i 3 H,-2-4i , -1+2;

47/5

How many possible positive real solutions are there in the polynomial: x^4 - 4x^3 + 7x^2 - 6x - 18 = 0

3 or 1

Find the point on the line x=y=z that is equidistant from the points (3,0,5) and (1,-1, 4)

(2,2,2)

Find the area above xy plane of that portion of the surface of sphere x^2 + y^2 + x^2 = a^2 intercepted by the cylinder x^2 + y^2 - ax=0

(π - 2)a^2

A steel ball is 120°C cools in 20 min to 80°C in a room 25°C. Find the temperature of the ball after half an hour

66.85°C

Evaluate ∫ (1-cosx) dx

-2√2 cos x/2 + C

Find the point on the line 3x+y+4=0 that is equidistant from the points (-5,6) and (3, 2)

(-2,2)

Find all real solutions to the logarithmic equation In (x2-1)-Ir (x-1)=ln4 .

Find the vertex of the parabola x^2 = 8y

(0,0)

A line tangent to the curve x= sqrt of y at the point P intersects to the x axis at the point Q. If P travels up the curve at a rate of 2 units per second, how fast is the point Q travelling along the x axis when P passes through (2, 4)?

0.2425 unit/sec

In the vicinity of a bonfire, the temperature T in degrees at distance of x meters from the center of the fire was given by. T= 762,500/x^2 + 300 At what range of distances from the fire's center was the temperature less than 500deg. C?

More than 35 meters

Spherical wedge has a volume of 8m^3 and a curve surface area of 6m^2 Determine the radius.

A and B working together can do a job in 5 days. B and C together can do the same in 4 days and A and C in 2.5 days. In how many days can all of them finish the job working together?

2.35

Find the value of sinh (pi i/3)

i(sqrt. of 3)/2

Find all differential equation of the family of lines passing through the origin

ydx + x dy = 0

The equation of a line that intersects the x-axis at x=4 and the y-axis at y=-6 is

3x - 2y = 12

A man is driving a car at the rate of 30 km/hr towards the foot of a monument 6 m high. At what rate is he approaching the top when he is 36m from the foot of the monument?

-29.59 km/hr

A weight is attached to one end of a 35 ft rope which passes over a pulley 18 ft above the ground. The other end is attached to a truck at a point 3 ft above the ground. If the truck moves away at a rate of 2 ft per sec. How fast is the weight rising when it is 8 ft from the ground (spot directly under the pulley)?

1.25 fps

The sides of a triangular lot are 130m, 180m, 190m. This lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line

125 m

A box contains 9 red balls and 6 blue balls. If two balls are drawn in succession, what is the probability that one of them is red and the other is blue?

18/35

If log 2=x and log 3=v find log 48 in terms of x and y

(4x + y)/(x + y)

Find the area bounded by y=x+3 the x-axis x=-2 and x=1

4.25

Find the radius of curvature of the parabola y^2 - 4x = 0 at the point (4.4)

22.36

The angular velocity of a rotating rigid body about an axis of rotation is given by w = 4i + j - 2k Find the linear velocity of a point P on the body whose position vector relative ot a point on the axis of rotation is 2i - 3j + k

- 5i - 8j - 14k

From past , it is known 90% of one-year old children can distinguish their mother's voice from the voice of a similar sounding female. . A random sample of 20 one-year olds are given this voice recognition test. Find the probability that all 20 children recognize their mother's voice.

0.122

Which of the following is a disadvantage of using the sample range to measures spread or dispersion?

The largest of the smallest observation (or both) may be a mistake or an outlier

A bicycle travels along a straight road. At to'clock, it is (t squared) miles from the end of the end of the road. Compute its average velocity in mi/hr from 1:00 to 4:00

Find the moment of inertia with respect to the x axis of the volume of a sphere generated by revolving a circle of radius r about a fixed diameter.

(8/15)Pi(r exp 5)

In the xy-plane, the set of points whose coordinates satisfy the equation √(x+3)^2+(y-2)^2 = √(x-3)^2+y^2

line

The chords of the ellipse 64x^2 + 25y^2 = 1600 having equal slopes of 1/5 are bisected by its diameter. Determine the equation of the diameter of the ellipse

64x + 5y = 0

Find the tangent's to the parabola x^2 = 6y + 10 through (7, 5)

4x - 3y = 13

A circular having a diameter of 20 meters is enclosed by a stone wall. A horse is tied on the outside of the garden to the wall by a rope 20 meters long Find the area of the ground the horse can graze over.

895 sq.m

A circle with center at the origin has a radius of 5. Find the equation of a parabola opening to the right that has its vertex on the circle and crossing the points of intersection of the circle and y-axis

5x + 25 = y^2

A right circular cylinder is inscribed in a right circular cone of radius, r. Find the radius R of the cylinder if its lateral area is a maximum?

R = r/2

r^2 = a^2cos(2θ) is the equation of a _______

lemniscate

A dive bomber losses altitude at a rate of 400mph. How fast is the visible surface of the earth decreasing when the bomber is 1 mile high?

2792 sq. mi/sec

Two vehicles A and B start at point P and traveiled East at rates of 10 kph and 30 kph respectively. An observer at Q. 1 km North of P. is able to observe both vehicles. What is the maximum angle of sight between the observer's view of A and B?

30 degrees

If sinx=2 find cos4x

Find the sum of the cube of the numbers from 20 to 50

1,436,400

Find the moment of inertia with respect to axis of the area in the first quadrant bounded by the parabola y^{2}=4x and the line x=1

1,067

Find the moment of inertia of the area bounded by the parabola y^{2}=4x and the line x=1 with respect to the x-axis.

32/15

Two sides of a triangle are 5 and 10 inches, respectively. The angle between them is decreasing at the rate of 5° per minute. How fast is the third side of the triangle growing when the angle is 60°?

-0.44 in/min

A wire 60 inches long is to be used to construct a circle and an equilateral triangle. How much is the maximum sum of area possible?

286.48

In how many ways can the letters of the word "ENGINEERING" be arranged by taking the letters all at a time?

277,200

Find the value of θ having a Cartesian coordinates of (3, 4, 5) using Cylindrical coordinates.

53°

In how many ways can a student going abroad accompanied by 3 teachers selecting from 6 teachers?

Find the coordinates of the centroid of the area enclosed by y=x-x^{2} and the y=0 about the x-axis.

(1/2, 1/10)

What is the length of the shortest line that can be drawn tangent to x^2/a^2+y^2/b^2 = 1 and meeting the coordinate axes.

a + b

Determine the simplified form of [cos2A- (cosA)^2]/(cosA)^2

- (tanA)^2

Determine the the infinite series S=(0.9) + (0.9)^2 + (0.9)^3 + ... +(0.9)^n +....

A merchant has 3 items on sale. A radio for $50.00, a clock for $30.00 and a flashlight for $1.00 At the end of the day, she has sold a total 100 of the three sale items and has taken in exactly $1,000 on the total sales. How many of each item did she sell? Disregard sales tax

16.4 and 80

What is the length of the shortest line that can be drawn tangent to x^{2}=9-y and meeting the positive coordinate axes

15.97

Find the orthogonal trajectory of the family of curves with center at origin and foci at x-axis.

y = Cx^(b^2/a^2)

Solve for the median of 15, 19, 25, 21, 16, 10, and 13.

How many triangles are determined by the vertices of a regular hexagon?

How many line segments can be formed with 6 distinct points, no three of which are collinear?

Find the remainder if we divide 4y^3 + 18y^2 + 8y - 4 by (2y+3)

The sum of the ninth roots of a complex quantity is always

Find the 12th term of the harmonic progression 1,1/3, 1/5 ......

1/21

The eccentricity of a given curve is between zero and one, the given curve is:

ellipse

Given a square with 20 cm sides. Another square is to be inscribed in the given square such that the vertices of the latter lies on the midpoint sides of the formér. Determine the area, in sq cm, of the smaller inscribed square?

200

An arch is in the form of an inverted parabola and has span of 12 feet at the base and a height of 12 feet. Determine the equation of the parabola and give the vertical clearance 4 feet from the vertical centerline

6.67 ft

The polynomial x^3 + 4x^2 - 3x + 8 is divided by x-5 then the remainder is

218

Determine the equation of the line through (3,4) which forms, with the positive x and positive the triangle with the area.

4x + 3y = 24

The third term of harmonic progression 9th term is 6. Find the 11h term

The area in the second quadrant of the circle x^2 + y^2 = 36 is revolved around the line x+10=0 What is the volume is generated

1324.14

The sum of the cube of the consecutive numbers from 1 to 30 is

216,225

A tetrahedron is a regular solid with surfaces. If each side is 10 cm, what is equilateral triangles for each of the 3 the volume of the tetrahedron?

117.85 cu cm

A and B working together can finish painting a home in 6 days. A working alone can finish it in five days less than B how long will it take each of them to finisn the work alone?

10,15

A spherical balloon is filled with air at a rate of 1 m/s. Compute the time rate of change in the surface area of the balloon when the volume is 1131 m^3

2/3 m^2/s

What conic section is represented by the equation 4x^2 + 8x - y^2 + 4y - 15 = 0?

Hyperbola

Find the greatest common factor (GCF) of 108 and 60.

Find the Laplace Transform of sinat

a/(s^2+a^2)

John started his egg farm business. His chickens produce 480 eggs per week. If he sells it at $2 a dozen (let 1 week = 7 days). How much does his chicken produce per week?

$80

A regular dodecagon (12-sided plane polygon) is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. Express your answer to the nearest hundredth.

149.08

At what point on the y-axis does the line segment joining (1. 1) and (9, 7) subtend the greatest angle?

y = 4

Find the expression for the sum of the following series 1^2 + 2^2 + 3^2 +....+ n^2

S = n(n + 1)(2n + 1)/6

The angle of inclination of ascend of a road having 8.25% grade is _________ degrees?

4.72

The difference of the squares of the digits of a two digit positive number is 27 If the digits are reversed in order and the resulting number subtracted from the original number, the difference is also 27. What is the original number?

What decimal value is nearest to x if x is equal to 1 plus the quantity 1 over the quantity one plus the quantity one over the quantity one plus the quantity one over and so on.

1.618

Evaluate the integral of xy with respect to y and then to x, for the limits from x = 0 to x=1, and the limits from y = 1 to y = 2

3/4

The orbit of Halley's Comet around the sun is an ellipse with the sun as a focus and eccentricity e = 0.967, the position where the comet is closest to the sun to the position where it is farthest from the sun is approximately 3.365 x (10 the 9th power) miles. Approximately how close the comet gets to the sun in million miles.

There are n couples at a party. Each man shakes hands with everyone else except his spouse. No handshakes take place between women. How many handshakes take place? (as a polynomial function of n)

(1/2)(3n^2 - 3)

A track is to be made into a circular path. What will be the radius if the direction changes 300 for every distance of 300 meters.

573 m

What is the lowest common factor of 10 and 32.

Simplify the trigonometric function 1/csc^2A

sin^2θ

100

In how many ways can 5 persons be seated in an automobile having places for 2 in the front seat and 3 in the back seat if only 3 can drive

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