MATH FLASHING

premopremo remo · 75問 · 2年前

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Find the area bounded by r = 2 / (1 + cos θ) and cos θ = 0

8/3

Find the general solution of dy/dx = ysecx.

y = secxtanx = C

Find the area in a single hump of a cycloid given by the parametric equation: x = a(θ-sin θ) y = a(1 - cos θ)

π a^2/8

A railroad is to be laid-off in a circular path. What should be the radius if the tract is to change direction by 30°at a distance of 157.08 metres?

300 m

Bobby is two younger than twice as old as Ellen. The sum of two times the age of Bobby and three times the age of Ellen is 66 How old is Bobby?

A railroad is should be the radius if the track is to change direction by 30 degrees at a distance of 157.08 m'

300 m

Larry finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees What is the height of the tower?

73.61 m

Listed below are the functions each denoted g(x) and each involving a real number x, constant c > 1 ff(f) =2^ * which of these functions yield the greatest value for f( g(x) for all x > 1'

g(x) = cx

A 20 ft light post casts a shadow 25 ft long casts a shadow 50 ft long. How tall is the At the same time, a building nearby building

40 ft

In an ellipse, a chord which contains a focus and serbaline perpendicular to the hyperbola major axis is a

Latus rectum

A point is choses at random inside a circle having a diameter pf 8 inches. What is the probability that the point is at least 15 inches away from the center of the circle?

55/64

Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft high if the height is increasing at 2 in/min?

130 288.13in^3/mi

Find the volume generated by revolving the circle x ^ 2 + y ^ 2 + 6x + 4y + 12 = 0 about the y-axis.

1:1:1

What is the curve described by the equation Ln|z - i| = 23

circle

A tangent to a conic is a line

Which touches the conic at only the point

Joseph gave of his candies to Joy and Joy gave 1/5 of what he got to Tim if tim receibed 2 candies how many did Joseph have originally?

Three circles externally tangent with each other has radii 3cm, 4cm, and 5cm Find the maximum angle formed by the triangle connecting the center of the circle.

73.4 deg

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

Evaluate the limit of z ^ 2 / (z ^ 4 + z + 1) as z approaches e to the (π i / 4)

sq.rt. of 2(1 + i)/2

What is a solution of the first-order differential equation y(h + 1) = y(h) + 5

y(h) = 20 + 5h

If a rock is dropped, its distance below the starting point at the end of t sec is given by s = 16 t square, where s is in ft. Find the rate of change of distance after 1.5 minutes

281 ft/sec

What is the curve describe by the equation Im (z ^ 2) = 4

Hyperbola

If a rock is dropped, its distance below the starting point at the end oft sec.is given by s = 16 t square, where s is in ft. Find the rate of change of distance after 1.5 minutes

2.880 ft/sec

From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their Mother's voice. Find the variance of x.

1.8

A point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing is known as

Inflection point

If f(x) = 10^x+1 then f(x + 1) - f(x) is equal to

9(10^x)

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

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

Find the unit vector which is orthogonal to 9i+9j and 9i+9k

(i-j-k)/sq.rt of 3

Water is running out a conical funnel at the rate of fou in is the radius of the base of the funnel is 4in, and the altitude is Bin., find the rate at which the water level is dropping when it is 2in, from the top

-1/9π in/s

The parabola y^2 = 4ax and the line x = p enclosed an area with the centroid at the focus of the parabola

5/3a

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?

- 52.8km / hr

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?

2.03

What is the smallest positive value for x where y = sin 2x reaches its maximum?

D/4

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

2.13

Jenny flipped a coin three times and got heads each time. What is the probability that she gets heads on the fourth flip

1/2

Bobby is two years younger than twice as old as Ellen. The sum of two times the age of Bobby and three times the age of Ellen is 66. How old is Bobby?

Carmela gives 1/4 of her cookies to Charly. In turn Charly gave 1/5 of what he received to Dennis. If Dennis received 2. How many cookies has Carmela?

Find k in of the line 5x - 2y + k = 0 that is tangent to y = 6 + x ^ 2

71/8

Find the limit of z ^ 2 / (z ^ 4 + z + 3) as z approaches e to the (π i / 2)

(-4 + i)/17

The tenth's and the unit's digit of a number are x and y respectively. Write the number in terms of its digits

y + x / 10

Find the weight the heaviest right circular cylinder that can be cut from a 100kg solid iron shot.

57.7 kg

Water is running out a conical funnel at the rate of 1cu. in./s. the radius of the base of the funnel is 4in, and the altitude is 8in., find the rate at which the water level is dropping when it is 2in, from the top.

- 1/9π in / s

The parabola y ^ 2 = 4ax and the line x = p enclosed an area with the centroid at the focus of the parabola.

5/3a

What conic section. B ^ 2 - 4AC = 0'

Parabola

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

Three cardes extemally tangent with each other has radii 3cm, 4cm, and 5cm Find the maximum angle formed by the triangle connecting the centers of the circle

73.4 deg

Evaluate sin(A + B) sin A = - 3/5 quad 4: cot B = 4 quad 3.

8/5 √17

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. What is the probability that the average time a student spend is at least 9.5 hours learning the software package?

84.134%

The towns are located near the straight shore of the lake. Their nearest distances to the point in the shore are 1km and 2 km respectively, and these points on the shore are 6 km apart. Where should the finishing port be located to maximize the total amount of paving necessary to build a straight road from each town to the pier?

2 km from the point on the shore nearest the first town

Evaluate tan3x if sin x = 2

-j26√3/45

Postal regulations require that a parcel post package to be no greater than 3m in the sum of its length and girth (perimeter of the cross section). What is the volume in cum of the largest package allowed by postal regulations if the package is to be rectangular in shape and has square ends

1/4 cu.m

Find the angle between adjacent faces of a regular octahedron.

109.47°

Evaluate ln( 3 +i4)

1.61+j0.927

What is the curve describe by the equation Im (z ^ 2) =4?

Hyperbola

Evaluate the limit of z ^ 2 / (z ^ 4 + z + 1) as z approaches e to the (π i / 4)

sq.rt. of 2(1+i)/2

The discriminant of a given curve is equal to one, the given curve is

hyperbola

If the lengths 2, 3, 5, 7 and 9 are to be used to form a triangle. What is the probability that a triangle is formed?

3/10

A can do a job in 4 days, B can do the job in 6 days and C can do the job in 8 days. How long will it take to do the job if A and B work for 1 day then B and C finish the job?

The current I following in an RL circuit is given by I = (E / R)(1 - e ^ R t/L) where E is the voltage applied to the circuit, R is the resistance and L is the inductance. Express I in terms of E and R when t = L / R

0:632 ( E / R )

Identify the curve r = a + b cos θ

Limacon

Given that sin theta = 3/5 , find cos theta?

-4/5

The eccentricity of a given curve is less than one, the given curve is

ellipse

The value of a computer is depreciated over 5 years for tax purposes. That is, at end of 5 years, the computer is worth 0. If a business paid P21,000 for a computer, how much will it have depreciated after 2 years?

P8, 400

Solve [y-square root of [(x + y)] dx- xdy = 0

Square root of (x" +y" )+ y = C

Which of the following is divisible by 9?

10^2019 + 9

A rubber ball is dropped from a height of 18 feet. On each rebound, it rises 2/3 of the height from which it last fell. Find the distance traversed by the ball before it comes to rest

90 ft

The probability of getting at least 2 heads when a fair coin is tossed 4 times

11/16

Find the area of the largest triangle that can be inscribed in a semi-circle of radius, 10

100

Find intergal In xdx.

xlnx - x + C

Five cards are drawn from a pack of 52 well-shuffled cards. Find the probability that 3 are 10's and 2 are queens

1/108,290

The value of x + y in the complex expression 3 + xi = y + 2i is:

Find the value of constant "h" in the 2x^2 - hx^2 + 4x + 5h = 0 so that the sum of the roots is 2

The value of x + y in the complex expression 3 + xi = y + 2i is

In a right triangle the bisector of the right triangle divides the hypotenuse in the ratio 1:2. In what ratio is the hypotenuse divided by the altitude dropped from the vertex of the right angle?

4:1

At what time between 2:00 and 3.00 will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o'clock mark?

2.18 6/13

Find the weight of the heaviest right circular cylinder that can be cut from a 100kg spherical shot

57.7 kg

A number is A number is less than 100 and its ten's digit is 2 more than its unit's digit. If the number with the digits reversed is subtracted from the original number. the remainder is 3 times the sum of the digits. Find the number

A hemispherical tank of radius 10 ft is full of water. Find the work done in pumping the water to the top of the tank

245 ft tons

Determine the equation describing the locus of point P (x, y) such that the sum of the distances between P and (-5, 0) and between P and (5, 0) is constant at 20 units

(x10)^ 2 + (y/8.66)^2 = 1

Evaluate integrate 12sin^5 x cos^5 x dx

0.20

Five cards are drawn from a pack of 52 well-shuffled cards. Find the probability that 3 are 10's and 2 are queens.

1/108, 290

Find the volume generated by revolving the area bounded by y = x ^ 3 y = 8 x = 0 about the y-axis.

96pi/5

What is the value of A between 270° and 360° if 2sin^2 A - sin A = 1

330°

At the minimum point, the slope of the tangent line is

zero

Find the derivative of cosh 3 4x.

12cosh^2 4x sinh 4x

A contractor wishes to build 5 houses, each different in design. In how many ways can he place these houses on a street if 6 lots are on one side on the street and 3 lots are on the opposite side.

362,880

A horizontal line has a slope of

Zero

Simplify (COSB - 1 )(COSB+1).

-1/CSC^2 B

Determine the inverse Laplace transform of. I(s) = 100 / ((s + 20) ^ 2

i (t) = 100te-201

Sand is pouring at 25pi ft³/min and forming a conical pile where the radius is always twice its height. Find the rate when the height is 5ft and height is increasing at the rate of 2 in/min?

0.58 ft/min

The segment from (-1, 4) to (2,-2) is extended 3 times its own length. The terminal point is

(11,-20)

At the inflection point, the value of the second derivative of the function is

zero

What is the value of A between 270 deg and 360 deg if 2 sin^2 A vdash sin A=1

330°

Arc tan [2cos (arcsin (sqrt(3))/2 ) rfloor is equal to:

π/4

Area of hypocycloid, x = acos^3 theta y = a sin^3 theta

(3/8) π a^2

The perimeter of the triangle ABC is equal to 8 m. sinA: sinB: sinC = 3/4 / 5 . Find the shortest side

The third term of a harmonic progression is 15 and the 9th term is 6. Find the 11 ^ m term

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

4x + 3y = 24

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

100

At the minimum point, the slope of the tangent line is

zero

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