MATH MODULE 2 101

100問 • 1年前

問題一覧

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

What is the limiting value of the following function as n approaches infinity y=[1+(1/n)]^n

2.7183

Evaluate the limit of sin~x all over x as x approaches zero.

Find the probability of getting eleven by throwing a pair of dice once

1/18

The smallest interior angle of a particular convex P has a measure of 1200 angle and moving clockwise around the polygon, each successive angle is 50 larger than its predecessor. How many sides does this polygon has?

Maria is 24 years old. Maria is twice as old as Ana was when Maria was as old as Ana is now. How old is Ana?

Evaluate an e^jtan(π/2)

∞

Which point is nearest to (3,2)

(1,1)

The Laplace Transform of coshbt is

s/(s^2 - b^2)

Find the values of x in the equation 24x^2 + 5x - 1 = 0.

-1/3, 1/8

What is 43.4% of 15?

6.51

In algebra this consists of products and quotients of ordinary numbers and letters which represents numbers

expression

If 10sin^2(x) + 11 sin(x) - 8 = 0, then what is (are) the value(s) of log2 [sin(x)]

-1

Find the equation of a line thru (4, 1) perpendicular to the line 2x - 3y + 4 = 0

3x + 2y - 14 = 0

Find the value of x in xy + xz = -8 xy + yz = 1 xz + yz = -3

Find the 7th and the 8th term of 1. 3, 6, 10

25,33

Find the bounded by the curve y^2 - 3x + 2y - 8 = 0 and the y-axis

Find the difference between the area of a regular nonagon and an octagon If the perimeter of each is 16cm

0.224 sq. cm

A projectile has an initial upward speed of 1,000 feet per second which is steadily decreased by gravity at the rate of 32.2 second, so that the upward speed at a subsequent time t is dv/dt=1000-32.2i ft/sec. If the initial position of the projectile is 200 ft above ground, what is the maximum height that the projectile will attain?

-15.728 ft

Foghorn C sounds every 34 sec, Foghorn D every 38 sec.. The sound together at noon How many seconds later will they next sound together?

1,444

Determine the inverse Laplace transform of I (s) = 100/[s^2 (s^2 + 10^2)]

i (t) = t - 0.1 sin10t

At noon a pan of very hot water (188°F) is put into a room whose air temperature is constant at 60^{0}F The difference of the temperature of the water and the constant room air temperature is halved in every 15 minutes. At what time is the difference between the temperature of the water and the temperature of the room air less than or equal to 1?

1:45 beyond

Evaluate ln(3+/4)

1.61+j0.927

Compute the sum of all the coefficients in the expansion of (x+2y-z)^3

between 5 to 3

The sum of two positive numbers is 8. Find one of the two numbers such that the sum of the cube of one number and the square of the other number is a minimum.

Find the equation of the line with y-intercept equal to 7 and m=0?

y - 7 = 0

Find the area between the curve y=2x^4 -x^2 the x-axis, and its two minimum ordinates

7/120

The interior angie of a regular polygon exceeds its exterior angle by 150 degrees How many sides has the polygon?

If the area bounded by x^2 - y^2 = 3 y = 2, and y = 0 revolved about x = 0. find the moment of inertia of the sclid generated with respect to the axis of revolution

202pi/5

If x + y = 2, x^2 + y^2 = 3, find the value of x^4 + y^4

8.50

A geometric progression is 1 + z + z^2 + z^3 + ... + z^n where z < 1 Determine the sum of the series as n approaches infinity.

1/(1-z)

What time between 6 and 7 o clock will the minute and hour hands of the clock form 60° for the first time?

6:21.82

Find the area between the curves r = 2/1+cosθ and cosθ = 0

8/3

The point B divides the line segment AC in the ratio min. Find the the length of the segment AB if AC=a

ma/m + n

Salve for x : x = log_ba • log_cd • log_dc

log_b a

Find the area of the sector to be cut off from a circular cardboard 20 om in diameter so that joining the ends of the remaining area will give a right circular cone of maximum volume.

57.649cm^2

Find the 1978^th digit in the decimal equivalent to 1785/9999 starting from decimal point

Given the equation y=(e^ln x)^2 find y'

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

Determine the value of B when 3x+3y-7=0 is perpendicular to the line 2x 3y-c=0

-2

ln a class of 40 students, 27 like calculus and 25 like chemistry How many like both calculus and chemistry?

How many degrees is 4800 mils?

270 deg

Evaluate the value of √-10x x √-7

-√7

If the area bounded by y = x. x = 2 and moment of inertia of the solid formed y=0 is revolved about y=0 find the with respect to the axis of revolution

16 pi/5

One side of a parallelogram is 10 m and its diagonals are 16 m and 24 m respectively. Its area is

158.754 sq. m

Find the slope of the curve defined the equation x^2 y - 8 = 0 at the point (2,2)

-2

Gravity causes a body to fall 16.1 feet in 1st second, 48.3 in the 2nd second, 80.5 in the 3rd second, and so on. How far did the body fall during the 10th second?

305.9 ft

Find the centroid of the area bounded by the curves y = x^2 y = 4x - x^2

(1,2)

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

What is the probability of getting a 7 or 11 when a pair of dice are thrown?

2/9

Compute the standard deviation of the following sets of number 2, 4, 6, 8, 10, 12.

3.416

In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate, and of the females 70% are literate. What is the female population?

600

A bookstore purchased a bestselling book at P200.00 per copy. At what price should this book be marked so that, giving a 20% discount, the profit is 30%.

325

One ship is 1 mile north of a certain pier and is traveling N30°E at the rate of 3 miles/hour. Another ship is 3/4 mile east of the pier and is traveling east at a rate of 7 miles per hour. How fast are the ships separating

5.4 mph

A chemist needs to dilute a 50% boric solution to a 10% solution. If he needs 25 liters of the 10% solution, how much of the 50% solution should be used?

5 liters

∫ tan^2 xdx

tan x - x + C

A circle has a 20 cm diameter Determine the moment of inertia of the circular area relative to the axis perpendicular to the area through the center of the circle, in cm^4.

15,708

In the expansion of (x+4y)^12 the numerical coefficient of the 5th term is:

126,720

If a circle of radius b rolls without slipping on the inside of the circle of radius a any point of the first circle traces a roulette known as

cycloid

∫ sin 2θdθ

-1/2 cos2θ + C

A car rental company offers two plans for renting a car Plan A $30/day and $0.20/mile Plan B $55/day with free unlimited mileage For what range of miles will plan B save a customer's money?

More than 126 miles

Three girls A. B and C get into a bus that has six vacant seats on each side in how many ways can, they be seated, if A insists on sitting on the right side

In a multiple-choice test consisting of 5 questions each with 4 possible answers of which only 1 is correct, in how many ways can a student check off one answer to each question and get all the answers wrong?

243

A rectangle with sides parallel to the coordinate axes has one vertex at the origin, one on the positive x-axis and its fourth vertex in the first quadrant on the line with equation 2x+y=100 What is the maximum possible area of the rectangle?

1250

A lot has the form of a right triangle with perpendicular sides 90m and 120m long. Find the length and width of the largest rectangular building that can be erected facing the hypotenuse of the triangle.

60m, 45m

What part of 90% alcohol solution must be replaced by an equal amount of pure alcohol to make a 95% alcohol solution?

50%

Find the equation of the asymptotes of 16(x - 3)^2 -9(y + 2)^2 = 144

4x - 3y = 18, 4x + 3y = 6

Pure tin and pure iron was added to a 50 kg of an alloy containing 10% tia 630 20% iron. The process produced a new alloy containing 20% tin and 50% iron What is the weight of the new alloy?

116.67 kg

What is the differential equation of the family of parabolas having their vertices at the ongin and their foci on the x-axis

y = 2xy'

A water tank consists of a right circular cone that has its central axis vertical and its vertex at the bottom. The radius at the the top is 10 feet, the height is 50 feet, and the water is 15 feet deep Determine the work required to pump all the water to the level of the top of the cone.

342x10^3 ft-lbs

A piece of paper is 0.03 inches thick. Each time the paper is folded in half the thickness is doubled. If the paper is folded in half 12 times, how thick to the nearest foot, would the paper be?,

10.24 ft

When eccentricity of a curve is zero, the curve is a/an

circle

A man wishes to buy a piece of land worth 15 million pesos. If it were possible for him to save one centavo for the first day, two centavos on the second day. 4 centavos on the third day and so on. In how many days would he save enough money to buy the land?

If the curve 4x^2 + 8xy + Cy^2 - 2x + 4y - 15 = 0 is to be an ellipse, find minimum value of C.

The lotto uses number 142. A winning number consists of six different numbers in any order. What are your chances of winning it?

1/5,245,786

find the integral of xdx over (e^x-1) from zero to infinity

pi to the fourth over fifteen

The cost per hour of running a boat is proportional to the cube of the speed of the boat. At what speed will the boat run against a current of 4 kph in order to go a given distance most economically?

6 kph

The cost per hour of running a boat is proportional to the cube of the speed of the boat. At what speed will the boat run along with a current of 4 kph in order to go a given distance most economically?

Suppose the dimension (in inches) of a rectangular box change from 9, 6, 4 to 9.02, 5.97, and 4.01 respectively. Find the exact change in volume.

-0.063906

Point P which vertices of a triangle with sides 4. 5 and 6. Find the distance from point P to the plane of the triangle

9.53

Find the radius of curvature at any point of the curve y + ln(cos x)=0

sec x

Determine the solution of the inequality x^2 < 9

-3 < x < 3

Find the area of one arc of the cycloid, x = a(θ - sinθ) y = a(1 - cosθ)

3a^2π

. Find the enclosed by the four-cusped hypocycloid defined by x = acos^3θ y = asin^3θ

(3/8)π a^2

Find the area enclosed by r = 2asinθ

a^2 π

Find the area inside the cardiod r = a(1 + cosθ) and the arc r=a

a^2(5π/4 - 2)

The centroid of the area bounded by the parabola y^2 = 4ax and the line x=p coincides with the focus of the parabola. Find the value p.

5/3 a

Find all the values of z for which e^4z = 1

1/8 pi i + 1/2 k pi i

One end of a 32-meter ladder resting on a horizontal plane leans on a vertical wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2 meters per minute. How fast is the top of the ladder rising when its foot is 10 meters from the wall?

+0.658 m/min

A wall "h" meters high is 2m away from the building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 6m. How high is the wall in meters?

2.24

Find the differential equation whose general solution is y=C_1x + C_2e^2

(x - 1)y" - xy' + y = 0

Seven people are at the beach for a clambake. They have dug 12.6 pounds of clams. They eat the following amounts of plaunds. How many pour bound. 0.7 pound, 1265 pounds. 1.569 pounds, 0.83 pounds. How many pounds of clams are left?

4.566 pounds

Find the general solution of y" + 10y' + 41y = 0

y = e^-5x ( C1cos4x + C2sin4x)

The suspension cable of a bridge of length 800 m takes form of a parabola. if the sag is 100m, what is the equation of the parabola if the lowest part is at the origin?

x^2 = 1600 y

A man on observation sees a fire directly south of him, a boy on another tower 20km east of the first tower observes the fire at a bearing 540°15°W What is the distance of the first tower from the fire?

23.62 km

What was the marked price of a shirt that sells at P225 after a discount of 25%?

300

The parabola defined by the equation 3y^2 + 4x = 0 opens

to the left

A/An ________ triangle is a triangle having three unequal sides.

scalene

Which of the following is true?

cos (-θ) = cosθ

100

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

latus rectum

DC CIRCUITS POWERLINE

premopremo remo · 75問 · 2年前

DC CIRCUITS POWERLINE