MATH PRE BOARD POWERLINE

98問 • 1年前

問題一覧

What is the radius of curvature at point (1, 2) of the curve 4x-v^2=0?

5.66

Determine the equation that expresses that G is proportional to k and inversely proportional to C and z. Symbols a b and c are constants

G=ck/zC

Determine all the values of (1 + 1)^i

e^ - π/4)+ 2kπ [cos(1/2 in 2)+i sin(1/2 In 2)]

During his major league career, Hank Aaron hit 38 more home runs than Babe Ruth hit during his career. Together they hit 1,524 home runs. How many home runs did Babe Ruth hit?

743 home runs

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

8/3

Carbon-14 is a radioactive isotope of carbon that has a half life of 5600 years, it is used extensive in dating organic material that is tens of thousands of years old. What fraction of the original amount of Carbon-14 in a sample would be present after 10,000 years?

30%

Find the area in [cm^2] of a regular octagon inscribed in a circle of radius 10cm.

283

Find the general solution of dy/dx = ysecx

y = C(secx+tanx)

How many maximum number of times of can 6 lines intersection?

What is 75% of 450?

337.5

Find the area in a single hump of a cycloid given by the parametric equation x = a(θ - sinθ), y=a(1-cosθ)

3πa^2

Given sin A=-4/5. A in Quadrant III cot B = 4.5, B in Quadrant III Evaluate sin (A+B)

19/5 square root of 17

A bug moved 3 centimeters along an arc with a central angle of 45 degrees. What is the radius of the circle?

12/π cm

Evaluate the expression: 12[cos45 + jsin45] + 3[cos15+jsin15]

2√3 + j2

15 Obtain L{t^n}

n!s^(n+1)

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 meters?

300 m

Jose is 5' 6" in height while Pedro is 6' 5" in height. Pedro is taller than jose?

13 inches

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

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

Gabby cuts a piece of rope into three pieces. One piece in 5 inches long, one piece is 4 inches long, and one piece is 3 inches long. The longest piece of rope is approximately what percent of the original length before the rope was cut?

42%

A rectangular tract of land measures 860 feet by 560 feet. Approximately how many acres is this? (one acre 43,560 square feet)

11.06 acres

Find the volume of a cube having its two faces laid in the planes 2x-y+2z-3= 0 and 6x-3y+6z+8=0

4913/729

A 5-foot girl is walking toward a 20-foot The light from the lamp post causes the length of the girl's shadow changing?

Evaluate the integral of x³dx over(e^x - 1) limits from zero to infinity

(π^4)/15

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

Which of the formulas below is incorrect?

sin2θ = 2cos^2θ-1

Find the sum of the coefficients in the expansion of (2x-3y+1)^35

-1

Evaluate sin4x if sinx=2

-j56√3

Three randomly chosen senior high school students were administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test t(N) Assume the possible combinations of the three student Drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely what is the probability at least one student gets negative result?

7/8

Which of the following is equivalent cos^2θ - sin^2θ

cos2θ

The number of red blood corpuscles in one cubic millimeter is about 5,000,000, and the number of white blood corpuscles in one cubic millimeter is about 8,000. What, then, is the ratio of white blood corpuscles to red blood corpuscles?

1:625

31. If z=6 e^πi/3 evaluate e^iz.

e^-3sqroot of 3

Solve for the median given 14, 11, 10, 13, 12, 6, 4

Solve the differential equation: y" - 4y' + 3y = sinx

y(x) = C1 e^3x + C2 e^x + 1/5 cosx + 1/10 sin x

A railroad is in a circular path. What should be the radius if the track is to change direction by 30 degrees at a distance of 57.08m?

300 m

Evaluate i^64002

-1

Listed below are the functions each denoted g(x) and each involving a real number x. constant c>1 If f(f)=2^{x}. which of these functions yield the greatest value for f(g(x) for all x>1"

g(x) = cx

The integral of a function between certain abcissas between those limits gives the limits divided by the difference in of the ______ function.

average

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

It is estimated that the annual cost of driving a certain new car is given by the formula C=0.25 m+1.600 where m represents the number of miles driven per year and C is the cost in dollars Jane purchases such a car and determines between $5,350 and $5.600 for next year's driving cost. What is the corresponding range of miles that she can drive her new car?

Between 15,000 mi and 16,000

What is the line normal to the curve x^2+y^2=25 thru (2,1)?

x - 2y = 0

The graph of r=a+ bcosθ is a

limacon

A garden hose fills a 32 liter waste bucket in 120 sec. If the diameter of the hose is 1 cm, what is the velocity of water as it leaves the hose?

3.4 m/sec

The locus of a pint which moves so that its distance from a fixed point and a fixed line is always equal is

Parabola

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

40 ft

When discriminant of a conic section. D=B^2-4AC=1 , the curve is a

hyperbola

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

Latus rectum

A man standing on a 48.5 m high building has an eyesight height of 1 5m from the top of the building, took a depression reading from the top of another nearby building and nearest wall, which are 50° and 80^{\circ} respectively. Find the height of the nearby building in meters and both buildings lie on the same horizontal plane

39.49

From past experience, it is known that 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female A random sample of 25 one year-old children are given this voice recognition test. Find the probability that at least 13 but not more than 18 children recognize their mother's voice

0.90%

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

A conic section whose eccentricity is equal to zero.

circle

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?

130 288.13 in^3/min

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

59.22

The arc length is equal to the radius of a circle is called

1 radian

What is the ratio of the sides of a triangle if the product of the sines of its angle is a maximum?

1:1:1

From past experience, it is known that 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female A random sample of 25 one year-old children are given this voice recognition test. Find the probability that at most 4 children do not recognize their mother's voice

7.10%

What is the curve described by the equation Ln lz-1l=2?

Circle

A tangent to a conic is a line

Which touches the conic at only the point

__________ passes through the foci, vertices and the center of the hyperbola

Transverse axis

Joseph gave ¼ of his candies to Joy and Joy gave 1/5 of what he got to Tim. If Tim received 2 candies, how many candies did Joseph have originally?

One end of a 32 m ladder resting on a horizontal plane leans on a vertical wall Assume ladder to be pushed towards the wall at the rate of 2 m/in, how fast does the top of the ladder increase when the foot is 10m from the wall?

0.658 m/min

A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soap, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. If a randomly selected consumer has seen an advertisement for the new soap, what is the probability that this consumer has tried the new soap?

37.5%

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

Evaluate sin3x if sinx = 2

-26

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

y = e^-5x (c1cos 4x + c2sin 4x)

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

73.4 deg

A triangular corner lot has perpendicular sides of lengths 90m and 60m. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides along the streets.

45mx30m

if 20 workers can fabricate 40 transistors in 8 hours, how many workers can fabricate 960 transistors in a week

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

3 or 1

A pendulum 1m long oscillates at an angle of 10 degrees Find the length of the arc subtended

1/18 pi

An arch is in 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

14 is 30% of what number?

46.67

Two perpendicular chords of a circle are cut thru 2 and 6 and the other chord at 3. Find the radius of the circumscribing circle?

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

-12 + 6i

Points A and B 1000m apart are plotted on a straight highway running east and west. From A. the bearing of the tower C is 32^{\circ}W of N and from B. the bearing of C is 26^{\circ}N of E. Approximate the shortest distance of the tower C to the highway

374 m

The sides of a right triangle are in arithmetic progression. The sides of a triangle are

3,4 and 5

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

2,880 ft/sec

Conic section whose eccentricity is equal to 1

parabola

Passes through the foci, vertices and the center of the hyperbola

Transverse Axis

Find the equation of the circle with center at the origin and passes through (-3,4).

x^2 + y^2 = 25

Which of the formulas below is incorrect?

cos2θ = 2cos^2θ - 1

In an engineering class of 40 students 30 passed Algebra 36 passed Trigonometry 2 failed on both subjects How many passed both Algebra and Trigonometry?

Liza thought she had the exact money to buy 10 chocolate bars. However the price per bar had increased by 50 centavos Consequently, she was able to buy only 8 bars and had P2 left. How much money did Liza have?

The product of the slopes of the equation of 2 lines is -1 One of the line is

Perpendicular

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

Find the change in volume of a sphere whose diameter increased from 4 in by 0.1in

2.5766

The Geometric Progression is 25/2-5, 2,4/5... Find the 5^th term?

10/387

Find the volume generated by revolving about the x-axis, the area bounded by the curve y=cosx from x=0 to x=pi/2

π^2/6

Find the differential equation of the family of parabola with vertex at the origin and focus at x-axis.

2xdy = ydx

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 15 minutes.

2,880 ft/sec

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

Hyperbola

A professor was given a grant and can bring 3 students How many ways can he choose from 6 students

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

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

There are m months in a year, w weeks in a month and d days in a week. How many days are there in a year?

mxwxd

Find the sum of all the odd integers between 100 and 1000

247,500

The geometric mean and the arithmetic respectively. What is the harmonic mean?

8.9

What curve is described by the equation 4x^2 - y^2 + 8x + 4y = 15

Hyperbola

DC CIRCUITS POWERLINE

premopremo remo · 75問 · 2年前

DC CIRCUITS POWERLINE