Math 3.1

100問 • 2年前

問題一覧

Find the transformed equation so that after rotating 2x2 + <<3 xy+ y2 = 8 at a certain angle, it will have no xy term.

5x2 + y 2 = 16

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.

(pi - 2)a^2

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

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.

546/729

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

cos (2 sq.rt of 2kpi) + i sin(2 sq.rt of 2kpi)

A man leaving his office one afternoon noticed the clock at past two o"clock. Between two to three hours, he returned to his office noticing the hands of the clock interchanged. At what time did he leave the office and the time that he returned to the office?

2:26.01, 5:12.17

Find the area bounded by the curve at the first quadrant by y = 4x, x = 1, and x = 3.

4 sqrt of 3 - 4/3

Im (1 + i)^(1 + i).

0.583

Find the general solution of dy/dx = tanx.

e^y = Csecx

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?

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

term

cosA + jsinA is equal to:

e^ jA

What is the curve described when e = 1?

Parabola

The centroid of half of an ellipse with respect to its minor-axis.

4a/3pi

Differentiate: y = arctan3x.

3/(1+9x2)

A rubber bail 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.

If the point (2, k) lies on the line with the slope 3 and passing through the point (1,6), find k.

If sinx =2, find sin4x.

- j56 sqrt 13

The derivative of In cos x is

- tan x

Find integral In x dx.

xInx - x + C

Evaluate sin [arccos (- 2/3) ].

sqrt(5)/3

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that the two napkin rings have the same height "h". Using cylindrical shells to compute the volume of a napkin ring created by drilling holes of radius "m" through the center of a sphere with radius "B" and express it in terms of "h"

1/6 pi h^3

A wall is 2m away from a 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?

2.24m

A certain radioactive substance has a half-life of 3 years. If 10 grams are present initially, how much of the substance remain after 9 years?

1.25 g

Ana bought ballpens for P90. Then she sold it all with a profit of P2 each ballpen. If after selling the ballpens, she will buy with additional 15 ballpens, what is the cost of each ballpen?

₱3.45

In how many ways can 6 people be seated in a row of 9 seats?

60,480

What is the coordinate of the vertex of the equation x^2 + 2x - y + 2 = 0.

(-1, 1)

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

11/16

Find the equation of the circle whose center is at (3, - 5) and whose radius is 4.

x^2 + y^2 - 6x + 10y + 18 = 0

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

100

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

A circle is inscribed in an isosceles triangle whose lateral sides 9 om and the base is 6 cm. Determine the distance between the two points of tangency.

Two positive numbers may be inserted between 3 and 9 meh that the first three are in geometric progression, while the last three are in arithmetic progression. What is the sum of these two positive numbers?

11.25

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

A balloon travels upwards 6 m, North and 8 m, East. What is the distance traveled from the starting point?

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

State the quadrant in which the coordinate (15, -2) lies

In conic section, if eccentricity e = 0, the locus is a

circle

The equation x^3 + y^3 - 3axy = 0 represents a curve called

Folium of Descartes

A rubber ball is dropped from a height of 15 meters. 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. The geometric progression occurs after the first rebound.

75 m

What is the equation of a circle that passes thru the vertex and latus rectum of the curve y^2 = 8x?

(x-5)^2 + y^2 = 25

the sum of the digits of a 2 digit number is 10. If the number is divided by the units digit, the quotient is 3 remainder is 4. Find the number.

The maximum possible number of positive roots that the equation x^4 + 2x^3 - 3x^2 + bx - 5 = 0 can have if b represents a positive real number is

1 or 3

In a conic section if the eccentricity e = 0, then the locus is a

circle

Evaluate j^174

-1

4x2 - y2 = 16 is the equation of

hyperbola

Find the maximum area that a 10m chord can enclose?

7.958 m^2

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

Evaluate Integral xdx / (4+x2)^3/2

- (4 + x2)^-1/2 + C

A cone with 4-in base radius and 8-in depth; if water flows inside the cone 1 cu. in/sec, find the rate on which the depth changes when the water is 2-in from the base.

1/9 π

A parabolic mirror has its focus 31 ft from its vertex, and the distance across the top is 64 ft. Determine the distance at the center. How deep is the center of the mirror?

64/93

The derivative of arccotu with respect to x is:

- du/dx ————— 1+x^2

Which of the following is the value of xy if x - y = 2, x^2 + 2xy + y^2 = 3?

- 1/4

Evaluate cos2x if sinx = 2.

-7

Two sides of a triangle are 5 and 10 inches, respectivelye third side between them is increasing 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

Boyet reads the clock differently such that he recognizes the hour hand as the minute hand and the minute hand as hour hand. How many minutes after 5 o'clock will he read the time correctly?

27.27

A cask containing 20 gallons of wine was emptied on one-ffth of its content and then is filled with water. If this is done 6 times, how many gallons of wine remain in the cask?

5.243

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

Evaluate the integral of sqrt of(1-cosxdx) as x approaches infinity.

indeterminate

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

57.7 kg

The average of 2016 numbers is 2017. If a number is neglected, the new average becomes 2015. What was the number neglected?

6047

The average of 2017 numbers is 2018. If a number is neglected, the new average becomes 2016. What was the number neglected? C. A. D.

6050

What is the sum of the coefficients of the expansion of (2x - 1)^21

The probability of John's winning whenever he plays a certain game is 1/3. If he plays 4 times, find the probability that he wins just twice. C. A. D.

0.2963

The sum of the sum of the digits of a 2-digit number is 10. If the number is divided by the unit's digit, the quotient is 3 remainder is 4. Find the number

The Laplace transform of t^2cos4t

25(s^2 - 48)(s^2 + 16)3

The Laplace Transforms of t^2 e^ -4t is

2/(s + 4)^3

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

A die is rolled and a coin is tossed. What is the probability that a three and a head will appear?

1/12

If a bus weighs 2.5 tons, how much pounds does it weigh? (1 ton = 2000 lbs)

5000

In how many ways can 2 integers be selected from the integers 1, 2, 3,…., 100 so that their difference is exactly 7?

A Manila High School has 85 seniors, each of whom plays on at least one of the school's three varsity sports teams: football, baseball, and basketball. It so happen that 74 are on the football team; 26 are on the baseball team; 17 are on both the football and basketball teams; 18 are on both the baseball and football teams; and 13 are on both the baseball and basketball teams. Determine the number of seniors playing all three sports given that twice this number is members of the basketball team.

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

What is the Laplace transform of e^-2t

1/(s+2)

3x2 + y^2 = 25 is an equation of a/an:

ellipse

Solve the differential equation cotxy and ydx = 0.

y= C cosx

Maria will buy in a store. In the store, if you buy at least P30, you will pay in cash f you buy P30 to P70, you will pay in gift checkhay does mean? 70. you will payin credit card. If Maria paid through gift check, what does it mean?

Maria bought an item worth P70.

What is the sum of the first 80 positive odd integers subtracted from the sum of the first 80 positive even integers?

A closed cylindrical tank with circular cross-section of radius, 2 feet and a height of 6 feet. Find the approximate volume of asbestos required to cover the tank completely with one inch thick of it.

8.378 cu. ft.

9 liters of wine are taken from a container full of wine. It is then filled with water. Then 9 liters of the mixture are taken and the container is again filled with water. If the ratio of the quantity of the wine now in the container to the quantity of the water in it is 16/9, what is the capacity of the container?

45 L

Find the equation of the family of orthogonal trajectories of the system of parabolas у2 = 2x + C..

y = Ce^-x

Evaluate limit of sin9x / 2x as x approaches zero.

9/2

The semi-axes of an ellipse 8cm and 6cm increases by 0.02 cm and 0.01 cm respectively. Find its approximate increase in the area.

0.6283 cm

A closed rectangular wooden block is painted 1/20 cm thick. Find the co of paint used up

18.8

Find the general solution of the differential equation 7y y’ = 5x.

5x^2 - 7y^2 = C

Find the radius of the circle x2 + y2 -4x + 8y =7.

3 sqrt of (3)

Find the area of the shaded region between y = 6y - 1 and y = 1/4x + 3, bounded by x = 0 and the intersection point.

32/23

Which of the formulas below is incorrect?

sin^3(θ) = 4sin^3 - 3sinθ

A project activity can be done by 25 men in 60 days. At the end of the 5 day, 6 men were laid off. At the start of the 33 day, 12 more men were hired to finish the job. How many days is the project advanced/ delayed?

0.19 advanced

Evaluate integral of 12 sin^5(x) cos^5(x) dx from 0 to π/2

0.20

If (5x - 3), (x + 2), and (3x - 11) form an arithmetic progression, find the fifteenth term

- 86

In how many ways can an IIEE Chapter with 15 directors choose a President, a Vice-President, a Secretary, a Treasurer, and an Auditor, if no member can hold more than one position?

360,360

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.

1.696

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 units

(x/10)^2+ (y/8.66)^2 = 1

If j= sqrt(-1), the quantity j^5248 is equal to,

-1

In any square matrix, when the elements of any two rows columns are interchanged the determinant is

negative of former value

An array of mn quantities which represents a single number and is composed of elements in rows and columns is known as

determinant

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

96pi/5

100

Find the area bounded by the parabola, x = 4y and y = 4.

21.33

Math

Ashley Calica · 10問 · 2年前

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10問 • 2年前

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Esas

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Esas 1

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EE objectives R2 R3

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問題一覧

Find the transformed equation so that after rotating 2x2 + <<3 xy+ y2 = 8 at a certain angle, it will have no xy term.

5x2 + y 2 = 16

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.

(pi - 2)a^2

0.658 m/min

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.

546/729

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

cos (2 sq.rt of 2kpi) + i sin(2 sq.rt of 2kpi)

2:26.01, 5:12.17

Find the area bounded by the curve at the first quadrant by y = 4x, x = 1, and x = 3.

4 sqrt of 3 - 4/3

Im (1 + i)^(1 + i).

0.583

Find the general solution of dy/dx = tanx.

e^y = Csecx

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?

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

term

cosA + jsinA is equal to:

e^ jA

What is the curve described when e = 1?

Parabola

The centroid of half of an ellipse with respect to its minor-axis.

4a/3pi

Differentiate: y = arctan3x.

3/(1+9x2)

A rubber bail 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.

If the point (2, k) lies on the line with the slope 3 and passing through the point (1,6), find k.

If sinx =2, find sin4x.

- j56 sqrt 13

The derivative of In cos x is

- tan x

Find integral In x dx.

xInx - x + C

Evaluate sin [arccos (- 2/3) ].

sqrt(5)/3

1/6 pi h^3

A wall is 2m away from a 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?

2.24m

A certain radioactive substance has a half-life of 3 years. If 10 grams are present initially, how much of the substance remain after 9 years?

1.25 g

Ana bought ballpens for P90. Then she sold it all with a profit of P2 each ballpen. If after selling the ballpens, she will buy with additional 15 ballpens, what is the cost of each ballpen?

₱3.45

In how many ways can 6 people be seated in a row of 9 seats?

60,480

What is the coordinate of the vertex of the equation x^2 + 2x - y + 2 = 0.

(-1, 1)

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

11/16

Find the equation of the circle whose center is at (3, - 5) and whose radius is 4.

x^2 + y^2 - 6x + 10y + 18 = 0

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

100

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

A circle is inscribed in an isosceles triangle whose lateral sides 9 om and the base is 6 cm. Determine the distance between the two points of tangency.

11.25

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

A balloon travels upwards 6 m, North and 8 m, East. What is the distance traveled from the starting point?

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

State the quadrant in which the coordinate (15, -2) lies

In conic section, if eccentricity e = 0, the locus is a

circle

The equation x^3 + y^3 - 3axy = 0 represents a curve called

Folium of Descartes

75 m

What is the equation of a circle that passes thru the vertex and latus rectum of the curve y^2 = 8x?

(x-5)^2 + y^2 = 25

the sum of the digits of a 2 digit number is 10. If the number is divided by the units digit, the quotient is 3 remainder is 4. Find the number.

The maximum possible number of positive roots that the equation x^4 + 2x^3 - 3x^2 + bx - 5 = 0 can have if b represents a positive real number is

1 or 3

In a conic section if the eccentricity e = 0, then the locus is a

circle

Evaluate j^174

-1

4x2 - y2 = 16 is the equation of

hyperbola

Find the maximum area that a 10m chord can enclose?

7.958 m^2

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

Evaluate Integral xdx / (4+x2)^3/2

- (4 + x2)^-1/2 + C

A cone with 4-in base radius and 8-in depth; if water flows inside the cone 1 cu. in/sec, find the rate on which the depth changes when the water is 2-in from the base.

1/9 π

A parabolic mirror has its focus 31 ft from its vertex, and the distance across the top is 64 ft. Determine the distance at the center. How deep is the center of the mirror?

64/93

The derivative of arccotu with respect to x is:

- du/dx ————— 1+x^2

Which of the following is the value of xy if x - y = 2, x^2 + 2xy + y^2 = 3?

- 1/4

Evaluate cos2x if sinx = 2.

-7

0.44 in/min

Boyet reads the clock differently such that he recognizes the hour hand as the minute hand and the minute hand as hour hand. How many minutes after 5 o'clock will he read the time correctly?

27.27

A cask containing 20 gallons of wine was emptied on one-ffth of its content and then is filled with water. If this is done 6 times, how many gallons of wine remain in the cask?

5.243

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

Evaluate the integral of sqrt of(1-cosxdx) as x approaches infinity.

indeterminate

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

57.7 kg

The average of 2016 numbers is 2017. If a number is neglected, the new average becomes 2015. What was the number neglected?

6047

The average of 2017 numbers is 2018. If a number is neglected, the new average becomes 2016. What was the number neglected? C. A. D.

6050

What is the sum of the coefficients of the expansion of (2x - 1)^21

The probability of John's winning whenever he plays a certain game is 1/3. If he plays 4 times, find the probability that he wins just twice. C. A. D.

0.2963

The sum of the sum of the digits of a 2-digit number is 10. If the number is divided by the unit's digit, the quotient is 3 remainder is 4. Find the number

The Laplace transform of t^2cos4t

25(s^2 - 48)(s^2 + 16)3

The Laplace Transforms of t^2 e^ -4t is

2/(s + 4)^3

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

A die is rolled and a coin is tossed. What is the probability that a three and a head will appear?

1/12

If a bus weighs 2.5 tons, how much pounds does it weigh? (1 ton = 2000 lbs)

5000

In how many ways can 2 integers be selected from the integers 1, 2, 3,…., 100 so that their difference is exactly 7?

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

What is the Laplace transform of e^-2t

1/(s+2)

3x2 + y^2 = 25 is an equation of a/an:

ellipse

Solve the differential equation cotxy and ydx = 0.

y= C cosx

Maria bought an item worth P70.

What is the sum of the first 80 positive odd integers subtracted from the sum of the first 80 positive even integers?

8.378 cu. ft.

45 L

Find the equation of the family of orthogonal trajectories of the system of parabolas у2 = 2x + C..

y = Ce^-x

Evaluate limit of sin9x / 2x as x approaches zero.

9/2

The semi-axes of an ellipse 8cm and 6cm increases by 0.02 cm and 0.01 cm respectively. Find its approximate increase in the area.

0.6283 cm

A closed rectangular wooden block is painted 1/20 cm thick. Find the co of paint used up

18.8

Find the general solution of the differential equation 7y y’ = 5x.

5x^2 - 7y^2 = C

Find the radius of the circle x2 + y2 -4x + 8y =7.

3 sqrt of (3)

Find the area of the shaded region between y = 6y - 1 and y = 1/4x + 3, bounded by x = 0 and the intersection point.

32/23

Which of the formulas below is incorrect?

sin^3(θ) = 4sin^3 - 3sinθ

0.19 advanced

Evaluate integral of 12 sin^5(x) cos^5(x) dx from 0 to π/2

0.20

If (5x - 3), (x + 2), and (3x - 11) form an arithmetic progression, find the fifteenth term

- 86

In how many ways can an IIEE Chapter with 15 directors choose a President, a Vice-President, a Secretary, a Treasurer, and an Auditor, if no member can hold more than one position?

360,360

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.

1.696

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 units

(x/10)^2+ (y/8.66)^2 = 1

If j= sqrt(-1), the quantity j^5248 is equal to,

-1

In any square matrix, when the elements of any two rows columns are interchanged the determinant is

negative of former value

An array of mn quantities which represents a single number and is composed of elements in rows and columns is known as

determinant

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

96pi/5

100

Find the area bounded by the parabola, x = 4y and y = 4.

21.33