Problem_Solving_06

30問 • 1年前

Jacky Shane Luyas Buhia

通報

問題一覧

Find the equation of the line passing through the origin and with a slope of 6 ?

A. y - 6x = 0

Find the equation of the line if the x-intercept and y-intercept are -2 and 4, respectively.

A. y - 2x - 4 = 0

Find the area of the triangle which the line 2x - 3y + 6 = 0 forms with the coordinate axis.

A. 3

Find the slope of a line having a parametric equation of x = 2 + t and y = 5 - 3t.

D. -3

In a cartesian coordinates, the vertices of a square are: ( 1, 1 ), ( 0, 8 ), ( 4, 5 ) and ( -3, 4 ). What is the area?

C. 25 sq. units

Find the inclination of the line passing through ( -5, 3 ) and ( 10, 7 ).

B. 14.93

If ( -2 , -4 ) is the midpoint of ( 6 , -7 ) and ( x , y ), then the values of x and y are

B. x = -10, y = -1

Find the derivative of arc cos 4x.

A. -4 / ( 1 - 16x²)^0.5

Differentiate the equation: y = x² / x + 1

A. x² + 2x / ( x + 1 )²

A certain angle has a supplement of 5 times its complement. What is the angle?

A. 67.5°

A boat travels downstream in 2/3 of the time as it goes going upstream. If the velocity of the river's current is 8 kph, determine the velocity of the boat in still water.

A. 40 kph

A person has 2 parents, 4 grandparents, 8 great grandparents and so on. How many ancestors during the 15 generations preceding his own, assuming no duplication?

B. 65534

The selling price of a TV set is double that of its cost. If the TV set was sold to a customer at a profit of 25% of the net cost, how much discount was given to the customer?

C. 37.5 %

Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.

A. 1075 m²

The area of a triangle inscribed in a circle is 39.19 cm² and the radius of the circumscribed circle is 7.14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side.

D. 14 cm

The angle of a sector is 30° and the radius is 15 cm. What is the area of the sector in cm² ?

C. 58.9

What is the radius of the circle x² + y² - 6y = 0?

B. 3

A circle whose equation is x² + y² + 4x + 6y -23 = 0 has its center at:

D. ( -2 , -3 )

What is the radius of a circle with the ff. equation: x² - 6x + y² - 4y - 12 = 0

C. 5

Find the location of the focus of the parabola y² + 4x - 4y - 8 = 0.

C. ( 2 , 2 )

The lengths of the major and minor axes of an ellipse are 10 m and 8 m, respectively. Find the distance between the foci.

D. 6

Find the major axis of the ellipse x² + 4y² - 2x - 8y + 1 = 0.

C. 4

An ellipse with an eccentricity of 0.65 and has one of its foci 2 units from the center. The length of the lactus rectum is nearest to

A. 3.5 units

A triangle has variable sides x, y, z subject to the constraint such that the perimeter is fixed to 18 cm. What is the maximum possible area for the triangle?

A. 15.59 cm²

A certain cable is suspended between two supports at the same elevation and 500 ft apart, the load is 500 lbs per horizontal foot including the weight of the cable. The sag of the cable is 30 ft. Calculate the total length of the cable.

C. 504.76 ft

A cable carries a horizontal load of 20 kg/m. Neglecting its own weight, find the maximum tension of the cable if the distance between the supports is 100 m and the sag is 5 m.

A. 5099 kg

A circle has a diameter of 20 cm. Determine the moment of inertia of the circular area relative to the axis perpendicular to the area through the center of the circle in cm⁴.

B. 15,708

A shot is fired at an angle of 45° with the horizontal and a velocity of 300 fps. Calculate, to the nearest value, the range of the projectile.

A. 932 yards

Find the value of k so that 4x² + 6x + k is a perfect square.

D. 2.25

The polynomial x³ + 4x² -3x + 8 is divided by x - 5, then the remainder is,

C. 218

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問題一覧

Find the equation of the line passing through the origin and with a slope of 6 ?

A. y - 6x = 0

Find the equation of the line if the x-intercept and y-intercept are -2 and 4, respectively.

A. y - 2x - 4 = 0

Find the area of the triangle which the line 2x - 3y + 6 = 0 forms with the coordinate axis.

A. 3

Find the slope of a line having a parametric equation of x = 2 + t and y = 5 - 3t.

D. -3

In a cartesian coordinates, the vertices of a square are: ( 1, 1 ), ( 0, 8 ), ( 4, 5 ) and ( -3, 4 ). What is the area?

C. 25 sq. units

Find the inclination of the line passing through ( -5, 3 ) and ( 10, 7 ).

B. 14.93

If ( -2 , -4 ) is the midpoint of ( 6 , -7 ) and ( x , y ), then the values of x and y are

B. x = -10, y = -1

Find the derivative of arc cos 4x.

A. -4 / ( 1 - 16x²)^0.5

Differentiate the equation: y = x² / x + 1

A. x² + 2x / ( x + 1 )²

A certain angle has a supplement of 5 times its complement. What is the angle?

A. 67.5°

A boat travels downstream in 2/3 of the time as it goes going upstream. If the velocity of the river's current is 8 kph, determine the velocity of the boat in still water.

A. 40 kph

A person has 2 parents, 4 grandparents, 8 great grandparents and so on. How many ancestors during the 15 generations preceding his own, assuming no duplication?

B. 65534

The selling price of a TV set is double that of its cost. If the TV set was sold to a customer at a profit of 25% of the net cost, how much discount was given to the customer?

C. 37.5 %

Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.

A. 1075 m²

D. 14 cm

The angle of a sector is 30° and the radius is 15 cm. What is the area of the sector in cm² ?

C. 58.9

What is the radius of the circle x² + y² - 6y = 0?

B. 3

A circle whose equation is x² + y² + 4x + 6y -23 = 0 has its center at:

D. ( -2 , -3 )

What is the radius of a circle with the ff. equation: x² - 6x + y² - 4y - 12 = 0

C. 5

Find the location of the focus of the parabola y² + 4x - 4y - 8 = 0.

C. ( 2 , 2 )

The lengths of the major and minor axes of an ellipse are 10 m and 8 m, respectively. Find the distance between the foci.

D. 6

Find the major axis of the ellipse x² + 4y² - 2x - 8y + 1 = 0.

C. 4

An ellipse with an eccentricity of 0.65 and has one of its foci 2 units from the center. The length of the lactus rectum is nearest to

A. 3.5 units

A triangle has variable sides x, y, z subject to the constraint such that the perimeter is fixed to 18 cm. What is the maximum possible area for the triangle?

A. 15.59 cm²

C. 504.76 ft

A cable carries a horizontal load of 20 kg/m. Neglecting its own weight, find the maximum tension of the cable if the distance between the supports is 100 m and the sag is 5 m.

A. 5099 kg

A circle has a diameter of 20 cm. Determine the moment of inertia of the circular area relative to the axis perpendicular to the area through the center of the circle in cm⁴.

B. 15,708

A shot is fired at an angle of 45° with the horizontal and a velocity of 300 fps. Calculate, to the nearest value, the range of the projectile.

A. 932 yards

Find the value of k so that 4x² + 6x + k is a perfect square.

D. 2.25

The polynomial x³ + 4x² -3x + 8 is divided by x - 5, then the remainder is,

C. 218