MATH BATAK 0419
MATH BATAK 0419 Quiz
Test your mathematical understanding and problem-solving skills with the MATH BATAK 0419 Quiz! This quiz consists of 41 questions covering a variety of mathematical topics, challenging your knowledge and application in real-world scenarios.
Key Features:
- 41 well-structured questions.
- Diverse mathematical concepts.
- Immediate feedback on your answers.
What type of curve is generated by a point that moves in uniform circular motion about an axis, while travelling with a constant speed parallel to the axis.
A cycloid
A hypocycloid
An epicycloid
A Helix
The rate of virus spread is jointly proportional to those infected and uninfected people. If there are 5000 inhabitants at the start of the year and after a week there were 160 people infected, after 2 weeks there are 1200 people infected, how many days will there be for 1500 people to be infected?
15days
20days
18days
23days
A ball is dropped from a height of 18 meters. On each rebound it rises 2/3 of the height from which it last fell. What distance has it traveled at the instant it strikes the ground for the 5th time?
37.89 m
75.78 m
73.89 m
57.78 m
Find the area bounded by the parabola √x + √y = 1 and the line x + y = a.
a²/5
a²/5
a²/3
A²/2
A cord of a circle of a diameter 10ft is decreasing in length 1ft/min. Find the rate of change of the smaller arc subtended by the cord when the cord is 8ft long.
3/5 ft/min
5/3 ft/min
3 ft/min
5 ft/min
Evaluate the integral of 1/(x-y) dxdy with inner bounds of 2y to 3y and outer bounds of 0 to 2.
Ln 2
ln 4
ln 1/2
Ln 3
Find the equation x = y = z that is equidistant from (3,0,5), and (1, -1,4)
(2,2,2)
(1,1,1)
(3,3,3)
(4,4,4)
The parabola y^2 = 4ax and the line x = p enclosed an area with the centroid at the focus of the parabola. Find p in terms of a.
3/5a
3/4a
5/3a
2/5a
What is the length of the shortest line that can be drawn tangent to the ellipse b2x2 + a2y2 =a2b2 and meeting the coordinate axes?
A2 + b2
A + b
√(a2+ b2)
½√(a2+ b2)
Find the moment of inertia of the area bounded by the curve y^2 = 4x and the line x =1 with respect on the x-axis.
2.18
2.38
2.13
3.13
Determine the differential equation of the family of circles with center at the y-axis?
Yx” –(x’)3 -y’ = 0
Yx” –(y’)3 -x’ = 0
xy” –(y’)3 -y’ = 0
Yx” –(x’)3 -y’ = 0
Solve (x + y)dy = (x – y)dx
Y2 + 2xy + x² = C
X3 + 2xy - y2 = C
Y2 + 2xy - x2 = C
X2 - 2xy - y2 = C
A water tank is shaped in such a way that the volume of water in the tank is V = 2y3/2 cu.in. When its depth is y inches. If water flows out through a hole at the bottom of the tank at the rate of 3sq.rt of ycu.in/min, at what rate does the water level in the tank fall?
11 in/min
0.11 in/min
1 in/min
1/11 in/min
What is the shape of the graph of the polar equation 𝑟 = 𝑎 + 𝑝 cos 𝜃?
Lemniscate
Helix
Limacon
Rose
A tank initially holds 100 gal of salt solution in which 50 lb of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm containing 2 lbs of dissolved salt per gallon. Assuming that the mixture is kept uniform by stirring a drain pipe draws out of the tank the mixture of 2 gpm. Find the amount of salt in the tank at the end of 30 minutes.
171.24 lbs
143.25 lbs
124.11 lbs
105.12 lbs
A cylindrical open container open at the top with minimum surface area at a given volume. What is the relationship of its radius to height?
r = h/2
R = 2h
R = h
R = h/4
Find the orthogonal trajectories of the family of parabolas y^2 = 2x + C.
Y = Ce^6
y = Ce^(-x)
Y = Ce^(2x)
Y = Ce^(-2x)
A cardboard 20 in x 20 in is to be formed into a box by cutting four equal squares and folding the edges. Find the volume of the largest box.
592 cu.in.
698 cu.in.
529 cu.in.
689 cu.in.
What percentage of the volume of a cone is the maximum volume right cylinder that can be inscribed in
24%
34%
44%
54%
Find the LT for f(x) = 2 when 03
1/s^2 + e^-3s (1/s^2 + 1/s)
1/s^2 e^-3s (1/s)
2/s+e^-3s (1/s^2 + 1/s)
2/s +1/s^2
Find the minimum distance from the point (4, 2) to the parabola y2 = 8x.
4 sq. rt. of 3
sq.rt. of 3
2 sq.rt. of 2
2 sq.rt. of 3
An open cylindrical through is constructed by bending a given sheet of tin and breadth 2a. Find the radius of the cylinder of which the trough forms a part when the capacity of the trough is a maximum.
0.376a
0.637a
0.367a
0.763a
If SinA = -4/5, Cot B = 4 and A and B in quadrant 3, find sin (A + B). A. 9/5√17 C. 19/4√17 B. 19/5√17✓
9/5√17
19/5√17
19/4√17
19/4√17
Find the volume of the solid common between intersecting cylinders with radius of 3 ft.
72
288
144
256
If cos x = 2, find cos 3x.
1.5sq.rt of 6
3sq.rt of 6
27
17
Water is running out a conical funnel at the rate of 1 cu.in/s. If the radius of the base of the funnel is 4 in, and the altitude is 8 in., find the rate at which the water level is dropping when it is 2in, from the top.
-1/8π in/s
-17/6π in/s
-1/7π in/s
-1/9π in/s
Find the value of C for which the area bounded by the curves y = x^2-C^2 and y = C^2-x^2 is 576. (pag may 6 sa choices, 6 sagot)
7
9
8
10
A ladder 10ft long is resting against the side of a building. If the foot of the ladder slips away from the wall at the rate of 2 ft/min, how fast is the angle between the ladder and the ground when the foot of the ladder is 6ft away from the building
1/2 rad/min
1/4 rad/min
1/3 rad/min
1 rad/min
Solve the differential equation y” – 4y’ + 3y = sin x
Y(x) = C1 e^3x C2 + e^x + 5sin x - 10 cos x
y(x) = C1 sin 3x + C2 x + 5sin x + 10 cos x
Y(x) = C1 e^3x + C2 e^x + 1/5 cos x + 1/10 sin x
Y(x) = C1 sin x + C2 x + 11/5 cos x - 1/10 sin x
If angle EDF and angle HIJ are supplementary angles, and angle SUV and angle EDF are also supplementary angles, then angle HIJ and angle SUV are:
Congruent angles
Obtuse angles
Right angles
Acute angles
Find the centroid of a semi-circular region of radius a.
A/2π
A/π
4a/3π
3a/4π
A line segment is a side of a square and also the hypotenuse of an isosceles right triangle. What is the ratio of the area of the square to the area of the triangle?
3 : 2
2 : 1
1 : 1
4 : 1
Two towns are located near the straight shore of a lake. Their nearest distance to point in the shore are 1 km and 2 km, respectively, and these points on the shore are 6 km apart. Where should the fishing port be located to minimize the total amount of pavement necessary to build a straight road from each town to the pier?
12 km from the point on the shore nearest the second town
2 km from the point on the shore nearest the second town
12 km from the point on the shore nearest the first town
2 km from the point on the shore nearest the first town
Sin θ/2 + sin 2θ/2² + sin 3θ/2³ + … =
2 cos θ / (5 + 4 sin θ)
2 sin θ / (5 – 4 cos θ)
2 sin θ / (5 + 4 cos θ)
2 cos θ / (5 – 4 sin θ)
Angles that share a common vertex point cannot:
Share interior points
Share a common angle side
Be right angle
Use the vertex letter name as an angle name
Which of the following equations is an exact differential equation?
Xdx + (3x – 2y)dy = 0
(x² + 1)dx – xydy = 0
Y²dx + (2x – 3y)dy = 0
(2xy + x)dx + (x² + y)dy = 0
The graph of r = a + bcos θ is a
Lemniscate
Lituus
Limacon
Cardioid
From a sample size of 100, the following description measures were calculated: median = 23; mean = 20; standard deviation = 5; range = 35. Seventy five sample values are between 5 and 35. If you know the sample mean, median, standard deviation were correct, which of the following conclusions might you draw?
The number of sample values between 10 and 30 were miscounted.
The range must have been calculated incorrectly because it should not be seven times the standard deviation`s value.
The distribution is skewed to the right because the median exceeds the mean.
The number of sample values between 5 and 35 have been miscounted because all 100 values must be in this interval.
Solve [y – square root of (x² + y²)]dx - xdy = 0.
Square root of (x + y) + y = C
Square root of (x² - y²) + y = C
Square root of (x² + y² + y) = C
Square root of (x² + y²) + y = C
What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis?
2ydx – xdy = 0
2xdx – ydy = 0
2xdy – ydx = 0
Dy/dx – x = 0
When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of water inside the cylinder increases by 0.6 cm. What is the radius of the ball bearing?
2.2 cm
0.6 cm
1.8 cm
1.2 cm
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