MATH FLASHING 1.2

premopremo remo · 75問 · 2年前

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At the maximum point, the slope of the tangent line is

zero

Obtain the differential equation of the family of circles with center on the y-axis

xy" - (y')^3 - y' = 0

A movie is scheduled for two hours. The theatre advertisements are 3.8 minutes long. There are two previews; one is 4.6 minutes long, and the other is.2.9 minutes long. The rest of time is devoted to the feature film. How long is the feature film?

108.7 minutes

Find the equation of the line passing through the intersection of x - y = 0 and 3x - 2y = 2 cutting from the first quadrant a triangle whose area is 9.

x + 2y - 6 = 0

Parcel charges of a courier company are follows P40 for the first 2 kilograms P15 for each of the succeeding kilogram weight of parcels. With these rates, what amount would be charged on a parcel weighing 30kg?

P460

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 all 25 children recognize their mother's voice.

7.10%

The time x a student spends leaming a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A sample of 4 students are selected at random. What is the probability that the average time students spend is less than 6 hours learning the software package?

0.383%

At exactly what time after 5 o'lock will the hour hand and the minute hand be perpendicular for the first time?

5:10 and 54 seconds

The time x a student spends computer learning a software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. What is the probability that the average learning time for 5 students exceeds 8.5 hours?

22.803%

Two posts, one 8 ft. high and the other 12 ft. high, stand 15 ft. apart. They are to be stayed by wires attached to a single stake at ground level, the wires running to the tops of the posts. How far from the shorter post should the stake be placed to use the least amount of wire?

6ft

Find the area of the region enclosed by the triangle with vertices (1. 1), (3, 2) and (2,-4)

5/2

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

2ydx ==x dy=0

Find the volume generated by revolving the area bounded by y = 12x and x = 3 about the line x = 3

181

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 rectangle?

1250

Evaluate the integral of sin^5 x + cos^3 x from 0 to pi/2,

1/60

A circle with center at the origin has a radius of 5. Find the equation of a parabola opening to the right that has its vertex on the circle and crossing the points of intersection of the circle and y-axis

5x + 25 = y^2

Whic of the following equations is an exact differential equation?

(2xy + x)dx + (x + y) dy = 0

Find the moment of inertia with respect to the x-axis of the area bounded by the parabola y ^ 2 = 4x and the line x = 1

2.13

Patrick has a rectangular patio whose length is 5m less than the diagonal and a width that is 7m less than the diagonal. If the area of his patio is 195m ^ 2 what is the length of the diagonal

20 m

What is the centroid of a semi-circular area of radius R?

4R/3π

Evaluate integrate (sin^5 x + cos^3 x) dx from 0 to pi / 2

1.2

A boat travelling Westward N45°E after travelling 5kms its angle is N67°W. Find Uthe distance of the lighthouse from both points?

3.81 km

What conic section, B ^ 2 - 4AC > 0'

Hyperbola

Carbon extracted from the ancient skull contained only 1/6 as much radioactive 14C as carbon extracted from present day bone. How old is the skull?

14,735 years

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

Cx = y^2

Integral of tan^2 θ d*θ from 0 to pi/2 is

inifinity

Re (1 - i) ^ (1+i)

2.808

The Laplace transform 1/2b tsinbt

s/(s^2 + b^2)^2

Compute log(3 - 2i)

0.5570-0.2554 i

The value of a computer is depreciated over 5 years for tax purposes. That is, at end of 5 years, the computer is worth 0. If a business paid P21,000 for a computer, how much will it have depreciated after 2 years?

P8,400

Find the equation of the line passing through the intersection of x - y = 0 and 3x - 2y = 2 cutting from the first quadrant a triangle whose area is 9.

x + 2y - 6 = 0

Determine the correct equation for the line with a slope of 7 and y-intercept of -4.

y = 7x - 4

If the side square can be expressed as a^2bcube, what is the area of the square in simplified form?

a^4b to the 6th power

A chord of a circle of a diameter 10 ft is decreasing in length 1 It/min. Find the rate of change of the smaller arc subtended by the chord when the chord is 8 ft. long.

5/3 ft/min

The temperature at 6 PM was 31%F. By midnight it had dropped 400F. What was the temperature at midnight?

-9 1/2F

The dimensions of a rectangular prism can be expressed as x + 1 , x - 2 and x + 4. In terms of x, what is the volume of the prism?

x^3 + 3x" - 6x - 8

if y = 2x + sin 2x find x when y' = 0

D/2

Evaluate f (- 3)' if f(x) = x ^ 2 - 2x + 1

When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of the water inside the container increases by 0.6 cm. What is the radius of the ball bearing?

1.2 cm

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