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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

A person 1.8 m tall is photographed, and the film image is 20.0 mm high. Under the same conditions, how tall is a person whose film image is 14.5 mm high?
Determine each of the following as being either true or false. If it is false, explain why.If 20 m is divided into two parts in the ratio of 3/2, the parts are 14 m and 6 m.
Determine each of the following as being either true or false. If it is false, explain why.If R varies jointly with s and the square of t, and inversely as the square of r, then k = ( ³³) (²) ² S
In Example 8, change “weight and height both increase by 5%” to “weight increases by 10% and height increases by 5%” and then solve the resulting problem.Data from Example 8A person’s body
The change L in length of a copper rod varies directly as the change T in temperature of the rod. Set up an equation for this relationship if L = 2.7 cm for T = 150°C.
Express the ratios in the simplest form.12V to 3V
Given that 1.00 in. = 2.54 cm, what is the length (in in.) of a computer screen image that is 7.24 cm long?
Express the ratios in the simplest form.63 ft2 to 18 ft2
Set up the general equations from the given statements. The speed v at which a galaxy is moving away from Earth varies directly as its distance r from Earth.
The perimeter of a rectangular solar panel is 210.0 in. The ratio of the length to the width is 7 to 3. What are the dimensions of the panel?
Express the ratios in the simplest form.96 h to 3 days
Find the indicated ratios.840 mg to 3 g
Set up the general equations from the given statements. The demand D for a product varies inversely as its price P.
The difference p in pressure in a fluid between that at the surface and that at a point below varies jointly as the density d of the fluid and the depth h of the point. The density of water is 1000
Express the ratios in the simplest form.120 s to 4 min
Find the indicated ratios.300 nm to 6 μm
Set up the general equations from the given statements. The electric resistance R of a wire varies inversely as the square of its diameter d.
The crushing load L of a pillar varies directly as the fourth power of its radius r and inversely as the square of its length l. If one pillar has twice the radius and three times the length of a
Express the ratios in the simplest form.20 qt to 2.5 gal
Find the indicated ratios.375 mL to 25 cL
Set up the general equations from the given statements. The volume V of silt carried by a river is proportional to the sixth power of the velocity v of the river.
Express the ratios in the simplest form.25 cm2 to 75mm2
Find the indicated ratios.12 ks to 2 h
Set up the general equations from the given statements. In a tornado, the pressure P that a roof will withstand is inversely proportional to the square root of the area A of the roof.
Express the ratios in the simplest form.0.175 kg to 3500 mg
Find the indicated ratios. The number π equals the ratio of the circumference c of a circle to its diameter d. To check the value of π, a technician used computer simulation to measure the
Set up the general equations from the given statements. During an adiabatic (no heat loss or gain) expansion of a gas, the pressure p is inversely proportional to the 3/2 power of the volume V.
Express the ratios in the simplest form.2000 μm to 6 mm
Find the indicated ratios. The mechanical advantage of a lever is the ratio of the output force F0 to the input force Fi. Find the mechanical advantage if F0 = 24 kN and Fi = 5000 N.
Find the indicated ratios. The ratio of the diagonal d of a square to the side s of the square is √2. The diagonal and side of the face of a glass cube are found to be d = 35.375 mm and s = 25.014
Set up the general equations from the given statements. The stiffness S of a beam varies jointly as its width w and the cube of its depth d.
Find the required ratios. The P/E ratio (price-to-earnings ratio) of a company’s stock is the ratio of the price of the stock to the company’s earnings (or profits) per share of stock, both
Find the indicated ratios. For an automobile, the ratio of the number n1 of teeth on the ring gear to the number n2 of teeth on the pinion gear is the rear axle ratio of the car. Find this ratio if
The average electric power P entering a load varies jointly as the resistance R of the load and the square of the effective voltage V, and inversely as the square of the impedance Z.
Express the meaning of the given equation in a verbal statement, using the language of variation. (k and π are constants.) S= k 开
Find the required ratios. For a particular acute angle in a right triangle, the ratio of the opposite side to the hypotenuse is 12/13. Find the ratio of the adjacent side to the hypotenuse.
Find the required ratios. The coefficient of friction for two contacting surfaces is the ratio of the frictional force between them to the perpendicular force that presses them together. If it takes
Find the indicated ratios. The pressure p exerted on a surface is the ratio of the force F on the surface to its area A. Find the pressure on a square patch, 2.25 in. on a side, on a tank if the
Express the meaning of the given equation in a verbal statement, using the language of variation. (k and π are constants.)A = πr2
Find the required ratios. The efficiency of a power amplifier is defined as the ratio of the power output to the power input. Find the efficiency of an amplifier for which the power output is 2.6 W
Find the required ratios. A virus 3.0 × 10−5 cm long appears to be 1.2 cm long through a microscope. What is the magnification (ratio of image length to object length) of the microscope?
Find the indicated ratios. The heat of vaporization of a substance is the amount of heat needed to change a unit amount from liquid to vapor. Experimentation shows 7910 J are needed to change 3.50 g
Find the indicated ratios. What is the ratio of the volume of Earth (R = 6380 km) to the volume of a bacterium (r = 0.0040 mm)?
Given that a/b = c/d (b and d not zero), show that indicated proportions are correct. a+b b c+d d
Express the meaning of the given equation in a verbal statement, using the language of variation. (k and π are constants.)V = πr2h
Find the required ratios. The Mach number of a moving object is the ratio of its speed to the speed of sound (1200 km/h). Find the Mach number of a military jet that flew at 7200 km/h.
Find the indicated ratios. The ratio of the commission for selling a home to the selling price of the home is the commission rate. What is this rate if the commission of $17,100 is charged for
Given that a/b = c/d (b and d not zero), show that indicated proportions are correct. a-b b c-d d
Give the specific equation relating the variables after evaluating the constant of proportionality for the given set of values.V varies directly as the square of H, and V = 48 when H = 4.
Find the required ratios. The capacitance C of a capacitor is defined as the ratio of its charge q (in C) to the voltage V. Find C (in F) for which q = 5.00 μC and V = 200 V. (1 F = 1 C/1 V.)
Find the indicated ratios. A total cholesterol level of 200 mg/dL is considered too high, but many doctors consider the ratio of the total cholesterol to HDL (high density lipids—the “good”
Give the specific equation relating the variables after evaluating the constant of proportionality for the given set of values.n is inversely proportional to the cube root of p, and n = 4 when p = 27.
Find the required ratios. The atomic mass of an atom of carbon is defined to be 12 u. The ratio of the atomic mass of an atom of oxygen to that of an atom of carbon is 4/3. What is the atomic mass of
Find the required ratios. An important design feature of an aircraft wing is its aspect ratio. It is defined as the ratio of the square of the span of the wing (wingtip to wingtip) to the total area
Give the specific equation relating the variables after evaluating the constant of proportionality for the given set of values.p is proportional to q and inversely proportional to the cube of r, and
Find the required ratios. For an automobile engine, the ratio of the cylinder volume to compressed volume is the compression ratio. If the cylinder volume of 820 cm3 is compressed to 110 cm3 , find
Give the specific equation relating the variables after evaluating the constant of proportionality for the given set of values.v is proportional to t and the square root of s, and v = 80 when s = 4
The specific gravity of a substance is the ratio of its density to the density of water. If the density of steel is 487 lb/ft3 and that of water is 62.4 lb/ft3 , what is the specific gravity of steel?
On a map of Hawaii, 1.3 in. represents 20.0 mi. If the distance on the map between Honolulu and Kaanapali on Maui is 6.0 in., how far is Kaanapali from Honolulu?
Find y when x = 10 if y varies directly as x, and y = 200 when x = 16.
Find the required ratios. The percent grade of a road is the ratio of vertical rise to the horizontal change in distance (expressed in percent). If a highway rises 75 m for each 1.2 km along the
Given that 1.000 lb = 453.6 g, what is the weight in pounds of a 14.0-g computer disk?
Find y when x = 5 if y varies directly as the square of x, and y = 6 when x = 8.
Find the required ratios. The percent error in a measurement is the ratio of the error in the measurement to the actual correct value, expressed as a percent. When writing a computer program, the
Given that 1.00 Btu = 1060 J, how much heat in joules is produced by a heating element that produces 2660 Btu?
Find s when t = 8.50 if s is inversely proportional to t, and s = 820 when t = 0.200.
Find the required ratios. The electric current in a given circuit is the ratio of the voltage to the resistance. What is the current (1 V/1Ω = 1 A) for a circuit where the voltage is 24.0 mV and the
Given that 1.00 L = 61.0 in.3, what is the capacity in liters of a cubical box that is 3.23 in. along an edge?
Find p for q = 0.8 if p is inversely proportional to the square of q, and p = 18 when q = 0.2.
Find the required ratios. The mass of an object is the ratio of its weight to the acceleration g due to gravity. If a space probe weighs 8.46 kN on Earth, where g = 9.80 m/s2 , find its mass in kg.
A computer printer can print 60 pages in 45 s. How many pages can it print in 3 min?
Find the required quantities from the given proportions. For two connected gears, the relationholds, where d is the diameter of the gear and N is the number of teeth. Find N1 if d1 = 2.60 in., d2 =
Find y for x = 6 and z = 0.5 if y varies directly as x and inversely as z, and y = 60 when x = 4 and z = 10.
Find the required ratios. Power is defined as the ratio of work done to the time required to do the work. If an engine performs 3.65 kJ of work in 15.0 s, find the power (in W) developed by the
A solar heater with a collector area of 58.0 m2 is required to heat 2560 kg of water. Under the same conditions, how much water can be heated by a rectangular solar collector 9.50 m by 8.75 m?
Find the required quantities from the given proportions.In an electric instrument called a “Wheatstone bridge,” electric resistances are related byR1= 6.00 ΩR3 = 62.5 Ω, andR4
Find r when n = 160 if r varies directly as the square root of n and r = 4 when n = 250.
According to Boyle’s law, the relation p1/p2 = V1/V2 holds for pressures p1 and p2 and volumes V1 and V2 of a gas at constant temperature. Find V1 if p1 = 36.6 kPa, p2 = 84.4 kPa, and V2 =
Find f when p = 2 and c = 4 if f varies jointly as p and the cube of c, and f = 8 when p = 4 and c = 0.1.
In a transformer, an electric current in one coil of wire induces a current in a second coil. For a transformer,where i is the current and t is the number of windings in each coil. In a neon sign
A partner invests $50,000 in a business and the other partner invests $20,000. If profits are to be shared in the ratio that each invested in the partnership, how much does each receive from $10,500
Find v when r = 2, s = 3, and t = 4 if v varies jointly as r and s and inversely as the square of t, and v = 8 when r = 8, s = 6, and t = 2.
On a certain blueprint, a measurement of 25.0 ft is represented by 2.00 in. What is the actual distance between two points if they are 5.75 in. apart on the blueprint?
A varies directly as x, and B varies directly as x, although not in the same proportion as A. All numbers are positive.Show that A + B varies directly as x.
The chlorine concentration in a water supply is 0.12 part per million. How much chlorine is there in a cylindrical holding tank 4.22 m in radius and 5.82 m high filled from the water supply?
A varies directly as x, and B varies directly as x, although not in the same proportion as A. All numbers are positive.Show that √AB varies directly as x.
Given that 1.00 in.2 = 6.45 cm2, what area in square inches is 36.3 cm2?
One fiber-optic cable carries 60.0% as many messages as another fiber-optic cable. Together they carry 12,000 messages. How many does each carry?
The amount of hydroelectric power produced by a dam is proportional to the flow rate of the water. If a particular dam produces 35,800 kW of power when the flow rate is 2250 ft3 s, how much power
Given that 1.000 kg = 2.205 lb, what mass in kilograms is equivalent to 175.5 lb?
Two types of roadbed material, one 50% rock and the other 100% rock, are used in the ratio of 4 to 1 to form a roadbed. If a total of 150 tons are used, how much rock is in the roadbed?
The blade tip speed of a wind turbine is directly proportional to the rotation rate ω. For a certain wind turbine, the blade tip speed is 125 mi/h when ω = 12.0 r/min. Find the blade tip speed when
Given that 1.00 hp = 746 W, what power in horsepower is 250 W?
To neutralize 80.0 kg of sodium hydroxide, 98.0 kg of sulfuric acid are needed. How much sodium hydroxide can be neutralized with 37.0 kg of sulfuric acid?
The amount of heat H required to melt ice is proportional to the mass m of ice that is melted. If it takes 2.93 ×105 J to melt 875 g of ice, how much heat is required to melt 625 g?
Given that 1.50 L = 1.59 qt, what capacity in quarts is 2.75 L?
For analysis, 105 mg of DNA sample is divided into two vials in the ratio of 2 to 5. How many milligrams are in each vial?
In electroplating, the mass m of the material deposited varies directly as the time t during which the electric current is on. Set up the equation for this relationship if 2.50 g are deposited in
Given that 2.00 km = 1.24 mi, what distance in kilometers is 750 mi?
A total of 322 bolts are in two containers. The ratio of the number of bolts in the first container to the number in the second container is 5/9. How many are in each container?

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