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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

One leg of a right triangle is 2√7 and the hypotenuse is 6. What is the area of the triangle?
Rationalize the denominator ofby using the equation a3 − b3 = (a − b)(a2 + ab + b2). 1 √x + √√x+1 薪+1
If f(x) = 2(9x), find f(2 − a).
The withdrawal resistance R of a nail of diameter d indicates its holding power. One formula for R is R = ks5/2dh, where k is a constant, s is the specific gravity of the wood, and h is the depth of
Evaluate r2 − s2 if and r = b + √√√b² - 4ac
Perform the required operation.Change to radicals of the same order: 3x2/3 ; 2y1/2 ; (5z)1/4.
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.(6√x − 4√y)2
If f(x) = 4x , find f(a + 2).
A plastic cup is in the shape of a right circular cone for which the base radius equals the height. (a) Express the base radius r as a function of the volume V using fractional
Perform the required operation.Change to radicals of the same order: √a; 3√b; 6√c.
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.(3√2 − √13)(5√2 + 3√13)
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. + 2r + 2r²
Is it true that, if x ≠0, [(− x− 2)− 2]− 2 = 1/x2?
(a) Express the radius of a sphere as a function of its volume v using fractional exponents. (b) If the volume of the moon is 2.19 × 1019m3, find its radius.
The period T of a satellite circling Earth is given bywhere R is the radius of Earth, d is the distance of the satellite above Earth, and k is a constant. Solve for R, using fractional exponents in
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √9x² - 6x +1
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.(2√7 − 3√a)(3√7 + √a)
Determine the relationship between a and c in ax2 + bx + c = 0 if the roots of the equation are reciprocals.
Is it true that [−20 − (−1)0]0 = 1?
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.(5√6 − 4)(3√6 + 5)
For the quadratic equation ax2 + bx + c = 0, if a, b, and c are integers, the product of the roots is a rational number. Explain.
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √4x² - 1 2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √a² + b² 2 va
A factor used in measuring the loudness sensed by the human ear is (I/I0),0.3 where I is the intensity of the sound and I 0 is a reference intensity. Evaluate this factor for I = 3.2 × 10−6
For what real values of x and y is √x + √y = √x + y?
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.(2 − 3√17B)(3 + √17B)
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √a² + 2ab + b²
By substitution, show that x = 1 − √2 is a solution of the equation x2 − 2x − 1 = 0.
For what integer value(s) of n is nπ > πn?
Are there any values of x or y such that √√x + √√√y = √x + y?
A factor used in determining the performance of a solar-energy storage system is (A/S)−1/4 , where A is the actual storage capacity and S is a standard storage capacity. If this factor is 0.5,
(a) By use of Eqs. (11.4) and (11.6), show that(b) Verify the equation in part (a) by evaluating each side with a = 3.576, b = 8.091, and n = 7. b. -n -11 = (2)"
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.3√5(√15m2 + 2√35m2)
Rationalize the numerator of each fraction. √3x + 4 + √√√3x 8
For what integer values of n is (−3)−n = −3−n? Explain.
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. C-2 VC + 2
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.
Perform the indicated operations.Is [(1) -1/3 + 118 of 5/6 (² 1/1-4/5 SH 8 32. 1?
Simplify (xn−1 ÷ xn−3)1/3 and express the result as a radical.
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √x² + 8-1
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √xy-¹ + x-¹y
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.7√8(5√2 − √6)
Rationalize the numerator of each fraction. √x + h = √x h
Rationalize the numerator of each fraction. √19 - 3 5
Express 1/81 (a) As a power of 9 (b) As a power of 3.
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.5√5(6√5 − √35)
Perform the indicated operations and express the result in simplest radical form with rationalized denominators. √√8a+ + ba
Express 42 × 64 (a) As a power of 4 (b) As a power of 2.
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 2 a b
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.4√2xy5 − 4√32xy
Rationalize the numerator of each fraction. √5 + 2√2 3√10
Is it true that (a + b)0 = 1 for all values of a and b?
Combine the terms into a single fraction, but do not rationalize the denominators. 4√√x² + 1 4x √x² + 1
Graph the given functions.f(V) = 4V3/2
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 5 4 8
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. n m 3
If x < 0, is it ever true that x−2 < x−1?
Graph the given functions.f(t) = t−4/5
Combine the terms into a single fraction, but do not rationalize the denominators. x ² √2x + 1 + 2x√2x + 1
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.2√m2n3 − n5
Perform the indicated operations and express the result in simplest radical form with rationalized denominators. a√√2x3+√√8a²x³
Express each of the given expressions in simplest form with only positive exponents.4(2x − 1)(x + 2)−1 − (2x − 1)2 (x + 2)−2
Graph the given functions.f(x) = 2x2/3
Three squares with areas of 150 cm2, 54cm2, and 24 cm2 are displayed on a computer monitor. What is the sum (in radical form) of the perimeters of these squares?
A rectangular piece of plywood 4 ft by 8 ft has corners cut from it, as shown in Fig. 11.8. Find the perimeter of the remaining piece in exact form and in decimal form.Fig. 11.8. 2 ft- 8 ft - 1 ft 4
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 2x V3c4
The current I (in A) passing through a resistor R (in Ω) in which P watts of power are dissipated is I = √P/R. If the power dissipated in the resistors shown in Fig. 11.7 is W watts, what is the
Combine the terms into a single fraction, but do not rationalize the denominators. 3 2√3x - 4 √3x - 4
Express each of the given expressions in simplest form with only positive exponents.(D − 1)−1 + (D + 1)−1
Graph the given functions.f(x) = 3x1/2
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.7√20 − √80 − 2√125
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √9+81
Express each of the given expressions in simplest form with only positive exponents.3x−1 − x−3 (y + 2)
Combine the terms into a single fraction, but do not rationalize the denominators. 2x + 혀
Simplify the given expressions. Express all answers with positive exponents.(3n − 1)−2/3 (1 − n) − (3n − 1)1/3
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √64 + 144
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. Then verify the result with a calculator. 3-7 – 12-2 15√7 - 12√2
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.√63 − 2√112 − √28
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √98x6y-7
Express each of the given expressions in simplest form with only positive exponents.2t−2 + t−1(t + 1)
The two legs of a right triangle are 2√2 and 2√6 units long. What is the perimeter of the triangle
Simplify the given expressions. Express all answers with positive exponents. 4x1/2 + 1/2x-1/² (4x + 1)
Simplify the given expressions. Express all answers with positive exponents.x2(2x − 1)−1/2 + 2x(2x − 1)1/2
Express each of the given expressions in simplest form with only positive exponents. x-²-y-² x-¹-y-¹ -1
Perform the indicated operations and express the result in simplest radical form with rationalized denominators. √36 + 4 - 2√10
Perform the indicated operations and express the result in simplest radical form with rationalized denominators.2√68x − √153x
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. Then verify the result with a calculator. 2√6 - √5 3/6-4/5
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. 28u3v-5
The adjacent sides of a parallelogram are √12 and √27 units long. What is the perimeter of the parallelogram?
Perform the indicated operations and express the result in simplest radical form with rationalized denominators. √a-3√√/b12
Express each of the given expressions in simplest form with only positive exponents. x - y-¹ x-¹-y
Without calculating the actual value, determine whether 10√11 − √1000 is positive or negative. Explain.
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √b² √a
Simplify the given expressions. Express all answers with positive exponents.[(a1/2 − a−1/2)2 + 4]1/2
Perform the indicated operations, expressing answers in simplest form with rationalized denominators. Then verify the result with a calculator.(2√5 − √7)(3√5 + √7)
Perform the indicated operations and express the result in simplest radical form with rationalized denominators. 164
For the quadratic equation ax2 + bx + c = 0, if a, b, and c are integers, the sum of the roots is a rational number. Explain.
Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. √n
Simplify the given expressions. Express all answers with positive exponents.(4N6)−1/2 − 2N−1
Express each of the given expressions in simplest form with only positive exponents. 6-1 4-2 +2

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