Algebra for College Students
10th Edition
ISBN: 9781285195780
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
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Chapter 6.3, Problem 66PS
To determine
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Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear.
Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar.
Find the value of r if the area of the triangle is formed by the points (-3,6),(4,4) and (r,-2) is
12 sq units.
Find the volume of tetrahedron whose vertices are A(1,1,0), B(-4,3,6), C(-1,0,3) and
D(2,4,-5).
- Consider the following system of linear equations in the variables a,b,c,d:
5a-3b 7c - 2d = 2
2ab
2c+ 5d = -3
→ (*)
4a 3b 5d = 3
6a b+2c+ 7d = −7
(a) Solve the system (*) by using Gauss elimination method.
(b) Solve the system (*) by using Cramer's rule method.
Solve for a 25 55 30 a=?
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- 9:41 … 93 Applying an Exponential Function to Newton's Law of Cooling 60. Water in a water heater is originally Aa ← 122°F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 60°F. The water cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00351. a. Write a function that models the temperature T (t) (in °F) of the water t hours after the water heater is shut off. b. What is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree. c. Dominic does not like to shower with water less than 115°F. If Dominic waits 24 hr. will the water still be warm enough for a shower? Mixed Exercises ger-ui.prod.mheducation.comarrow_forwardPlease use the infinite series formula and specify how you did each step. Thank you.arrow_forward8) Solve the given system using the Gaussian Elimination process. 2x8y = 3 (-6x+24y = −6arrow_forward
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- [25 points] Given the vector let v = ER² and the collection of vectors ε = E-{)·()}-{☹) (9)} = {(A)·(9)}· B: = and C = · {(6)·(})}· answer the following question. (a) (b) (c) (d) (e) verify Verify is a basis for R² and find the coordinate [] of under ε. Verify B is a basis for R2 and find the coordinate []B of ʊ Verify C is a basis for R2 and find the coordinate []c of under ε. under ε. Find the change-of-basis matrix [I]+B from basis B to basis ε, and EE+BUB Find the change-of-basis matrix [I]B+ε from basis Ɛ to basis B, and verify [U]B= [] B+EVEarrow_forwardExplain the following terms | (a) linear span (b) dimension of vector space (c) linearly independent (d) linearly dependent (e) rank of matrix Aarrow_forward3. Let u = 3/5 √ = and = -4/5 -() Define V span{ū, }. (a) (b) (c) Show that {u, } is orthonormal and forms a basis for V. Explicitly compute Projy w. Explicitly give a non-zero vector in V+.arrow_forward
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