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Algebra
Find the value of a for which the polynomial x^5-ax²-ax+1has −1 as a root with multiplicity at least 2.
Algebra
A cable stretches by an amount d when it supports a crate of mass M. The cable is replaced by another cable of the same material having the same length and twice the diameter. If the same crate is supported by the thicker cable, by how much will the cable stretch?
Algebra
A tree is losing its leaves. 2/3 fall off in the first week, 2/3 of those remaining fall off in the second week, and 2/3 of those remaining fall off in the third week. Now there are 37 leaves. How many leaves did the tree start with?
Algebra
Ali has 18new magazines to read.
Let M be the number of magazines he would have left to read after reading R of them.
Write an equation relating M to R. Then use this equation to find the number of magazines he would have left to read after reading 7 of them.
Let M be the number of magazines he would have left to read after reading R of them.
Write an equation relating M to R. Then use this equation to find the number of magazines he would have left to read after reading 7 of them.
Algebra
Which of the following statements are true? Justify your answers.
i) The collection of all Class 5 students is a set.
ii) {«} is the empty set.
iii) No purely imaginary number is a real number.
iv) For any z∈C, if |z| , then ∈R z∈ R .
v) A biquadratic equation must have at least one real root.
vi) The system of equations 2x + 3y + z5 = 1and 5 3x + 2y + z = 5has a unique solution.
vii) The AM of 1,0 − ,1 is greater than or equal to their GM.
viii) ‘A is sufficient for B’ is equivalent to ‘the negative of A is necessary for the
negative of B’.
ix) The Gaussian elimination method can only be applied for solving a system of 4
linear equations if the number of variables is 4.
i) The collection of all Class 5 students is a set.
ii) {«} is the empty set.
iii) No purely imaginary number is a real number.
iv) For any z∈C, if |z| , then ∈R z∈ R .
v) A biquadratic equation must have at least one real root.
vi) The system of equations 2x + 3y + z5 = 1and 5 3x + 2y + z = 5has a unique solution.
vii) The AM of 1,0 − ,1 is greater than or equal to their GM.
viii) ‘A is sufficient for B’ is equivalent to ‘the negative of A is necessary for the
negative of B’.
ix) The Gaussian elimination method can only be applied for solving a system of 4
linear equations if the number of variables is 4.
Algebra
The total monthly costs, including an installation fee, charged by two cable television companies are shown on the graph below.
What are the coordinates of the point where the total costs for both companies are the same?
What are the coordinates of the point where the total costs for both companies are the same?
Algebra
Let A,B,C be subsets of a set. Prove that A ∩ B ⊆ C iff A ⊆ Bc ∪ C
Algebra
Let A,B,C be subsets of a set. Prove that A ∩ B ⊆ C iff A ⊆ Bc ∪ C
Algebra
The system of equations 2x + 3y + 5z = 1 and 3x + 2y + z = 5 has a unique solution.
Algebra
A biquadratic equation must have at least one real root. Is it true or false? give reasons.
