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2 years ago

What is 10984 rounded to the nearest 10 thousand?

Mathematics

1 answer:

Gelneren [198K]2 years ago

3 0

10984 rounded to the nearest thousand is 11,000

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CAN SOMEONE HELP PLEASE m4A=42°, b=10, c= 12. What is the length of a to the nearest tenth?

kipiarov [429]

Answer:

a = 8.1

Step-by-step explanation:

Use the cosine rule:

$a = \sqrt{b^2 + c^2 -2 bc \space\ cosA }$

Substituting the values:

$a = \sqrt{10^2 + 12^2 -2(10)(12) \space\ cos 42 \textdegree\ }$

⇒ $a = \sqrt{4 \space\ cos 42\textdegree\ }$

⇒ $a = 8.1$

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1 year ago

An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false

asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let $p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1)$ be the characteristic polynomial of B.

a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)

b) Remember that $p(\lambda)=\det(B-\lambda I)$ . 0 is a root of p, so we have that $p(0)=\det(B-0 I)=\det B=0$ .

c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.

d) det(B)=0 by part c) so B is not invertible.

e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.

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2 years ago

The product of two consecutive positive integers is 29 more than their sum. Find the integers

Rina8888 [55]

The consecutive positive integers would be: x and (x+1),
We would have to solve the following equation to find these numbers:
x(x+1)-[x+(x+1)]=29
x²+x-2x-1=29
x²-x-30=0
x=[1⁺₋√(1+120)]/2
x=(1⁺₋11)/2
We have two possible solutions:
x₁=(1-11)/2=-5 then: (x+1)=-5+1=-4 This is not the solution.
x₂=(1+11)/2=6 then: (x+1)=6+1=7 This solution is right.

Answer: the numbers would be 6 and 7.

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2 years ago

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Wewaii [24]

Answer:

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1 year ago

What is equivalent to 2/5 where the numerator is 18 less than the denominator/

zmey [24]

Answer:

12/30

Step-by-step explanation:

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2 years ago