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3 years ago

The table below shows the cube roots of different numbers

1 answer:

8 0

Part A : Yes, it represents y as a function of x. There are not 2 different y values for the same x value.
f ( x ) = ∛ x ( or : y = ∛x )
Part B : f ( x ) = 10 + 20 x
f ( 100 ) = 10 + 20 · 100 = 10 + 2,000 = 2,010
f ( 100 ) represents the total cost for renting a bike for 100 hours.

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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.

8 0

3 years ago

What is the answer to the top question

Dimas [21]

3.2w/8 l=x w/5 l
X= 5• 3.2/8= 16/8=2 centimeters

7 0

3 years ago

Chips numbered 1 through 80 are shuffled in a basket. One chip is randomly selected.

meriva

1/16

multiples 15,30,45,60, and 75 making 5/80 then you simplify to 1/16

8 0

3 years ago

Read 2 more answers

In 2006, the population of the country was 30.4 million. This represented an increase in population of 7.6 % since 2001. What w

Molodets [167]

Answer:

28.25 million

Step-by-step explanation:

Population of the country:

in 2001 - x million
in 2006 - 30.4 million

Population of the country as percent:

in 2001 - 100%
in 2006 - 100% + 7.6% = 107.6%

Write a proportion:

$\dfrac{x}{30.4}=\dfrac{100}{107.6}$

Cross multiply:

$107.6\cdot x=30.4\cdot 100$

Divide by 107.6:

$x=\dfrac{30.4\cdot 100}{107.6}=\dfrac{3,040}{107.6}\approx 28.25$

6 0

3 years ago

A chemical factory has 2 cylindrical chemical tanks, one containing Chemical X and the other containing Chemical Y. The tank con

Mashutka [201]

The tank with Chemical X "takes up" a space of 25ft³. Ordinarily we think of something "taking up" space as being area or surface area; however, area is a square measurement, and this is cubic; this must be volume. The volume of the tank with Chemical X is 1.5 times the volume of the tank containing Chemical Y; setting this up in an equation we would have
25 = 1.5<em>V</em>
We would divide both sides by 1.5 to get the volume of the tank containing Chemical Y:
$\frac{25}{1.5}=\frac{1.5V}{1.5} \\16 \frac{2}{3}=V$
To find the volume of a cylinder, we find the base area and multiply by the height. We know the volume and we know the base area, so our equation to find the height of the tank containing Chemical Y would look like:
$16 \frac{2}{3}=3.2h \\ 16 \frac{2}{3}=3 \frac {2}{10}h$
We would now divide both sides by 3 2/10:
$\frac{16 \frac{2}{3}}{3 \frac{2}{10}}= \frac{3 \frac{2}{10}h}{3 \frac{2}{10}}$
This is the same as:
$\frac{\frac{50}{3}}{\frac{32}{10}}=h \\ \\ \frac{50}{3}* \frac{10}{32}=h \\ \\ \frac{500}{96}$
So the height of the tank containing Chemical Y is 500/96 = 5 5/24 feet.

8 0

3 years ago