The approximate value of 5,700,000 x 200 is

A salesperson earns a base salary of $4000 per month plus 15% commission on sales. her monthly income f(s) is given by the funct

artcher [175]

9.) Given that the salesperson earns a base salary of $4000 per month plus 15% commission on sales if the salesperson's commission is lowered to 5%, then <span>her monthly income g(s) is given by the function g(s)=4000 +0.05s where s is monthly sales in dollars

10) </span>Given that the salesperson earns a base salary of $4000 per month plus 15% commission on sales if the salesperson's base salary is doubled, then her monthly income h(s) is given by the function g(s)=8000 +0.15s where s is monthly sales in dollars

11) Given that the salesperson earns a base salary of $4000 per month plus 15% commission on sales <span>if the salesperson's base salary is cut in half and her commission is doubled</span>, then her monthly income k(s) is given by the function k(s)=2000 +0.3s where s is monthly sales in dollars.

8 0

3 years ago

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This is due today pls help! :)

STALIN [3.7K]

Answer:

D

Step-by-step explanation:

8.4 minus 3 equals 5.4

10¹⁰ minus 10⁷ is 10³

7 0

3 years ago

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Work our the surface area of this cylinder?

tankabanditka [31]

Answer:

$A=522.97\ \text{cm}^2$

Step-by-step explanation:

Given that,

The diameter of the cylinder, d = 8 cm

Radius, r = 4 cm

Height of the cylinder, h = 16.8 cm

We need to find the surface area of this cylinder. The formula for the surface area of the cylinder is given by :

$A=2\pi r^2+2\pi rh\\\\=2\pi r(r+h)\\\\=2\times \dfrac{22}{7}\times 4\times (4+16.8)\\\\=522.97\ \text{cm}^2$

So, the surface area of the cylinder is $522.97\ \text{cm}^2$

6 0

3 years ago

Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (

galben [10]

Answer:

(a) Yes, $λ_{A}+λ_{B}$

(b) Yes, $λ_{A}λ_{B}$

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation $λ_{A}$ to denote Lambda(A) sign.

$v$ is an eigenvector of matrix A with eigenvalue $λ_{A}$

$v$ is also eigenvector of matrix B with eigenvalue $λ_{B}$

So we can write this in equation form as

$Av=λ_{A}v$

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector that is in the same direction as of $Av$ , then this $v$ is called the eigenvector of $A$ . $Av$ is $λ_{A}$ times the original $v$ . The number $λ_{A}$ is the eigenvalue of A.

$λ_{A}$ this number is very important and tells us what is happening when we multiply $Av$ . Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of $Av$ by using the following equation:

$det(A-λI)=0$

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that $v$ is an eigenvector of $A + B$ and find its associated eigenvalue.

The eigenvalues of $A$ and $B$ are $λ_{A}$ and $λ_{B}$ , then

$(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)$

so, $(A+B)(v)=(λ_{A}+λ_{B})(v)$

which means that $v$ is also an eigenvector of $A+B$ and the associated eigenvalues are $λ_{A}+λ_{B}$

(b) Show that $v$ is an eigenvector of $AB$ and find its associated eigenvalue.

The eigenvalues of $A$ and $B$ are $λ_{A}$ and $λ_{B}$ , then

$(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)$

so,

$(AB)(v)=λ_{A}λ_{B}(v)$

which means that $v$ is also an eigenvector of $AB$ and the associated eigenvalues are $λ_{A}λ_{B}$

5 0

3 years ago

How to solve 1/2(1/3w+4)+6=10 and -5(h+4)=12

olga nikolaevna [1]

$\frac{1}{2}(\frac{1}{3}w+4)+6=10\\\\
\frac{1}{6}w+\frac{4}{2}+6=10\\\\
\frac{1}{6}w+2+6=10\\\\
\frac{1}{6}w+8=10\ \ \ |Subtract\ 8\\\\
\frac{1}{6}w=2\ \ \ |Multiply\ by\ 6\\\\
\boxed{w=12}\\\\\\
-5(h+4)=12\\\\
-5h-20=12\ \ \ |Add\ 20\\\\
-5h=32\ \ |Divide\ by\ -5\\\\
h=-\frac{32}{5}=-6\frac{2}{5}\\\\
\boxed{h=-6\frac{2}{5}}$

6 0

4 years ago

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