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3 years ago

5

a deer tick measures 29 centimeters in length in a photograph. if the photo has been enlarged by a factor of 100, what is the ac

tual length of the deer tick?

1 answer:

N76 [4]3 years ago

3 0

.29 cm in length

29 ÷ 100 = .29

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Sin(x+22)°=cos(2x−7)°

Alekssandra [29.7K]

To answer this, it must be noted that the trigonometric functions sine and cosine will have the same values if the angles are complementary (meaning, their sum is 90°).
90 = (x + 22) + (2x - 7)
The value of x from the equation is 25.

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3 years ago

Read 2 more answers

Dawn has 5\6 yard of lace. She uses 4\5 of it on a dress and the rest on a jewel box. How much does she use on the jewel box

mr_godi [17]

Answer:

Jewelry box: 1/6 yard

Step-by-step explanation:

4/5 (not 4\5) of her 5/6 yard goes into a dress: (4/5)(5/6 yd) = 2/3 yard.

This is the same as 4/6 yard. The amount of lace remaining, to be used on a jewelry box, is 5/6 - 4/6, or 1/6 yard.

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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

2 years ago

Which of the quotients is equivalent to -5/8 select all that apply

Crank

Answer:

a b e

Step-by-step explanation:

not sure could be wrong

4 0

1 year ago

When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is f

valkas [14]

Answer:

The new pressure of the gas is 42 pounds per square inches.

Step-by-step explanation:

When the temperature remains constant, the volume of a gas is inversely proportional to the pressure of the gas.

$V\propto \frac{1}{P}$

We can rewrite the above equation is

$\frac{V_1}{V_2}=\frac{P_2}{P_1}$ [at constant temperature]

At a pressure of 14 pounds per square inches, a balloon is filled with 93 cubic inches of gas.

The volume of the gas is decreased to 31 cubic inches.

Here,

$V_1$ = 93 cubic inches, $P_1$ = 14 pounds per square inches,

$V_2$ =31 cubic inches, $P_2$ = ?

$\frac{V_1}{V_2}=\frac{P_2}{P_1}$

$\Rightarrow \frac{93}{31}=\frac{P_2}{14}$

$\Rightarrow \frac{P_2}{14}=\frac{93}{31}$

$\Rightarrow {P_2}=\frac{93}{31}\times 14$

$\Rightarrow {P_2}=42$ pounds per square inches

The new pressure of the gas is 42 pounds per square inches.

4 0

3 years ago