MATHEMATICS COLLEGE

How are exponents related to taking the root of a number?

Answers

Answer 1

Answer:

Answer:

with exponents, you take a number and multiply it by itself.

Step-by-step explanation:

the root of a number is the number that can be multiplied a certain amount of times to get us that number.

therefore roots get you to the root of a number.

Hope it helps!

(even if its two weeks late.....)

Related Questions

A genetic test is used to determine if people have a predisposition for thrombosis, which is the formation of a blood clot inside a blood vessel that obstructs the flow of blood through the circulatory system. It is believed that 3% of people actually have this predisposition. The genetic test is 98% accurate if a person actually has the predisposition, meaning that the probability of a positive test result when a person actually has the predisposition is 0.98. The test is 97% accurate if a person does not have the predisposition. What is the probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition? (Round your answer to four decimal places.)
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shawn has a bag containing seven balls: one green, one orange, one blue, one yellow, one purple, one white, and one red. All balls are equally are equally likely to be chosen. Shawn will choose one ball without looking in the bag. What is the possibility that Shawn will choose the purple ball out of the bag?

Answers

Seven Balls , one of each color. Then 1/7 possibility to choose purple

Please help me. Full explanation. WIll mark brainliest.

Answers

Answer:

Step-by-step explanation:

Answer:

B) 50%

Step-by-step explanation:

There are two correct answers to the question :A and D. Therefore you have a 50% of getting the correct answer.

Hope the helps :)

Just as there are simultaneous algebraic equations (where a pair of numbers have to satisfy a pair of equations) there are systems of differential equations, (where a pair of functions have to satisfy a pair of differential equations).Indicate which pairs of functions satisfy this system. It will take some time to make all of the calculations.
y_1' = y_1 -2 y_2 \qquad y_2' = 3y_1 - 4 y_2

A. y_1 = \sin(x) +\cos(x) \qquad y_2 = \cos(x) - \sin(x)
B. y_1 = \sin(x) \qquad y_2 = \cos(x)
C. y_1 = \cos(x) \qquad y_2 = -\sin(x)
D. y_1 = e^{-x} \qquad y_2=e^{-x}
E. y_1 = e^x \qquad y_2=e^x
F. y_1 = e^{4x} \qquad y_2 = e^{4x}
G. y_1 = 2e^{-2x} \qquad y_2 = 3e^{-2x}

As you can see, finding all of the solutions, particularly of a system of equations, can be complicated and time consuming. It helps greatly if we study the structure of the family of solutions to the equations. Then if we find a few solutions we will be able to predict the rest of the solutions using the structure of the family of solutions.

Answers

Answer: D and G.

Step-by-step explanation:

For options D and G we will show that both differential equations are satisfied. For the other options we will show the pairs don't solve one of the equations.

A. $y_1 '= \cos(x)-\sin x$ and $y_1-2y_2= \sin x+\cos x -2(\cosx -\sin x )=3\sin x- \cos x \neq \cos x-\sin x$ (when x=0 the left side is -1 and the right side is 1) so the equation $y_1'=y_1 - 2y_2$ is not satisfied.

B. $y_2 '= -\sin x$ and $3y_1-4y_2= 3\sin x-4\cos x \neq -\sin x$ so the equation $y_2'=3y_1-4y_2$ is not satisfied.

C. $y_1 '= -\sin(x)$ and $y_1-2y_2= \cos x -2\sin x \neq -\sin x$ so these pairs don't solve the equation $y_1'=y_1-2y_2$ .

D. Since $y_1=y_2=e^(-x)$ then $y_1'=y_2'=-e^(-x)$ . The first equation is satisfied, because $y_1-2y_2=e^(-x)-2e^(-x)=-e^(-x)=y_1'$ . The second equation is also satisfied: $3y_1-4y_2=3e^(-x)-4e^(-x)=-e^(-x)=y_2'$ .

E. $y_2'=e^x$ and $3y_1-4y_2= 3e^x-4e^x=-e^x\neq -e^x$ so they don't satisfy the equation $y_2'=3y_1-4y_2$ .

F. $y_1 '= 4e^(4x)$ and $y_1-2y_2= e^(4x)-2e^(4x)=-e^(4x) \neq 4e^(4x)$ , then the equation $y_1'=y_1-2y_2$ is not satisfied.

G. In this case, $y_1=2e^(-2x)$ and $y_2=3e^(-2x)$ . Computing derivatives, $y_1'=-4e^(-2x)$ and $y_2'=-6e^(-2x)$ . The first equation is satisfied, because $y_1-2y_2=2e^(-2x)-6e^(-2x) =-4e^(-2x)=y_1'$ . The second equation is also satisfied: $3y_1-4y_2= 6e^(-2x)-12e^(-2x)=-6e^(-2x)=y_2'$ .

Final answer:

The pairs of functions that satisfy the given system of differential equations are Option D (y_1 = e^(-x), y_2 = e^(-x)) and Option E (y_1 = e^x, y_2 = e^x).

Explanation:

The given system of differential equations is:

y_1' = y_1 - 2y_2

y_2' = 3y_1 - 4y_2

To determine which pairs of functions satisfy this system, we can substitute each option into the system and check if they satisfy the equations.

Let's go through each option:

Option A: y_1 = sin(x) + cos(x), y_2 = cos(x) - sin(x)
By substituting these functions into the system, we get:
y_1' = cos(x) - sin(x) - 2(cos(x) - sin(x)) = -sin(x) - 4cos(x)
y_2' = sin(x) + cos(x) - 4(cos(x) - sin(x)) = 5sin(x) - 3cos(x)
These functions do not satisfy the system of differential equations.
Option B: y_1 = sin(x), y_2 = cos(x)
By substituting these functions into the system, we get:
y_1' = cos(x) - 2cos(x) = -cos(x)
y_2' = 3sin(x) - 4cos(x)
These functions do not satisfy the system of differential equations.
Option C: y_1 = cos(x), y_2 = -sin(x)
By substituting these functions into the system, we get:
y_1' = -sin(x) + 2sin(x) = sin(x)
y_2' = 3cos(x) - 4(-sin(x)) = 3cos(x) + 4sin(x)
These functions do not satisfy the system of differential equations.
Option D: y_1 = e^(-x), y_2 = e^(-x)
By substituting these functions into the system, we get:
y_1' = -e^(-x) - 2e^(-x) = -3e^(-x)
y_2' = 3e^(-x) - 4e^(-x) = -e^(-x)
These functions satisfy the system of differential equations.
Option E: y_1 = e^x, y_2 = e^x
By substituting these functions into the system, we get:
y_1' = e^x - 2e^x = -e^x
y_2' = 3e^x - 4e^x = -e^x
These functions satisfy the system of differential equations.
Option F: y_1 = e^(4x), y_2 = e^(4x)
By substituting these functions into the system, we get:
y_1' = 4e^(4x) - 2e^(4x) = 2e^(4x)
y_2' = 3e^(4x) - 4e^(4x) = -e^(4x)
These functions do not satisfy the system of differential equations.
Option G: y_1 = 2e^(-2x), y_2 = 3e^(-2x)
By substituting these functions into the system, we get:
y_1' = -2e^(-2x) - 2(3e^(-2x)) = -8e^(-2x)
y_2' = 3(2e^(-2x)) - 4(3e^(-2x)) = -6e^(-2x)
These functions satisfy the system of differential equations.

Therefore, the pairs of functions that satisfy the given system of differential equations are Option D (y_1 = e^(-x), y_2 = e^(-x)) and Option E (y_1 = e^x, y_2 = e^x).

Learn more about Systems of Differential Equations here:

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A garden hose fills a 2-gallon bucket in 5 seconds. The number of gallons, g, is proportional to the number of seconds, t, that the water is running. Select all the equations that represent the relationship between g and t. A g= 0.4t
B t= 0.4G
C g=2.5t
D t=2.5g
E g= 2/5 t

Answers

The correct options are (A), (D) and (E).

What is a linear equation?

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

Given that,

The time taken to fill 2 gallon bucket is 5 seconds.

Suppose the number of gallons be g.

And, the time in seconds is t.

The given options are considered one by one for the given case as,

(A) g = 0.4 t

Substitute g = 2 and t =5 in the above expression to get,

LHS = 2

RHS = 0.4 × 5

= 2

Since LHS = RHS, the given option represent the proportional relationship.

(B) t= 0.4g

Substitute g = 2 and t =5 in the above expression to get,

LHS = 5

RHS = 0.4 × 2

= 0.8

Since LHS ≠ RHS, the given option does not represent the proportional relationship.

Substitute g = 2 and t =5 in the above expression to get,

LHS = 2

RHS = 2.5 × 5

= 12.5

Since LHS ≠ RHS, the given option does not represent the proportional relationship.

(D) t = 2.5g

Substitute g = 2 and t =5 in the above expression to get,

LHS = 5

RHS = 2.5 × 2

= 5

Since LHS = RHS, the given option represents the proportional relationship.

(E) g= 2/5 t

Substitute g = 2 and t =5 in the above expression to get,

LHS = 2

RHS = 2/5 × 5

= 2

Since LHS = RHS, the given option represents the proportional relationship.

Hence, the correct relationship is represented by options (A), (D) and (E).

To know more about linear equation click on,

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Answer:

I beleive it should be

A. g = 0.4t

And

D. t = 2.5g

Sorry if i'm wrong though! Let me know if is correct!

Which coordinates represent the plotted point? Check all that apply. (StartRoot 13 EndRoot, 146.3 degrees) (StartRoot 13 EndRoot, 213.7 degrees) (negative StartRoot 13 EndRoot, negative 33.7 degrees) (Negative StartRoot 13 EndRoot, negative 146.3 degrees) (−3, 2) (3, −2) (−2, 3)