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2 years ago

Given a non-zero rational number, a, and an irrational number, b, what can be said about the product of a and b?

Mathematics

1 answer:

laiz [17]2 years ago

7 0

Answer:

The product of a non-zero rational number and an irrational number is irrational.

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A cooler has a temperature of 32 degrees Fahrenheit. A bottled drink is placed in the cooler with an initial temperature of

FinnZ [79.3K]

Answer:

$k \approx 0.44$

Step-by-step explanation:

Given function:

$f(t) = (ce)^{-kt}+32$

As per question statement:

Initial temperature of bottle is 70 $^\circ F$ .

i.e. when time = 0 minutes, f(t) = 70 $^\circ F$

$70 = ce^{-k\times 0}+32\\\Rightarrow 38 = ce^{0}\\\Rightarrow c = 38$

After t = 3, f(t) = 42 $^\circ F$

$42 = 38 \times e^{-k\times 3}+32\\\Rightarrow 42-32 = 38 \times e^{-3k} \\\Rightarrow 10 = 38 \times e^{-3k} \\\Rightarrow e^{3k} = \dfrac{38}{10}\\\Rightarrow e^{3k} = 3.8\\\\\text{Taking } log_e \text{both the sides:}\\\\\Rightarrow log_e {e^3k} = log_e {3.8}\\\Rightarrow 3k \times log_ee=log_e {3.8} (\because log_pq^r=r \times log_pq)\\\Rightarrow 3k \times 1=log_e {3.8}\\\Rightarrow 3k = 1.34\\\Rightarrow k = \dfrac{1.34}{3}\\\Rightarrow k \approx 0.44$

Hence, the value is:

$k \approx 0.44$

8 0

3 years ago

Solve equation r/3-4=11 r = 45 r = 35 r = 33 r = 28

Molodets [167]

Answer:

r=-11

Step-by-step explanation:

7 0

2 years ago

Point (, ) is dilated from the origin by scale factor = . What are the coordinates of point ′?

Igoryamba

Answer:idk how to do this im in 7th grade

4 0

3 years ago

Solve the following equations x-1=6/x

Whitepunk [10]

Answer:

or,x2-x=6

or,x2-x-6=0

or,x2-3x+2x-6=0

or,x(x-3)+2(x-3)=0

or,(x-3)(x+2)=0

so either x=3

or x=-2

3 0

3 years ago

What Force would be needed to extend a spring with a spring constant k=7 N/m that extends 0.3m?

vladimir2022 [97]

Answer:

Force = - 2.1 Newton

Step-by-step explanation:

According to question ,

The value of Spring constant , K = 7 N/m Newton per meter

And the spring is extended up to 0.3 meter

The Force experience on the spring is calculated from the Hook's Law

The principal state that , the force applied on spring to extend or compress the spring to some distance is proportion to that distance. 

Let the force be F

So, F = - K X

where K is spring constant and X is its displacement

Negative sign shows displacement of spring once it is stretched

And K is spring constant

So ,Force = ( - ) 7 × 0.3

I.e Force = - 2.1 Newton Answer

4 0

2 years ago