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Sloan [31]
3 years ago
8

Item 3write 90% as a fraction or mixed number in simplest form.the simplest form is

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
6 0
9/10 :DDDDDDDDDDDDDDDDDDDD
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At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as
MAXImum [283]

<u>Answer-</u>

At x= \frac{1}{2304e^4-16e^2} the curve has maximum curvature.

<u>Solution-</u>

The formula for curvature =

K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}

Here,

y=4e^{x}

Then,

{y}' = 4e^{x} \ and \ {y}''=4e^{x}

Putting the values,

K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

 {k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}

Now, equating this to 0

(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0

\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})

\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})

\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}

\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}

\Rightarrow 2304e^{2x}-16e^{2x}-1=0

Solving this eq,

we get x= \frac{1}{2304e^4-16e^2}

∴ At  x= \frac{1}{2304e^4-16e^2} the curvature is maximum.




6 0
2 years ago
Fiona divided 3x2 + 5x – 3 by 3x +2. The expression represents the remainder over the divisor. x + 1 + What is the value of a?
grigory [225]
                    x + 1
         __________
3x+2 I 3x² +5x -3
           3x² +2x
           ----------
                    3x -3
                    3x+2
                    --------
                          -5 is the remainder 
                 
8 0
3 years ago
Read 2 more answers
8 x 6 = (4 x 6) (__x 6) <br> = 24 + __<br> =
guajiro [1.7K]

Answer:

8x6= (4x6) + (4x6)

= 24+24

= 48

Step-by-step explanation:

Hope this helps :)

8 0
3 years ago
Read 2 more answers
Which equation has infinite solutions?
AnnyKZ [126]

The equation that has an infinite number of solutions is 2x + 3 = \frac{1}{2}(4x + 2) + 2

<h3>How to determine the equation?</h3>

An equation that has an infinite number of solutions would be in the form

a = a

This means that both sides of the equation would be the same

Start by simplifying the options

3(x – 1) = x + 2(x + 1) + 1

3x - 3 = x + 3x + 2 + 1

3x - 3 = 4x + 3

Evaluate

x = 6 ----- one solution

x – 4(x + 1) = –3(x + 1) + 1

x - 4x - 4 = -3x - 3 + 1

-3x - 4 = -3x - 2

-4 = -2 ---- no solution

2x + 3 = \frac{1}{2}(4x + 2) + 2

2x + 3 = 2x + 1 + 2

2x + 3 = 2x + 3

Subtract 2x

3 = 3 ---- infinite solution

Hence, the equation that has an infinite number of solutions is 2x + 3 = \frac{1}{2}(4x + 2) + 2

Read more about equations at:

brainly.com/question/15349799

#SPJ1

<u>Complete question</u>

Which equation has infinite solutions?

3(x – 1) = x + 2(x + 1) + 1

x – 4(x + 1) = –3(x + 1) + 1

2x + 3 = \frac{1}{2}(4x + 2) + 2

\frac 13(6x - 3) = 3(x + 1) - x - 2

5 0
2 years ago
Ellen drove 277.2 miles. For each gallon of gas, the car can travel 21 miles. How many gallons of gas did Ellen use?
Paul [167]

Answer:

the answer is 13.2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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