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2 years ago

Eight less than a number is no more than 14

Mathematics

1 answer:

myrzilka [38]2 years ago

5 0

Answer:

x - 8 ≤ 14

Step-by-step explanation:

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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]

Answer-

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

Solution-

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.

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2 years ago

Which statements are true about the place values in the number 22.222? Choose all answers that are correct. A. The 2 in the tent

Vinvika [58]

B. THE 2 IN THE TENTHS PLACE IS 10 TIMES THE VALUE OF THE 2 IN THE HUNDREDTHS PLACE.

2 2 . 2 2 2
tens ones decimal point tenths hundredths thousandths

2 in the tenths place = 0.20
2 in the hundredths place = 0.02

0.02 x 10 = 0.20

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3 years ago

One equation in a system is y=3x+7. Which equation gives the system no solution

atroni [7]

Answer:

Step-by-step explanation:

Because I know how to do it

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1 year ago

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What is 3 4/15 divided by (8 divided by 6 3/10)

kenny6666 [7]

8 / 6 3/10

= 8 * 10/63
=80/63

3 4/15 / 80/63

= 49/15 * 63/80

=2.5725

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3 years ago

What is the unit rate of 88 students for 4 classes

Nat2105 [25]

So, We Have A Rate That We Need To Simplify. We Have:
88 students for every 4 classes
So, We Need To Simplify This Rate. In Order To Do This, We Need To Change Is To A Fraction. It Is:
88 students
---------------
4 classes

Now, We Have To Simplify. We Can Do That By Remembering How To Simplify Fractions.

So,
88 ÷ 2 = 44 ÷ 2 = 22 students
--- --- ---------------
4 ÷ 2 = 2 ÷ 2 = 1

So, The Unit Rate For 88 Students For 4 Classes Is:
22 Students For One Class

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3 years ago