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3 years ago

Evaluate 3a2 4b2 for a = 2 and b = 3.

Mathematics

1 answer:

olasank [31]3 years ago

5 0

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A room decorator wants to purchase fabric. Each yard of fabric costs $2.90. Write a rule for the cost of the fabric. Let c equal

STatiana [176]

Expression: 2.90f = c

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3 years ago

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

3 years ago

F(x) =- (3x +9) – 13 find f(-5)

belka [17]

$f(x) = -(3x + 9) - 13\\f(-5) = -(3 \cdot (-5) + 9) - 13\\= -(-15 + 9) - 13\\= -(-6) - 13\\= 6 - 13\\= - 7$

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3 years ago

Write a rule for the given transformation. PLEASE HELP a. rotation 180° about the origin b. translation (x,y) -> (x +6, y+2)

Serggg [28]

Answer:

thank you so much for free points

and I don't know the answer but really sorry I don't want to ask some questions on this that's why I did this and thank you for free points

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3 years ago

Please help you kind people

mafiozo [28]

Answer:

All I know is that the first picture is 8

Step-by-step explanation:

I know because one times eight is eight so um yeah

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3 years ago