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3 years ago

What is x if the other angles are 61 and 42

Mathematics

1 answer:

Lady_Fox [76]3 years ago

4 0

Answer:

The answer is 180°. Hope this helps!

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What is the slope of the line below? If necessary, enter your answer as a

Westkost [7]

9514 1404 393

Answer:

6/5

Step-by-step explanation:

The slope formula is useful for finding the slope.

m = (y2 -y1)/(x2 -x1)

m = (-1 -11)/(-5 -5) = -12/-10

m = 6/5

The slope of the line through the given points is 6/5.

3 0

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

Gusy help asap due in 5 minutes...!

charle [14.2K]

Answer:

c) πr2h is the answer

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Which statements describes this trapozoid?

Anna11 [10]

A trapezoid/trapezium is a quadrilateral (4 sided shape) with exactly one pair of parallel sides.

It is a quadrilateral (a closed plane shape with four linear sides) that has at least one pair of parallel lines for sides

4 0

3 years ago

(Algebra II) Extra points!!Determine whether y varies directly with x

ludmilkaskok [199]

Answer:

k = 1.6
y = 1.6x

Step-by-step explanation:

If the variation is proportional dividing the y-value by the x-value will give the same result for all table entries. That quotient is the constant of variation (k).

Here 6.4/4 = 11.2/7 = 16/10 = 20.8/13 = 1.6

The value of y varies directly as x, and the constant of variation is 1.6. The equation is ...

y = 1.6x

8 0

3 years ago