6 weeks to 12 days answer?

if a letter in the word calculator is chosen at random what is the probability that it has a vertical line of symmetry

Troyanec [42]

Answer:

down the middle of an object with vertical symmetry, the two sides

will be mirror images of each other.

Examples of capital letters that have vertical symmetry are:

A H I M O T U V W X Y

Step-by-step explanation:

3 0

3 years ago

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Use implicit differentiation to find the slope of the tangent line at the given point:

Salsk061 [2.6K]

Answer:

$\frac{dy}{dx}=0$

Step-by-step explanation:

So we have the equation:

$(x^2+y^2)^2=4x^2y$

And we want to find the slope of the tangent line at the point (1,1).

So, let's implicitly differentiate. Take the derivative of both sides:

$\frac{d}{dx}[(x^2+y^2)^2]=\frac{d}{dx}[4x^2y]$

Let's do each side individually.

Left:

We can use the chain rule:

$(u(v(x))'=u'(v(x))\cdot v'(x)$

Let's let v(x) be x²+y². So, u(x) is x². Thus, the u'(x) is 2x. Therefore:

$\frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)(\frac{d}{dx}[x^2+y^2])$

We can differentiate x like normal. However, for y, we must differentiate implicitly. pretend y is y(x). This gives us:

$\frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)(\frac{d}{dx}[x^2]+\frac{d}{dx}[y^2(x)])$

Differentiate:

$\frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)(2x+2y\frac{dy}{dx})$

Therefore, our left side is:

$2(x^2+y^2)(2x+2y\frac{dy}{dx})$

Right:

We have:

$\frac{d}{dx}[4x^2y]$

Let's move the 4 outside:

$=4\frac{d}{dx}[x^2y]$

Use the product rule:

$=4(\frac{d}{dx}[x^2]y+x^2\frac{d}{dx}[y])$

Differentiate:

$=4(2xy+x^2\frac{dy}{dx})$

Therefore, our entire equation is:

$2(x^2+y^2)(2x+2y\frac{dy}{dx})=4(2xy+x^2\frac{dy}{dx})$

So, to find the derivative at (1,1), substitute 1 for x and 1 for y.

$2((1)^2+(1)^2)(2(1)+2(1)\frac{dy}{dx})=4(2(1)(1)+(1)^2\frac{dy}{dx})$

Evaluate.

$2((1)+(1))(2+2\frac{dy}{dx})=4(2+\frac{dy}{dx})$

Simplify. Also, let's distribute the right:

$2(2)(2+2\frac{dy}{dx})=8+4\frac{dy}{dx}$

Multiply.

$4(2+2\frac{dy}{dx})=8+4\frac{dy}{dx}$

Distribute the left:

$8+8\frac{dy}{dx}=8+4\frac{dy}{dx}$

Subtract 8 from both sides:

$8\frac{dy}{dx}=4\frac{dy}{dx}$

Subtract 4(dy/dx) from both sides:

$4\frac{dy}{dx}=0$

Divide both sides by 4:

$\frac{dy}{dx}=0$

Therefore, the slope at the point (1,1) is 0.

And we're done!

We can verify this using the graph. The slope of the line tangent to the point (1,1) seems like it would be horizontal, giving us a slope of 0.

Edit: Typo

5 0

4 years ago

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-g-15 = -12. what does g equal to?

iren [92.7K]

I think g equals -3

Step-by-step explanation:

7 0

4 years ago

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Write the function below in slope intercepts form. Show all the steps

Bezzdna [24]

we need to find the equation in the form y=mx+b, so:

4x+y=5

y=-4x+5

the "4x" go subtracting to the other side

and we have m=-4 and b=5

so the answer is: y=-4x+5

8 0

1 year ago

The measures of the angles of a convex polygon form an arithmetic sequence. The least measurement in the sequence is 128º. The g

Over [174]

$\bf \qquad \qquad \textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\ a_n=n^{th}~value\\
----------\\
\stackrel{least}{a_1}=128\\\\
\stackrel{greatest}{a_n}=172
\end{cases}$

$\bf S_n=\cfrac{n}{2}(128~+~172)\implies S_n=\cfrac{n}{2}(300)\implies S_n=150n
\\\\\\
\textit{but we also know that sum of all interior angles is }180(n-2)
\\\\\\
\stackrel{\textit{sum of the angles}}{S_n}=\stackrel{\textit{sum of the angles}}{180(n-2)}=150n
\\\\\\
180n-360=150n\implies 30n=360\implies n=\cfrac{360}{30}\implies n=12$

7 0

3 years ago

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