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Mathematics

2 answers:

Usimov [2.4K]2 years ago

5 0

Answer:

Step-by-step explanation:

This will be D because the beaker already has 0.2 mL of water. If Jovita needs to add more water to the beaker, and then it is 0.8. In D, the diagram shows you 0.2 + x = 0.8, which makes it the right diagram.

Hope that helps!

Anettt [7]2 years ago

3 0

Answer:

The Answer would be D.

Step-by-step explanation:

Because O.8 is the sum of how much 0.2+x equals to.

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In figure 2, find x if the perimeter is 4. Does each answer make sense? Why or why not?

stealth61 [152]

The value of x is equal to 1.5.

It is required to find x.

<h3>What is quadratic equation?</h3>

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power. The quadratic formula to solve a quadratic equation ax2 + bx + c = 0 is x = [-b ± √(b2 - 4ac)]/2a.

Given that:

So for the triangle, the perimeter would be:

$(x^{2} +x+3)+(x^{2} +2x-2)+(x^{2} +2x-9)=4$

By solving in above equation, we get

$(x^{2} +x+3)+(x^{2} +2x-2)+(x^{2} +2x-9)=4\\\\\\\2x^{2}+5x-8=4\\\\2x^{2}+5x-12=0\\\\2(x + 4)(x - 1.5)=0\\\\ x=-4\\\\ x=1.5$

So, we take x= 1.5 and neglect -4 because we can't take negative roots of the quadratic equation.

Hence, the value of x is equal to 1.5.

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2 years ago

Find the values of m and b that make the following function differentiable.

dimaraw [331]

Now, bearing in mind that, for a graph, to be "differentiable", means a "smooth transition", not an abrupt edge or a "cusp", the first subfunction of the piece-wise is just a quadratic, the second subfunction is a linear, well, so the linear needs to hit the quadratic "smoothly", not make an abrupt edge, for that, the linear must continue the quadratic from 2 onwards, since 2 is the range edge.

now, what is the piece-wise when x = 2? well, f(2) = x² or (2)² or 4

that means, the linear needs to hit it at that point, to make it so, let's make it the slope of the linear, the same as the quadratic's.

what's the quadratic's slope? well, simple enough

$\bf \left. \cfrac{dy}{dx}=2x \right|_{x=2}\implies 4\impliedby \textit{this means }
\begin{array}{llll}
mx+b\\
\uparrow \\
4
\end{array}$

so we have y = 4x + b

now, recall, for the quadratic, when x =2, y = 4, so for the linear, when x = 2, y = 4 as well, this means

$\bf 4 = 4(2) + b\implies 4=8+b\implies 4-8=b\implies \boxed{-4=b}
\\\\\\
mx+b\implies 4x-4\\\\
-------------------------------\\\\
f(x)=
\begin{cases}
x^2&x\le 2\\
4x-4&x\ \textgreater \ 2
\end{cases}$

check the picture below.