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2 years ago

Rewrite each radian measure in degrees. 5л/2

Mathematics

1 answer:

Alex_Xolod [135]2 years ago

7 0

$\frac{5\pi}{2} \times \frac{180}{\pi} = \frac{900\pi}{2\pi} = 450 \: degrees$

ok done. Thank to me :>

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4 years ago

Part 1: Identify the vertex, focus, and directrix of each. Then sketch the graph.

Lina20 [59]

Answer: $\bold{1.\quad \text{Vertex}:(4,-1)\qquad \text{Focus}:\bigg(4,-\dfrac{9}{8}\bigg)\qquad \text{Directrix}:y=-\dfrac{7}{8}}$

$\bold{2.\quad \text{Vertex}:(2,1)\qquad \text{Focus}:\bigg(\dfrac{9}{4},1\bigg)\qquad \text{Directrix}:y=\dfrac{7}{4}}$

<u>Step-by-step explanation:</u>

The vertex form of a parabola is y = a(x - h)² + k or x = a(y - k)² + h

(h, k) is the vertex

p is the distance from the vertex to the focus

-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = -2(x - 4)² - 1 → a = -2 (h, k) = (4, -1)

$a=\dfrac{1}{4p}\quad \rightarrow \quad -2=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{8}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{-8}{8}+\dfrac{-1}{8}\\\\.\qquad =-\dfrac{9}{8}\qquad \rightarrow \qquad \text{Focus}=\bigg(4,-\dfrac{9}{8}\bigg)\\\\\\\text{Directrix: y=Vertex - p}\\\\.\qquad \qquad y=\dfrac{-8}{8}-\dfrac{-1}{8}\\\\.\qquad \qquad y=-\dfrac{7}{8}$

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2) x = (y - 1)² + 2 → a = 1 (h, k) = (2, 1)

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{4}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{8}{4}+\dfrac{1}{4}\\\\.\qquad =\dfrac{9}{4}\qquad \rightarrow \qquad \text{Focus}=\bigg(\dfrac{9}{4},1\bigg)\\\\\\\text{Directrix: x=Vertex - p}\\\\.\qquad \qquad x=\dfrac{8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=\dfrac{7}{4}$

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3 years ago

The brain volumes (cm cubed) of 20 brains have a mean of 1105.1 cm cubed and a standard deviation of 123.5 cm cubed. Use the g

kramer

Answer:

$1332.1 \:cm^3$ is neither significantly low nor significantly high.

Step-by-step explanation:

From the information given, we know that:

The mean is $\bar{x}=1105.1 \:cm^{3}$ and the standard deviation is $\sigma=123.5 \:cm^{3}$ .

The range rule of thumb says that:

$minimum \:usual \:value=\bar{x}-2\sigma\\\\maximum \:usual \:value=\bar{x}+2\sigma$

Applying these definitions, we get that

$minimum \:usual \:value=1105.1-2(123.5)=858.1 \:cm^3\\\\maximum \:usual \:value=1105.1+2(123.5)=1352.1 \:cm^3$

We note that $1332.1 \:cm^3$ is between $858.1 \:cm^3$ and $1352.1 \:cm^3$ , which indicates $1332.1 \:cm^3$ is neither significantly low nor significantly high.

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4 years ago