Which point is on the graph of the function

Mathematics

1 answer:

natulia [17]3 years ago

4 0

Answer:

Step-by-step explanation:

$(x,\ y)\\\\\text{Put thecoordinates of the points to the equation of}\ f(x)\ \text{and check the equality}:\\f(x)=\dfrac{1}{2}(2)^x\\\\(0,\ 1)\to x=0,\ y=1\\L=1\\R=\dfrac{1}{2}(2)^0=\dfrac{1}{2}(1)=\dfrac{1}{2}\\\\L\neq R\\\\(0,\ 2)\to x=0,\ y=2\\L=2\\R=\dfrac{1}{2}\\\\L\neq R\\\\\left(1;\ \dfrac{1}{2}\right)\to x=1,\ y=\dfrac{1}{2}\\L=\dfrac{1}{2}\\R=\dfrac{1}{2}(2)^1=\dfrac{1}{2}(2)=1\\\\L\neq R\\\\(1,\ 1)\to x=1,\ y=1\\L=1\\R=1\\\\L=R$

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Hey you!<br><br> I think I need your help with this one - Thanks~

timofeeve [1]

Hey Gary!

The volume of a cylinder is PiR^2h, or 3.14(r^2)h.
Let's define our measures.
Pi is 3.14 (simplified). However, our answer is requested in terms of Pi.
Our radius is 5.
Our height is 14.
Let's plug in our numbers.

5^2 • 14 • Pi
5^2 = 25
25 • 14 = 350.

350Pi is our answer.
However, rememver that we need to end our answer in units cubed, as we are using a 3-dimensional figure. Our answer is 350Pi in^3.
Your answer is B.)

I hope this helps!

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3 years ago

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4 years ago

Find the volume of the garden shed

Leno4ka [110]

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<h3><u>Volume of a rectangular prism</u></h3>

$\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}$

<h3><u>Volume of a pyramid</u></h3>

<u />

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

$\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}$

Therefore:

$\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}$

<h3><u>Volume of the garden shed</u></h3>

$\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}$