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kodGreya [7K]
3 years ago
12

Let ​ f(x)=x+2 ​ and ​ g(x)=

align="absmiddle" class="latex-formula">+1 ​ .
Graph the functions on the same coordinate plane.


What are the solutions to the equation f(x)=g(x) ?



Enter your answers in the boxes.

x = ___ or x = ____

Mathematics
1 answer:
pychu [463]3 years ago
8 0
Answer: x = 0 and x = 1

Explanation:

The image of the graph is in the figure attached.

There you can observe two intersection points which are (0,2) and (1,3), therefore the solutions are x = 0 and x = 1.

You can draw the graph by constructing a table with x from - 2 to 4, like this:

x             f(x) = x + 2            g(x) = 2^x + 1

-2             -2 + 2 = 0             2^2 + 1 = 4 + 1 = 5

- 1            -1 + 2 = 1             2^1 + 1 = 2 + 1 = 3

0                0 + 2 = 2             2^0 + 1 = 1 + 1 = 2  => this is one solution

1                1+ 2 = 3              2^1 + 1 = 2 + 1 = 3 => this is the other solution

2                2 + 2 = 4             2^2 + 1 = 4 + 1 = 5


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in triangle PQR, <P - <Q = 20 degrees, <Q - <R = 50 degrees, find <P, <Q, <R

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3 years ago
Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the ra
bearhunter [10]

Answer:

\frac{dh}{dt}=-\frac{1}{2\pi}cm/min

Step-by-step explanation:

From similar triangles, see diagram in attachment

\frac{r}{4}=\frac{h}{16}


We solve for r to obtain,


r=\frac{h}{4}


The formula for calculating the volume of a cone is

V=\frac{1}{3}\pi r^2h


We substitute the value of r=\frac{h}{4} to obtain,


V=\frac{1}{3}\pi (\frac{h}{4})^2h


This implies that,

V=\frac{1}{48}\pi h^3


We now differentiate both sides with respect to t to get,

\frac{dV}{dt}=\frac{\pi}{16}h^2 \frac{dh}{dt}


We were given that water is drained out of the tank at a rate of 2cm^3/min


This implies that \frac{dV}{dt}=-2cm^3/min.


Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means h=8cm.


We substitute this values to obtain,


-2=\frac{\pi}{16}(8)^2 \frac{dh}{dt}


\Rightarrow -2=4\pi \frac{dh}{dt}


\Rightarrow -1=2\pi \frac{dh}{dt}


\frac{dh}{dt}=-\frac{1}{2\pi}






3 0
3 years ago
Read 2 more answers
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