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nature of mathematics

Questions and Answers of Nature Of Mathematics

Identify the curves in Problems 24-27.a. \(2 y^{2}+8 y-20 x+148=0 \quad\)b. \(9 x^{2}-6 y^{2}+18 y-23=0\)c. \(9 x^{2}+6 y^{2}+18 x-23=0\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y>\frac{1}{5} x\)
Sketch the graph of each equation in Problems 3-30.\(y=-2 x^{2}+3\)
Use the vertical line test in Problems 27-32 to determine whether the curve is a function. Also state the probable domain and range. Xmin=-5 Xmax=5 Xsc)=1 Ysc1=1 Ymin= -5 Ymax=5
Sketch the curves using the equations given in Problems 28-51.\(x^{2}+y^{2}=1\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(3 x \leq 2 y\)
Use the vertical line test in Problems 27-32 to determine whether the curve is a function. Also state the probable domain and range. t 8min=-5 Ymin=-10 Ymax=5 Xmax=5 Xsc1=1 Ysc1=1
Sketch the graph of each equation in Problems 3-30.\(y=x^{2}-2 x+1\)
Use the vertical line test in Problems 27-32 to determine whether the curve is a function. Also state the probable domain and range. Xmin=-19 Xmax=10 Xsc1=2 Ysc1=10 Ymin=-199 Ymax=199
Sketch the curves using the equations given in Problems 28-51.\(x^{2}+y^{2}=64\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(2 x
Sketch the graph of each equation in Problems 3-30.\(y=x^{2}+4 x+4\)
Use the vertical line test in Problems 27-32 to determine whether the curve is a function. Also state the probable domain and range. At Xmin=-5 Ymin=-10 Xmax=5 Ymax=5 Xsc1=1 Ysc1=1
Sketch the curves using the equations given in Problems 28-51.\(x^{2}+y^{2}=50\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x \geq 2 y\)
Sketch the graphs of the equations in Problems 31-38.\(y=3^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(x^{2}+y^{2}=250\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(2 x \leq y\)
Sketch the graphs of the equations in Problems 31-38.\(y=4^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\)
In Problems 33-38, graph each function and then classify as a linear, quadratic, exponential, logarithmic, or probability function.\(f(x)=2 x^{2}\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(3 x \geq 5 y\)
Sketch the graphs of the equations in Problems 31-38.\(y=5^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(\frac{x^{2}}{25}+\frac{y^{2}}{36}=1\)
In Problems 33-38, graph each function and then classify as a linear, quadratic, exponential, logarithmic, or probability function.\(f(x)=2 x\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(5 x \geq 3 y\)
Sketch the graphs of the equations in Problems 31-38.\(y=-3^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(x^{2}+\frac{y^{2}}{9}=1\)
In Problems 33-38, graph each function and then classify as a linear, quadratic, exponential, logarithmic, or probability function.\(f(x)=\log x\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y \geq 0\)
Sketch the graphs of the equations in Problems 31-38.\(y=-6^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(4 x^{2}+9 y^{2}=36\)
In Problems 33-38, graph each function and then classify as a linear, quadratic, exponential, logarithmic, or probability function.\(f(x)=\left(\frac{1}{2}\right)^{x}\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x \leq 0\)
Sketch the graphs of the equations in Problems 31-38.\(y=-7^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(25 x^{2}+16 y^{2}=400\)
In Problems 33-38, graph each function and then classify as a linear, quadratic, exponential, logarithmic, or probability function.\(f(x)=\frac{e^{-x^{2} / 2}}{\sqrt{2 \pi}}\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x+3 y \leq-9\)
Sketch the graphs of the equations in Problems 31-38.\(y=10^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(16 x^{2}+9 y^{2}=144\)
In Problems 33-38, graph each function and then classify as a linear, quadratic, exponential, logarithmic, or probability function.\(\underset{\text { linear }}{f(x)}=5-x\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x+4 y>-12\)
Sketch the graphs of the equations in Problems 31-38.\(y=100-2^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(x^{2}-y^{2}=1\)
Find the difference quotient, \(\frac{f(x+h)-f(x)}{h}\), for the functions given in Problems 39-44.\(f(x)=3 x-5 \)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x+2 y+4 \leq 0\)
Sketch the graphs of the equations for \(x \geq 0\) in Problems 39-42.\(y=\left(\frac{1}{2}\right)^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(y^{2}-x^{2}=4\)
Find the difference quotient, \(\frac{f(x+h)-f(x)}{h}\), for the functions given in Problems 39-44.\(f(x)=3 x^{2}-5\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(2 x-3 y+6 \leq 0\)
Sketch the graphs of the equations for \(x \geq 0\) in Problems 39-42.\(y=\left(\frac{1}{3}\right)^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(\frac{x^{2}}{9}-\frac{y^{2}}{4}=1\)
Find the difference quotient, \(\frac{f(x+h)-f(x)}{h}\), for the functions given in Problems 39-44.\(f(x)=x^{3}\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x-5 y \leq 125\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(x+3 y>420\)
Sketch the curves using the equations given in Problems 28-51.\(\frac{x^{2}}{4}-\frac{y^{2}}{9}=1\)
Find the difference quotient, \(\frac{f(x+h)-f(x)}{h}\), for the functions given in Problems 39-44.\(f(x)=5 x^{3}\)
Sketch the graphs of the equations for \(x \geq 0\) in Problems 39-42.\(y=-\left(\frac{1}{10}\right)^{x}\)
Sketch the curves using the equations given in Problems 28-51.\(\frac{y^{2}}{36}-\frac{x^{2}}{9}=1\)
Find the difference quotient, \(\frac{f(x+h)-f(x)}{h}\), for the functions given in Problems 39-44.\(f(x)=\frac{1}{x}\)
a. Graph \(h=-16 t^{2}+96 t\).b. Does the parabola in part a open upward or downward?c. If we relate the graph in part a to cannonball in Figure 15.17, can \(t\) be negative? Draw the graph of the
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(3 x+y \leq-2\)
Find the difference quotient, \(\frac{f(x+h)-f(x)}{h}\), for the functions given in Problems 39-44.\(f(x)=\frac{1}{x^{2}}\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(6 x-7 y
a. Graph \(d=16 t^{2}\).b. Does the parabola in part a open upward or downward?c. Graph the parabola in part a for \(0 \leq t \leq 16\).
The velocity \(v\) (in feet per second) of the rock dropped into the well in the B.C. cartoon at the beginning of this section is also related to time \(t\) (in seconds) by the formula\[v=32
Sketch the curves using the equations given in Problems 28-51.\(36 y^{2}-25 x^{2}=900\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(2 x-3 y+4 \leq 1\)
Using the table of values in Problem 45, find the velocity of the rock at the instant it was released, after 8 seconds, and when it hit the bottom of the well. Write your answers in the form \((t, v)
Draw the graphs in Problems 45-50.\(y=-2 x^{2}+4 x-2\)
Sketch the curves using the equations given in Problems 28-51.\(3 y^{2}=4 x^{2}+12\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(3 x+2 y-3>1\)
Draw the graphs in Problems 45-50.\(y=\frac{1}{4} x^{2}-\frac{1}{2} x+\frac{1}{4}\)
Sketch the curves using the equations given in Problems 28-51.\(4 y^{2}-x^{2}=9\)
An independent distributor bought a new vending machine for \(\$ 2,000\). It had a probable scrap value of \(\$ 100\) at the end of its expected 10-year life. The value \(V\) at the end of \(n\)
Using the table of values in Problem 47, find the value of the machine when it is purchased, when it is 5 years old, and when it is scrapped. Write your answers in the form \((n, V)\).Data from
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y \leq \frac{2}{3} x-\frac{3}{100}\)
Draw the graphs in Problems 45-50.\(y=\frac{1}{2} x^{2}+x+\frac{1}{2}\)
Sketch the curves using the equations given in Problems 28-51.\(x^{2}-y^{2}=9\)
Graph the first-degree inequalities in two unknowns in Problems 13-48.\(y
Draw the graphs in Problems 45-50.\(y=x^{2}-2 x+3\)
Sketch the curves using the equations given in Problems 28-51.\(3 y^{2}-4 x^{2}=12\)
Let \(P(x)\) be the number of prime numbers less than \(x\). Finda. \(P(10)\)b. \(P(-10)\)c. \(P(100)\)
Søren is designing an exhibit of his paintings and has up to 450 square feet of wall space to display them. His small paintings take up 6 square feet each, and his larger paintings take up 24 square
Draw the graphs in Problems 45-50.\(x=3 y^{2}+12 y+14\)
Sketch the curves using the equations given in Problems 28-51.\(3 y^{2}=4 x^{2}+5\)
Let \(S(x)\) be the exponent on a base 2 that gives the result \(x\). Finda. \(S(32)\)b. \(S\left(\frac{1}{8}\right)\)c. \(S(\sqrt{2})\)For each verbal description in Problems 51-54, write a rule in
Theron needs to purchase mechanical pencils at a cost of \(\$ 12\) each and writing tablets at \(\$ 15 /\) dozen. He can spend up to \(\$ 65\), but not more. Write an inequality to describe his
Draw the graphs in Problems 45-50.\(x=4 y-y^{2}-4\)
Sketch the curves using the equations given in Problems 28-51.\(4 y^{2}-4 x^{2}=5\)
For each number \(x\) in the domain, the corresponding range value \(y\) is found by multiplying by 3 and then subtracting 5 .
Hannah is purchasing chocolate truffles for her mother and nana on Mother's Day. Chocolate truffles come in boxes of 6 pieces each and milk chocolate truffles come in boxes of a dozen. If she can
Rework Example 6 for a \(12 \%\) interest rate.Data from Example 6Suppose that you deposit \(\$ 100\) at \(10 \%\) interest. Graph the total amounts you will have if you invest your money at simple
Sketch the curves using the equations given in Problems 28-51.\(3 x^{2}-4 y^{2}=5\)
For each number \(x\) in the domain, the corresponding range value \(y\) is found by squaring and then subtracting 5 times the domain value.
Cole is going to participate in a fundraiser by running laps. He can run on the college track (5,000 meters) or on the high school track ( 3,000 meters). He wants to run more than 20,000 meters for
If the length of the major axis of the earth's orbit is \(186,000,000 \mathrm{mi}\) and its eccentricity is 0.017 , how far is the earth from the sun when it is at aphelion and at perihelion?
For each number \(x\) in the domain, the corresponding range value \(y\) is found by taking the square root of the domain value subtracted from 5.
"Well, Billy, can I make it?" asked Evel. "If you can accelerate to the proper speed, and if the wind is not blowing too much, I think you can," answered Billy. "It will be one huge money-maker, but
In economics, the Laffer curve is an economic model named after Arthur Laffer, but it actually dates back to the 14th-century Muslim philosopher Ibn Khaldun. The Laffer curve postulates that no tax

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