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Marley was asked to solve x2 - 4x + 9 = 0 using the Quadratic Formula. She found the discriminant first and decided she did not

saveliy_v [14]

We have been given Marley was asked to solve $x^2-4x+9 = 0$ using the Quadratic Formula. She found the discriminant first and decided she did not need to continue with the Quadratic Formula.

We are asked to determine whether Marley is correct or not.

We know when an equation is in form $ax^2+bx+c=0$ , we can use discriminant to check for the real solutions of equation.

$D=b^2-4(a)(c)$

If $D>0$ , then the equation will have two real solutions.

If $D=0$ , then the equation will have one real solution.

If $D$ , then the equation will have no real solutions.

Let us find discriminant.

$a=1,b=-4\text { and }c=9$

$D=(-4)^2-4(1)(9)$

$D=16-36$

$D=-20$

Since $-20$ , therefore, the equation will have no real solutions, so Marley is correct.

8 0

3 years ago

Optimization Calculus Problem

frosja888 [35]

$\bf \begin{cases}
V_c=\textit{cylinder's volume}\\
V_h=\textit{hemisphere's volume}\\
A_c=\textit{area of the cylinder}\\
A_h=\textit{area of the hemisphere}
\end{cases}
\\\\\\
V_c+V_h=6000\implies (\pi r^2h)+\left( \frac{2\pi r^3}{3} \right)
\\\\\\
6000=\cfrac{3\pi r^2h+2\pi r^3}{3}\implies 18000-2\pi r^3=3\pi r^2h
\\\\\\
\boxed{\cfrac{6000}{\pi r^2}-\cfrac{2r}{3}=h}
\\\\
-------------------------------\\\\$

$\bf A_c=2\pi rh+2\pi r^2\implies A_c=2\pi r\left(\cfrac{6000}{\pi r^2}-\cfrac{2r}{3} \right)+2\pi r^2
\\\\\\
A_c=\cfrac{12000}{r}-\cfrac{4\pi r^2}{3}\impliedby \textit{say it has a cost of 1, so stays the same}\\\\
-------------------------------\\\\
A_h=2\pi r^2\impliedby \textit{has a cost of 8 times the cylinder's}
\\\\\\
A_h=16\pi r^2\\\\
-------------------------------\\\\$

$\bf \textit{total cost is }A_c+A_h
\\\\\\
\cfrac{12000}{r}-\cfrac{4\pi r^2}{3}+16\pi r^2\implies \cfrac{12000}{r}-\cfrac{4\pi r^2}{3}+\cfrac{48\pi r^2}{3}
\\\\\\
\boxed{C(r)=\cfrac{12000}{r}+\cfrac{44\pi r^2}{3}}$

7 0

3 years ago

What is the median of this set of data? 100, 102, 103, 106, 109

rodikova [14]

Answer:103

Step-by-step explanation:

100,102,103,106,109

There median is the middle number which is 103

5 0

3 years ago

Read 2 more answers

Which expression is represented on the number line? 0 – (-6) -6 ÷ -2 2(-3) -2 • -3

hammer [34]

Answer:

So the expression is represented on the number line is

2(-3) .

Step-by-step explanation:

Given:

Shifting of a number on a number line.

To Find:

Expression is represented on the number line

Solution:

Two time - 3 is shifted to the Left hand side of the number line.

So it will express as Twice of (- 3 ) which will come to -6

So the expression is represented on the number line is

2(-3)

3 0

3 years ago

2. In an experiment with a mass attached to a spring, a student measures the period of the oscillation t as follows: 1.94 s, 1.9

Fed [463]

Answer: a) The average of this set of numbers is 1.98 s. b) the standard deviation is 0.02 s.

Step-by-step explanation: The average is calculated by adding all numbers found in the experiment divided by the number of values. $average = \frac{Sumxi}{n}$

The standard deviation is given by the square root of the squared sum of the difference between each number and the average divided by the total number of values. For instance, std deviation = $\frac{sqrt{(1.94-1.98)^{2}+(1.96-1.98)^2+(2.01-1.98)^2...}}{11}$ and that is done with all 11 terms of data minus the average to find the standard deviation.

In excel, the average of a certain set of numbers (displayed in cells A1 to A5) can be found by the commands =average(A1:A5). The standard deviation can be found by the commands =stdedv.p(A1:A5) in which p is the population. You can decrease decimals by clicking on the icon displayed in the Ribbon.

8 0

4 years ago