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3 years ago

√3x+1=x+1 how to do you solve this equation using step by step

Mathematics

1 answer:

11111nata11111 [884]3 years ago

6 0

Answer:

The solutions are x=0 and x=1

Step-by-step explanation:

Assuming your equation is

$\sqrt{3x + 1} = x + 1$

Square both sides to get:

$3x + 1 = ( {x + 1)}^{2}$

Expand the RHS,

$3x + 1 = {x}^{2} + 2x + 1$

Rewrite in standard quadratic form:

${x}^{2} + 2x - 3x + 1 - 1 = 0$

${x}^{2} - x = 0$

$x(x - 1) = 0$

x=0 or x=1

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The number of salmon swimming upstream to spawn is approximated by the following function:

umka2103 [35]

Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

Step-by-step explanation:

Let $S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965$ , for $6 \leq x \leq 20$ . $x$ represents the temperature of the water, measured in degrees Celsius, and $S$ is the number of salmon swimming upstream to spawn, dimensionless.

We compute the first and second derivatives of the function:

$S'(x) = -3\cdot x^{2}+4\cdot x +405$ (Eq. 1)

$S''(x) = -6\cdot x +4$ (Eq. 2)

Then we equalize (Eq. 1) to zero and solve for $x$ :

$-3\cdot x^{2}+4\cdot x +405 = 0$

And all roots are found by Quadratic Formula:

$x_{1} \approx 12.305\,^{\circ}C$ , $x_{2}\approx -10.971\,^{\circ}C$

Only the first root is inside the given interval of the function. Hence, the correct answer is:

$x \approx 12.305\,^{\circ}C$

Now we evaluate the second derivative at given result. That is:

$S''(12.305) = -6\cdot (12.305)+4$

$S''(12.305) = -69.83$

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

5 0

3 years ago

Bella is planing to write in a journal.some pages will have one journal entry on them,and other pages will have two journal entr

loris [4]

Bella can times 2x5 and that would equal to 10.

8 0

2 years ago

Read 2 more answers

Find point P that divides segments AB into a 2:3 ratio.

nasty-shy [4]

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
A(-3,1)\qquad B(3,5)\qquad
\qquad \stackrel{\textit{ratio from A to B}}{2:3}
\\\\\\
\cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-3,1)=2(3,5)\\\\
-------------------------------\\\\
P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)$

$\bf -------------------------------\\\\
P=\left(\cfrac{(3\cdot -3)+(2\cdot 3)}{2+3}\quad ,\quad \cfrac{(3\cdot 1)+(2\cdot 5)}{2+3}\right)
\\\\\\
P=\left(\cfrac{-9+6}{5}~~,~~\cfrac{3+10}{5} \right)\implies P=\left(-\frac{3}{5}~~,~~\frac{13}{5} \right)$

6 0

3 years ago

[15 Points] Solve for x.<br> <img src="https://tex.z-dn.net/?f=45x%2B34%3D24x%2B16" id="TexFormula1" title="45x+34=24x+16" alt="

sergiy2304 [10]

Answer:

6/7

Step-by-step explanation:

45x+34=24x+16

collect like terms, we now have;

45x-24x=16-34

21x=-18

X=18/21

X=6/7

8 0

2 years ago

Problem Solving each problem by solving a simpler problem. solve There are two identical figures with all sides of equal length.

PolarNik [594]

Pentagon and each side is 2 units

3 0

2 years ago