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3 years ago

1. What is an extraneous solution of an equation?

1 answer:

6 0

“Extraneous solutions are not solutions at all. They arise from outside the problem, from the method of solution. They are extraneous because they are not solutions of the original problem. ... To tell if a "solution" is extraneous you need to go back to the original problem and check to see if it is actually a solution.”

Basically, they are an answer you get when you solve a problem, but they don’t actually make the equation true so you disregard it.

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A water gauge in a pond measured 2358 in. At the beginning of the week. After five days of rain, the gauge read 3414 in. By how

V125BC [204]

Answer:

1056 inches

Step-by-step explanation:

Given that :

Initial measurement = 2358 in

Guage level after 5 days of rain (final reading) = 3414 in

Change in water level rise :

Final reading - Initial reading

(3414 - 2358) in

= 1056 inches

3 0

3 years ago

Solve the equation 2 sec² x = 3 - tan x for the domain 0° ≤ x ≤ 360°

vodka [1.7K]

$2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\$

$\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\$

$x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\$

$\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]$

4 0

2 years ago

Use a whole number, a fraction, one plus sign, and four 2's to make 23.

alexira [117]

22+2/2=23

22 is whole number
one plus sign
and 2/2 is the fraction
4 digits are 2

6 0

3 years ago

Help a girl out ?? i'm confused as to solve this

Rom4ik [11]

Answer:

(5 1/2 miles, $12.50)

Step-by-step explanation:

Looking at the graph, identify as best you can the coordinates of the point at which the two graphs cross. I read (5 1/2 miles, $12.50).

3 0

3 years ago

PLEASE SHOW YOUR WORK WITH YOUR ANSWER. Two bags had 50 kilograms of sugar each. After taking out 3 times as much sugar from bag

Svetllana [295]

Answer:

Bag 1: 20

Bag 2: 40

Step-by-step explanation:

Let x be the amount taken out of bag 2

Then the amount left in each bag can be written as:

Bag 1: 50-3x

Bag 2: 50-x

Since we know that half of bag 2 is bag 1, that gives us:

50-3x = 1/2(50-x)

-> 50-3x = 25-x/2

Now lets isolate x and solve:

25 = 5x/2

-> 50 = 5x

-> x = 10

So plug x bag in for the original equations:

Bag 1: 50-3x = 50-3(10) = 20

Bag 2: 50-x = 50-10 = 40

4 0

3 years ago