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3 years ago

7

The length of a side of a cube can be determinad

1 answer:

erik [133]3 years ago

7 0

Answer:

4 cm

which is none of the listed answers

Step-by-step explanation:

∛64 = 4

proof:

4x4x4 = 64

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Prove that the limit x tends to 1 (2x^4-6x^3+x^2+3)÷(x-1)=-8

elixir [45]

First note that if $x\neq1$ , you have

$\dfrac{2x^4-6x^3+x^2+3}{x-1}=2x^3-4x^2-3x-3$

Now, you're looking for $\delta>0$ such that for any $\varepsilon>0$ , you have

$|x-1|$

Note that you can divide through the left side of the $\varepsilon$ inequality by $x-1$ once more:

$\dfrac{2x^3-4x^2-3x+5}{x-1}=2x^3-2x-5\implies 2x^3-4x^2-3x+5=(x-1)(2x^2-2x-5)$

So it follows that you need to find an appropriate $\delta$ that will guarantee

$|(x-1)(2x^2-2x-5)|=|x-1||2x^2-2-5|$

For the moment, let's fix $\delta=1$ . Then by this assumption, we have

$|x-1|$

From this we get

$\implies0$
$\implies0$
$\implies0$
$\implies-5$
$\implies1$

where the upper bound is what we care about. With this assumption, we then get that

$|x-1||2x^2-2-5|$

which suggests that $\delta$ can be taken to be either the smaller of 1 or $\dfrac{\varepsilon}5$ , or $\delta=\min\left\{\dfrac{\varepsilon}5,1\right\}$ , to guarantee that the function gets arbitrarily close to -8.

5 0

3 years ago

The parking spaces in a city lot were created by painting rows of parallel line segments, then painting a line that cuts through

frosja888 [35]

65 is the correct option

8 0

3 years ago

Read 2 more answers

(y + 4)^2 – 2(y + 4) + 1

almond37 [142]

Answer:

y = -3 and y = -3

or y = -3 with a multiplicity of 2

Step-by-step explanation:

$(y+4)^2-2(y+4)+1$

If you want to factor this, heres what you do:

$(y+4)(y+4)-2(y+4)+1$

$y^2+8y+16-2y-8+1$

$y^2+6y+9$

Then factor:

$(y+3)(y+3)$

$(y+3)^2$

The value of y:

y + 3 = 0 and y + 3 = 0

y = -3 and y = -3

or y = -3 with a multiplicity of 2

8 0

2 years ago

Read 2 more answers

Find the y intercepts of 3x^2+24x-51. quadratic formula

julia-pushkina [17]

Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , with a = x^2 coefficient, b = x coefficient, and c = constant.

Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:

$y=3*0^2+24*0-51\\y=0+0-51\\y=-51$

<u>Your y-intercept is (0,-51).</u>

Next, using our equation plug the appropriate values into the quadratic formula:

$x=\frac{-24\pm \sqrt{24^2-4*3*(-54)}}{2*3}$

Next, solve the multiplications and exponent:

$x=\frac{-24\pm \sqrt{576-(-648)}}{6}\\\\x=\frac{-24\pm \sqrt{576+648}}{6}$

Next, solve the addition:

$x=\frac{-24\pm \sqrt{1224}}{6}$

Now, simplify the radical using the product rule of radicals as such:

Product Rule of Radicals: √ab = √a × √b

√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34

$x=\frac{-24\pm 6\sqrt{34}}{6}$

Next, divide:

$x=-4\pm \sqrt{34}$

<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>

Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

$x=-4+ \sqrt{34},-4- \sqrt{34}\\x\approx 1.83, -9.83$

<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>

5 0

3 years ago

Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100

SpyIntel [72]

Well, drop 65 cents (the first 250 grams) to get 90 remaining cents. These are 900 additional grams. So, the mass is 0.25+0.9=1.15 kg.

4 0

3 years ago