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2 years ago

Find the limit if it exists lim x→0 sqrtx+7-sqrt7 over x

Mathematics

1 answer:

Triss [41]2 years ago

6 0

Answer:

$\frac{1}{ 2\sqrt{7} }$

Step-by-step explanation:

$\lim_{x\to 0} \frac{ \sqrt{x + 7} - \sqrt{7} }{x} \\ \\ = \lim_{x\to 0} \frac{( \sqrt{x + 7} - \sqrt{7}) }{x} \times \frac{( \sqrt{x + 7} + \sqrt{7}) }{( \sqrt{x + 7} + \sqrt{7}) } \\ \\ = \lim_{x\to 0} \frac{( \sqrt{x + 7} )^{2} - (\sqrt{7})^{2} }{x( \sqrt{x + 7} + \sqrt{7})} \\ \\ = \lim_{x\to 0} \frac{( {x + 7} - {7}) }{x( \sqrt{x + 7} + \sqrt{7})} \\ \\ = \lim_{x\to 0} \frac{ {\cancel x}}{\cancel x( \sqrt{x + 7} + \sqrt{7})} \\ \\ = \lim_{x\to 0} \frac{ {1}}{\sqrt{x + 7} + \sqrt{7}} \\ \\ = \frac{1}{ \sqrt{0 + 7} + \sqrt{7} } \\ \\ = \frac{1}{ \sqrt{7} + \sqrt{7} } \\ \\ = \frac{1}{ 2\sqrt{7} }$

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a toy manufacturer has designed a new piece for use in building models. It is a cube with side lengths 7 mm and has a 3 mm in di

Ray Of Light [21]

Given that the cubical piece has side (s) 7 mm, and a cylindrical hole of diameter (d) as 3 mm.

The volume of the piece can be calculated as,

$\begin{gathered} \text{Volume of piece}=\text{ Volume of cube}-\text{ Volume of cylinder} \\ V=s^3-\frac{\pi}{4}d^2s \\ V=7^3-\frac{\pi}{4}(3)^2(7) \\ V=343-\frac{63\pi}{4} \\ V\approx293.52mm^3 \\ V\approx293.52\times10^{-9}\text{ }m^3 \end{gathered}$

It is mentioned that the material costs $207 per cubic meter, so the cost (c) of 1 piece is calculated as,

$\begin{gathered} \text{Cost of 1 piece}=\text{ Cost per unit volume}\times\text{ Volume of 1 piece} \\ c=207\times293.52\times10^{-9} \\ c\approx60758.64\times10^{-9} \end{gathered}$

This is the cost (in dollars) for 1 piece.

Given that the manufacturer wants to produce 1,000,000 such pieces, so the total cost (TC) is calculated as,

$\begin{gathered} \text{Total Cost}=\text{ Cost per piece}\times\text{ No. of pieces} \\ TC=60758.64\times10^{-9}\times1,000,000 \\ TC=60758.64\times10^{-9}\times10^6 \\ TC=60758.64\times10^{-3} \\ TC=60.75864 \\ TC\approx60.75 \end{gathered}$

Thus, the total prototypes will cost around $60.75

7 0

10 months ago

What did I do wrong so I don’t do it again on the test

denpristay [2]

Answer:

nothing

Step-by-step explanation:

all of them seem to be right. if you need practice work on alternate interior angles, exterior angles

8 0

1 year ago

Write a polynomial equation of degree 4 in standard form that has the solutions i, −i, 1, −1.

Brut [27]

Answer:

x⁴ + 2 x² + 1

Step-by-step explanation:

given solution of the polynomial

i, −i, 1, −1.

equation of the polynomial will be equal to

=(x - i)(x + i)(x - 1)(x + 1)

= (x² + i x - i x - i²)(x² + x - x + 1)

=(x² - (-1))(x² + 1 )

= (x² + 1)(x² + 1)

= x⁴ + x² + x² + 1

= x⁴ + 2 x² + 1

hence, the required polynomial equation is x⁴ + 2 x² + 1

4 0

2 years ago

Can y'all help me on 1,2,3,4,5,6,7

victus00 [196]

Look up the answers on google. Just look up lesson 3-2 rate of change and slope practice and problem solving: C
You should find all the answers there

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2 years ago

The balance owed on your credit card triples from $700 to $2100 in 12 months. If the balance is growing linearly then it would t

Fofino [41]

Answer:

If the balance is growing exponentially the balance after 45.4 months will be $44,925.94.

Step-by-step explanation:

The exponential growth equation is:

$f(x)=700(1+0.096)^{x}$

Compute the value of f (x) for <em>x</em> = 45.4 as follows:

$f(x)=700(1+0.096)^{x}$

$=700(1+0.096)^{45.4}\\\\=700\times (1.096)^{45.4}\\\\=700\times 64.1799181\\\\=44925.94267\\\\\approx 44925.94$

Thus, if the balance is growing exponentially the balance after 45.4 months will be $44,925.94.

5 0

3 years ago