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Annette [7]
3 years ago
13

It says find the surface area of the pyramid. and the answer if the surface area is.

Mathematics
1 answer:
Debora [2.8K]3 years ago
6 0

Answer:

you need to add all those numbers

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Calculate the limit values:
Nataliya [291]
A) This particular limit is of the indeterminate form,
\frac{ \infty }{ \infty }
if we plug in infinity directly, though it is not a number just to check.

If a limit is in this form, we apply L'Hopital's Rule.

's
Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_ {x \rightarrow \infty } \frac{( ln(x ^{2} + 1 ) ) '}{x ' }
So we take the derivatives and obtain,

Lim_ {x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ \frac{2x}{x^{2} + 1} }{1}

Still it is of the same indeterminate form, so we apply the rule again,

Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ 2 }{2x}

This simplifies to,

Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ 1 }{x} = 0

b) This limit is also of the indeterminate form,

\frac{0}{0}
we still apply the L'Hopital's Rule,

Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ (tanx)'}{x ' }

Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ \sec ^{2} (x) }{1 }

When we plug in zero now we obtain,

Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ \sec ^{2} (0) }{1 } = \frac{1}{1} = 1
c) This also in the same indeterminate form

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ ({e}^{2x} - 1 - 2x)'}{( {x}^{2} ) ' }

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ (2{e}^{2x} - 2)}{ 2x }

It is still of that indeterminate form so we apply the rule again, to obtain;

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ (4{e}^{2x} )}{ 2 }

Now we have remove the discontinuity, we can evaluate the limit now, plugging in zero to obtain;

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = \frac{ (4{e}^{2(0)} )}{ 2 }

This gives us;

Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } =\frac{ (4(1) )}{ 2 }=2

d) Lim_ {x \rightarrow +\infty }\sqrt{x^2+2x}-x

For this kind of question we need to rationalize the radical function, to obtain;

Lim_ {x \rightarrow +\infty }\frac{2x}{\sqrt{x^2+2x}+x}

We now divide both the numerator and denominator by x, to obtain,

Lim_ {x \rightarrow +\infty }\frac{2}{\sqrt{1+\frac{2}{x}}+1}

This simplifies to,

=\frac{2}{\sqrt{1+0}+1}=1
5 0
3 years ago
The sum of the measures of the interior angles of a polygon with n sides is
defon

ANSWER

(n - 2) \times 180 \degree

EXPLANATION

The sum of the interior angles of a triangle is 180°

We can rewrite this as:

1 \times 180 \degree = (3 - 2) \times 180 \degree = 180 \degree

The sum of interior angles of a quadrilateral is 360°

We can also rewrite this as:

2 \times 180 \degree = (4- 2) \times 180 \degree = 360 \degreeIn general an n-sided polygon has

the sum of the interior angles given by the formula:

(n - 2) \times 180

8 0
3 years ago
Help me please and thank you
fiasKO [112]

Answer:

$51.70

Step-by-step explanation:

I don't know how to explain it actually so I am just going to do this...

y= 0.1(x + 20) +7

y=0.1x + 2 + 7

y=0.1x +9

y=0.1(427)+9

y=42.7+9

y=51.7

So, maybe the answer is $51.70.

7 0
2 years ago
In a southern state, it was revealed that 5% of all automobiles in the state did not pass inspection. what is the probability th
Jobisdone [24]
Fortune Battle Royale
8 0
2 years ago
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down,drag into the correct p
boyakko [2]

Answer:

\boxed{\sf \ \ 9x^2-18x-7 \ \  divided \ by \ (3x+1) \ is \ (3x-7) \ }

Step-by-step explanation:

Hello,

let's find a and b reals so that

9x^2-18x-7=(3x+1)(ax+b)

(3x+1)(ax+b)=3ax^2+(3b+a)x+b

we identify the terms in x^2

   9 = 3a

we identify the terms in x

   -18 = 3b + a

we identify the constant terms

   -7 = b

so ti goes with a = 9/3 = 3, b = -7

so we can write

9x^2-18x-7=(3x+1)(3x-7)

so 9x^2-18x-7 \ divided \ by \ (3x+1) \ is \ (3x-7)

hope this helps

8 0
3 years ago
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