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tensa zangetsu [6.8K]
3 years ago
11

If f(x + 2) = 6x2 + 5x − 8. Find f(6).

Mathematics
1 answer:
Blababa [14]3 years ago
6 0

Answer:

  108

Step-by-step explanation:

We can rewrite f(x+2) to make it easier to evaluate:

  f(x+2) = (6x +5)x -8

Since we want f(6), we want x+2 = 6, or x=4.

  f(6) = (6·4 +5)·4 -8 = 29·4 -8

  f(6) = 108

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Setler79 [48]
You can find the numerical part of the answer because it is the same on the right side.

For example:
 ¹      <<==== Regrouped
  89
+
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146   <<=== I had to press space so I could position it.

So that also happens in subtraction, the left side can be found by doing the same steps in the right column.
For example:

67
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5 0
3 years ago
What is the value of n in the equation shown<br> below?<br> 2² x 2 = (24)
ANEK [815]

The answer I get


8=24
No solution
3 0
3 years ago
PLZ HELP!!! Use limits to evaluate the integral.
Marrrta [24]

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

r_i=\dfrac{2i}n

where 1\le i\le n. Each interval has length \Delta x_i=\frac{2-0}n=\frac2n.

At these sampling points, the function takes on values of

f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}

We approximate the integral with the Riemann sum:

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3

Recall that

\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4

so that the sum reduces to

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}

Just to check:

\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28

4 0
2 years ago
5. The recursive algorithm given below can be used to compute gcd(a, b) where a and b are non-negative integer, not both zero.
s2008m [1.1K]

Implementating the given algorithm in python 3, the greatest common divisors of <em>(</em><em>124</em><em> </em><em>and</em><em> </em><em>244</em><em>)</em><em> </em>and <em>(</em><em>4424</em><em> </em><em>and</em><em> </em><em>2111</em><em>)</em><em> </em>are 4 and 1 respectively.

The program implementation is given below and the output of the sample run is attached.

def gcd(a, b):

<em>#initialize</em><em> </em><em>a</em><em> </em><em>function</em><em> </em><em>named</em><em> </em><em>gcd</em><em> </em><em>which</em><em> </em><em>takes</em><em> </em><em>in</em><em> </em><em>two</em><em> </em><em>parameters</em><em> </em>

if a>b:

<em>#checks</em><em> </em><em>if</em><em> </em><em>a</em><em> </em><em>is</em><em> </em><em>greater</em><em> </em><em>than</em><em> </em><em>b</em>

return gcd (b, a)

<em>#if</em><em> </em><em>true</em><em> </em><em>interchange</em><em> </em><em>the</em><em> </em><em>Parameters</em><em> </em><em>and</em><em> </em><em>Recall</em><em> </em><em>the</em><em> </em><em>function</em><em> </em>

elif a == 0:

return b

elif a == 1:

return 1

elif((a%2 == 0)and(b%2==0)):

<em>#even</em><em> </em><em>numbers</em><em> </em><em>leave</em><em> </em><em>no</em><em> </em><em>remainder</em><em> </em><em>when</em><em> </em><em>divided</em><em> </em><em>by</em><em> </em><em>2</em><em>,</em><em> </em><em>checks</em><em> </em><em>if</em><em> </em><em>a</em><em> </em><em>and</em><em> </em><em>b</em><em> </em><em>are</em><em> </em><em>even</em><em> </em>

return 2 * gcd(a/2, b/2)

elif((a%2 !=0) and (b%2==0)):

<em>#checks</em><em> </em><em>if</em><em> </em><em>a</em><em> </em><em>is</em><em> </em><em>odd</em><em> </em><em>and</em><em> </em><em>B</em><em> </em><em>is</em><em> </em><em>even</em><em> </em>

return gcd(a, b/2)

else :

return gcd(a, b-a)

<em>#since</em><em> </em><em>it's</em><em> </em><em>a</em><em> </em><em>recursive</em><em> </em><em>function</em><em>,</em><em> </em><em>it</em><em> </em><em>recalls</em><em> </em><em>the function</em><em> </em><em>with </em><em>new</em><em> </em><em>parameters</em><em> </em><em>until</em><em> </em><em>a</em><em> </em><em>certain</em><em> </em><em>condition</em><em> </em><em>is</em><em> </em><em>satisfied</em><em> </em>

print(gcd(124, 244))

print()

<em>#leaves</em><em> </em><em>a</em><em> </em><em>space</em><em> </em><em>after</em><em> </em><em>the</em><em> </em><em>first</em><em> </em><em>output</em><em> </em>

print(gcd(4424, 2111))

Learn more :brainly.com/question/25506437

6 0
2 years ago
&lt;333
Gnom [1K]
(210+200+190+180+300+150+90+x)/8=200
(1320+x)/8=200 /*8
1320 +x=1600
X=1600-1320
X= 280
6 0
2 years ago
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