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3 years ago

Ing Up Angles

Mathematics

2 answers:

natima [27]3 years ago

7 0

Answer:

180° is the correct answer. Hope this helped :)

Step-by-step explanation:

irga5000 [103]3 years ago

6 0

Answer:

180°

Step-by-step explanation:

a convex polygon has n sides, then its interior angle sum is

S = ( n −2) × 180°

S=(3-2)*180°=180°

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A pair of corresponding side of two similar pentagons have length of 12cm and 28cm

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The ratio of their areas = 12^2 / 28^2

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3 years ago

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WARRIOR [948]

Answer:

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A student is given the rectangle and square shown. The student affirms that the two figures have the same perimeter. Is the stud

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3 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

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3 years ago

Find two positive real numbers whose product is a maximum. the sum is 80

Eduardwww [97]

Let's say the numbers are "a" and "b"

thus $\bf y=ab\qquad 
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b=80-a
\end{cases}\implies y=a(80-a)\implies y=80a-a^2\\\\
-----------------------------\\\\
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set the derivative to 0, and check the critical points, there's only one anyway

and do a first-derivative test, to see if it's a maximum

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3 years ago

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