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3 years ago

Is one side of a rectangular fish tank best represented by a point, line, plane, or ray?

Mathematics

1 answer:

Nataly_w [17]3 years ago

7 0

Probably a plane unless there's more to the question

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Use induction to prove that 2? ?? for any integer n>0 . Indicate type of induction used.

Hoochie [10]

Answer with explanation:

The given statement is which we have to prove by the principal of Mathematical Induction

$2^{n}>n$

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

$2^{k}>k$

---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement is true for, n=k+1.

$\rightarrow 2^{k+1}>k+1\\\\L H S=\rightarrow 2^{k+1}=2^{k}\times 2\\\\\text{Using 1}\\\\2^{k}>k\\\\\text{Multiplying both sides by 2}\\\\2^{k+1}>2k\\\\As, 2 k=k+k,\text{Which will be always greater than }k+1.\\\\\rightarrow 2 k>k+1\\\\\rightarrow2^{k+1}>k+1$

Hence it is true for, n=k+1.

So,we have proved the statement with the help of mathematical Induction, which is

$2^{k}>k$

3 0

3 years ago

Bob has 26 candy bars he eats 20 what does he have now?

abruzzese [7]

Bob has 6 candy bars and diabetes

8 0

3 years ago

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What do I do about the variables

Shkiper50 [21]

3x(9x² + 11x - 5) + 2(2x³ + 11x - 5x²) - 5x² + 8

Simplify.

27x³ + 33x² - 15x + 4x³ + 22x - 10x² - 5x² + 8

Add like terms.

(27x³ + 4x³) + (33x² - 10x²) + (-15x + 22x) + 8

Simplify.

31x³ + 23x² - 7x + 8

~Hope I helped!~

6 0

3 years ago

Given: ΔPSQ, PS = SQ

horrorfan [7]

<h2>Answer:</h2>

To solve this problem we will use Heron's formula:

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Where $a, \ b \ and \ c$ are the side lengths of the triangle and $s$ is the semiperimeter (half the perimeter of the triangle). We know that:

$Perimeter \ P=\triangle PSQ=PS+PQ+SQ: \\ \\ \triangle PSQ=P=50 \\ \\ Semiperimeter \ s: \\ \\ s=\frac{P}{2}=25$

Also:

$(I) \ PS=SQ \\ \\ (II) \ SQ-PQ = 1 \\ \\ (III) \ PS+PQ+SQ=50 \\ \\ \\ (I) \ into \ (III): \\ \\ SQ+PQ+SQ=50 \\ \\ \therefore (IV) \ 2SQ+PQ=50 \\ \\ From \ (II): \\ \\ PQ=SQ-1 \\ \\ (II) \ into \ (IV): \\ \\ 2SQ+(SQ-1)=50 \\ 3SQ-1=50 \\ 3SQ=51 \\ \\ \boxed{SQ=17} \\ \\ \boxed{PS=17} \\ \\ PQ=SQ-1=17-1 \therefore \boxed{PQ=16}$

Finally:

$A=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ A=\sqrt{s(s-PS)(s-SQ)(s-PQ)} \\ \\ A=\sqrt{s(s-17)(s-17)(s-16)} \\ \\ A=\sqrt{25(25-17)(25-17)(25-16)} \\ \\ \boxed{A=120}$

7 0

3 years ago

What is 8 4/15 minus 3 9/15?

Vsevolod [243]

first make them into improper fractions 124/15 and 54/15 then subtract so it would be 70/15 then turn it into a mixed number 4 10/15

3 0

3 years ago

Read 2 more answers