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2 years ago

Please answer as quick as you can! Answer questions 1-3 please!

Mathematics

1 answer:

Aliun [14]2 years ago

6 0

1) his time would have to be less than 11.54
2)each member would have to run a time of about 11.91
3) Assuming that Dwane ran a time of 11.53 the average amount of time it took each member to run the 100 meters will be about 12.2 seconds per 100 meters

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All possible solutions for 6sin^2(3x)=-3

vova2212 [387]

Answer:

Please check the step-by-step explanation for the answer.

Step-by-step explanation:

Considering the trigonometric expression

$6sin^2\left(3x\right)=-3$

Steps

$\mathrm{Let:\:}\sin \left(3x\right)=u$

$6u^2=-3$

$\mathrm{Divide\:both\:sides\:by\:}6$

$\frac{6u^2}{6}=\frac{-3}{6}$

$u^2=-\frac{1}{2}$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$u=\sqrt{-\frac{1}{2}},\:u=-\sqrt{-\frac{1}{2}}$

$\mathrm{Simplify}\:\sqrt{-\frac{1}{2}}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}$

$=\sqrt{-1}\sqrt{\frac{1}{2}}$

$\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i$

$=i\sqrt{\frac{1}{2}}$

Similarly,

$-\sqrt{-\frac{1}{2}}=\quad -i\sqrt{\frac{1}{2}}$

So,

$u=i\sqrt{\frac{1}{2}},\:u=-i\sqrt{\frac{1}{2}}$

$\mathrm{Substitute\:back}\:u=\sin \left(3x\right)$

$\sin \left(3x\right)=i\sqrt{\frac{1}{2}},\:\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}$

So,

$\sin \left(3x\right)=i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}$

and

$\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}$

$\mathrm{Combine\:all\:the\:solutions}$

$\mathrm{No\:Solution\:for}\:x\in \mathbb{R}$

Keywords: trigonometric equation, solution

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5 0

3 years ago

How do I graph in R for the following inequality?<br> -3 ≤ xV-6 > x

dedylja [7]

Answer:

I don't know if this will help you or not and I'm sorry if it doesn't.

Have a great day! :)

(The graph is what I got when I graphed the equation.)

4 0

3 years ago

Determine The Value Of X

Nastasia [14]

Step-by-step explanation:

x = 40 degree

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8 0

3 years ago

Find four consecutive positive integers such that the product of the first and fourth is four less than twice the first multipli

r-ruslan [8.4K]

Four consecutive integers... n, n+1, n+2, n+3.

The product of the 1st and 4th is four less than twice the 1st multiplied by the 4th.

n(n+3)=2n(n+3)-4 perform indicated multiplications...

n^2+3n=2n^2+6n-4 subtract n^2 from both sides

3n=n^2+6n-4 subtract 3n from both sides

n^2+3n-4=0 factor

n^2-n+4n-4=0

n(n-1)+4(n-1)=0

(n+4)(n-1)=0, and since n>0

n=1

So the four numbers are 1, 2, 3, 4

check...

1(4)=2(1)4-4

4=8-4

4=4

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3 years ago

Lucia and Maria are business women who decided to invest their money by buying farmland in Brazil. They started their investment

melamori03 [73]

The Answer is 7, I promise with all of my heart.

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3 years ago

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