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2 years ago

F(x)=(4t^2-t) (t^3-8t^2+12) in product rule.

1 answer:

6 0

$\dfrac{d}{dt} [(4t^2-t)(t^3 -8t^2+12)]\\\\\\=(4t^2-t)\dfrac{d}{dt}(t^3-8t^2 +12) + (t^3 -8t^2 +12) \dfrac{d}{dt} (4t^2 -t)\\\\\\=(4t^2 -t)(3t^2-16t)+(t^3-8t^2+12)(8t-1)\\\\=12t^4-64t^3 -3t^3+16t^2+8t^4-64t^3+96t-t^3+8t^2-12\\\\=20t^4-132t^3+24t^2+96t-12$

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Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x – 40? Determine the solution set algebr

Elden [556K]

Answer:

<u>Therefore, the value of x is 5.</u>

Step-by-step explanation:

We can match each equation to find the solutions.

$8x-40=x^{2}-2x-15$

$0=x^{2}-2x-8x-15+40$

$x^{2}-10x+25=0$

Now, we need solve this quadratic equation.

$(x-5)^{2}=0$

<u>Therefore, the value of x is 5.</u>

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I hope it helps you!

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3 years ago

Which equation represents a proportional relationship that has a constant of proportionality equal to One-fifth?

Sedbober [7]

Answer:

Option C)

$y = \dfrac{1}{5}x$

Step-by-step explanation:

We are given the following in the question:

$y \propto x$

Removing the sign of proportionality and introducing the constant of proportionality, we have

$y = kx$

where k is constant of proportionality.

We are given

$k = \dfrac{1}{5}$

Putting value, we get,

$y = \dfrac{1}{5}x = \dfrac{x}{5}$

Thus, the equation representing the relationship is

Option C)

$y = \dfrac{1}{5}x$

4 0

3 years ago

Read 2 more answers

Which fraction is equivalent to the decimal 0.15?With the line over.

melisa1 [442]

Answer:

Step-by-step explanation:

divide 100 and dive 15 by 5

7 0

3 years ago

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If I roll two six-sides dice, what is the probability that the sum of the numbers that show up on the dice is 3 or less?

liq [111]

Answer:

1/12

Step-by-step explanation:

first we have to find all the possibilities of getting a sum of 3 or less: 1+1 or 1+2 and we count the second combination 2 times because the numbers can be on either of the dices so we have a total of 3 possibilities. all the possible pairimg of dice are 6*6=36 because each dice has 6 sides and we can get either of them. so the probability would be the chance of getting a sum of 3 or less divided by all the diff combination which equals 3/36 or 1/12 which is roughly around 8.3%

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3 years ago

Find sin4a and cos4α, if tanα=3

Mashcka [7]

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

Sin2α = 2SinαCosα.

Cos2α = (Cosα)^2 - (Sinα)^2.

Sin4α can be written as Sin2(2α).

Similarly Cos4α can be written as Cos2(2α).

$Sin 4\alpha = 2Sin 2\alpha \times Cos 2\alpha = 2Sin 2\alpha \times(Cos^{2} \alpha - Sin^{2} \alpha ) = 4Sin \alpha \times Cos \alpha \times (Cos^{2} \alpha - Sin^{2} \alpha )$

It is given that tanα=3.

Sinα(Sinα) = $\frac{9}{10}$ [ $Sec^{2} \alpha = 1 + 3^{2} = 10.\\Cos^{2} \alpha = \frac{1}{10} \\Sin^{2} \alpha = 1 - \frac{1}{10} = \frac{9}{10}$ ], the values either be both positive or both negative, as the value of tanα is positive only on first and third quadrant.

Sin4α = $4\times \sqrt{(\frac{9}{10} )} \times \sqrt{(\frac{1}{10} )} \times (\frac{1 - 9}{10} ) = -\frac{4\times8\times3}{100} = -\frac{96}{100}$ .

Cos4α = $Cos^{2} 2\alpha - Sin^{2} 2\alpha = (Cos^{2} \alpha - Sin^{2} \alpha )^{2} - Sin^2 {2\alpha } = (Cos^{2} \alpha - Sin^{2} \alpha )^{2} - (2Sin \alpha Cos \alpha )^{2} = (-\frac{8}{10} )^{2} - \frac{4\times9}{100} = \frac{64 - 36}{100} = \frac{28}{100} = \frac{7}{25}$

7 0

3 years ago

F(x)=(4t^2-t) (t^3-8t^2+12) in product rule.​

F(x)=(4t^2-t) (t^3-8t^2+12) in product rule.