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Leni [432]
3 years ago
13

If y= -3x7+2x3+ x, the derivative of y with respect to x is

Mathematics
1 answer:
larisa [96]3 years ago
8 0

Answer:

\frac{dy}{dx} = - 21x^{6} + 6x² + 1

Step-by-step explanation:

Differentiate each term using the power rule

\frac{d}{dx} (ax^{n} ) = nax^{n-1}

Given

y = - 3x^{7} + 2x³ + x , then

\frac{dy}{dx} = (7 × - 3 )x^{6} + (3 × 2)x² + (1 × 1 )x^{0}

    = - 21x^{6} + 6x² + 1

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An experiment consists of ranomly drawing three cards in succession without replacement from a standard deck of 52 cards. Let A
nadya68 [22]

Answer:

0.0045248 ;

0.1312218 ;

0.0001809 ;

0.1659729

Step-by-step explanation:

Number of Kings in deck = 4

Total number of cards in deck = 52

Picking without replacement :

A = King on first draw :

P(A) = 4 / 52

A = King on 2nd draw :

P(B) = 3 / 51

A = King on 3rd draw :

P(C) = 2 / 50

1.) P(A n B) = P(A) * P(B)

P(A n B) = 4/52 * 3/51 = 12 / 2652 = 0.0045248

2.) P(A u B) = P(A) + P(B) - P(AnB)

P(AuB) = 4/52 + 3/51 - 0.0045248 = 0.1312218

3.) P(A ∩ B ∩ C) = P(A) * P(B) * P(C)

P(A ∩ B ∩ C) = 4/52 * 3/51 * 2/50 = 0.0001809

4.) P(A U B U C) =

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) - P(AnBnC)

P(AnC) = P(A) * P(C) = 4/52 * 2/50 = 0.0030769

P(BnC) = P(B) * P(C) = 3/51 * 2/50 = 0.0023529

4/52 + 3/51 + 2/50 - 0.0045248 - 0.0030769 - 0.0023529 + 0.0001809 = 0.1659729

6 0
3 years ago
Please help!!As soon as possible!!
pychu [463]

Answer: Their equations have different y-intercept but the same slope

Step-by-step explanation:

Since, the slope of the line passes through the points (2002,p) and (2011,q) is,

m_1 = \frac{q-p}{2011-2002} = \frac{q-p}{9}

Similarly, the slope of the line asses through the points (2,p) and (11,q) is,

m_2 = \frac{q-p}{11-2} = \frac{q-p}{9}

Since, m_1 = m_2

Hence, both line have the same slope.

Now, the equation of the line one having slope m_1 and passes through the point (2002,p) is,

y - p = \frac{q-p}{9}(x-2002)

Put x = 0 in the above equation,

We get, y = \frac{2000(p-q)}{9}+p

The y-intercept of the line one is (0, \frac{2000(p-q)}{9}+p)

Also, the equation of second line having slope m_2 and passes through the point (2,p)

y-p=\frac{q-p}{9}(x-2)

Put x = 0 in the above equation,

We get, y = \frac{2(p-q)}{9}+p

The y-intercept of the line one is (0, \frac{2(p-q)}{9}+p)

Thus, both line have the different y-intercepts.

⇒ Third option is correct.

6 0
3 years ago
Please Help!!
algol13
When you see questions of this nature, test the individual inequalities and look out for their intersection.

For
y < \frac{2}{3} x
Choose a point in the lower or upper half plane created by the line
y = \frac{2}{3} x
The above line is the one which goes through the origin.

Now testing (1,0) yields,

0 < \frac{2}{3} (1)
That is,

0 < \frac{2}{3}
This statement is true. So we shade the lower half of
y = \frac{2}{3} x

For
y \geqslant - x + 2
We test for the origin because, it is not passing through the origin.

0 \geqslant - (0) + 2
This yields
0 \geqslant 2
This statement is false so we shade the upper half.

The intersection is the region shaded in B. The top right graph
8 0
3 years ago
Sin2alpha+cos2alpha-cos6alpha/sin4alpha+2sin²alpha-1<br><br> if alpha is -135°​
balandron [24]

Answer:

=  \frac{\sin(2 \alpha )  +  \cos(2 \alpha )  -  \cos(6 \alpha ) }{ \sin(4 \alpha )  + 2 { \sin }^{2}  \alpha  - 1}  \\  =  \frac{ \sin( - 270) +  \cos( - 270)  -  \cos( - 810)  }{ \sin( - 540)  + 2 { \sin }^{2}( - 135) - 1 }  \\  =  \frac{1}{ - 2}  \\  =  - 0.5

5 0
2 years ago
Quiero saber como se resuelve este problema ? 6+2-a3
Andreyy89
Answer: 8-a^3
You just simply the expression.
6 0
3 years ago
Read 2 more answers
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