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zvonat [6]
3 years ago
7

Find derivative of 2cosx+2cos2x

Mathematics
1 answer:
Zarrin [17]3 years ago
7 0
Derivitive of cosx=-sinx
dy/dx sinx=cosx
and use chain rue

2cosx=-2sinx
2cos2x=-4sin2x
so
-2sinx-4sin2x id the deritivitve
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F(x) has only one x-intercept when x=0

g(x)=-x^2-6

g(x)=-(x^2+6) so g(x) will have no x-intercepts as its maximum value will be -6.

g(x) is f(x) reflected about the x axis and shifted downwards by 6 units.
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A cyclist travels 4 miles in 20 minutes and then a further 6 miles in 30 minutes without stopping. Calculate the cyclist's avera
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11 miles per hr because 10 miles took 50 minutes so add 1 mile and it is 1hr. Which is 11 miles per hr

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What is an expression equivalent to 4d-4?
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3 years ago
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Solve the 3 × 3 system shown below. Enter the values of x, y, and z. X + 2y – z = –3 (1) 2x – y + z = 5 (2) x – y + z = 4 (3)
Svet_ta [14]
<h2>Answer:</h2>

\boxed{x=1, \y=-1, \ z=2}

<h2>Step-by-step explanation:</h2>

We will use the Gaussian elimination method to solve this problem. To do so, let's follow the following steps:

Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:

\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}

Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:

\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}

Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:

\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}

Step 4: solve for z, then for y, then for x:

\frac{ 1 }{ 5 } ~ z & = \frac{ 2 }{ 5 } \\ \\ \boxed{z & = 2}

-5y+3z &= 11\\-5y+3\cdot 2 &= 11\\ \\ \boxed{y &= -1}

By substituting y=-1 \ and \ z=2 into the first equation, we get the x. So:

x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}

6 0
3 years ago
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If you divide one of the roots of the equation 4x2+bx−27=0 by the other root, the quotient will be −3. Find b.
klio [65]
<h3>Answer:</h3>

  ±12   (two answers)

<h3>Explanation:</h3>

Suppose one root is <em>a</em>. Then the other root will be -3<em>a</em>. The product of the two roots is the ratio of the constant coefficient to the leading coefficient:

  (<em>a</em>)(-3<em>a</em>) = -27/4

  <em>a</em>² = -27/(4·(-3)) = 9/4

  <em>a</em> = ±√(9/4) = ±3/2

Then the other root is

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We know the opposite of the sum of these roots will be the ratio of the linear term coefficient to the leading coefficient: b/4, so ...

  -(a + (-3a)) = b/4

  2a = b/4

  b = 8a = 8·(±3/2)

  b = ±12

_____

<em>Check</em>

For b = 12, the equation factors as ...

  4x² +12x -27 = (2x -3)(2x +9) = 0

  It has roots -9/2 and +3/2, the ratio of which is -3.

For b = -12, the equation factors as ...

  4x² -12x -27 = (2x +3)(2x -9) = 0

  It has roots 9/2 and -3/2, the ratio of which is -3.

4 0
3 years ago
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