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3 years ago

Which of the following is a step in evaluating: ∫ cos2 5x dx

Mathematics

1 answer:

Sav [38]3 years ago

4 0

From the following choices, the correct step in evaluating: ∫ cos2 5x dx is 1 - cos 10x / 2dx.

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Which equation is an example of the community property of multiplication

mafiozo [28]

its commutative property of multiplication.

it says result of product of numbers does not change by altering or reordering the numbers in multiplication.

A × B = B × A

2 × 3 = 6 = 3 × 2

5 0

3 years ago

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Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b

Ronch [10]

Answer:

$4^x-5=6$ gives the solution $x=\frac{\log(11)}{\log(4)}$ .

$4^{x-5}=6$ gives the solution $x=\frac{\log(6)}{\log(4)}+5$ .

Step-by-step explanation:

I will solve both interpretations.

If we assume the equation is $4^{x}-5=6$ , then the following is the process:

$4^x-5=6$

Add 5 on both sides:

$4^x=6+5$

Simplify:

$4^x=11$

Now write an equivalent logarithm form:

$\log_4(11)=x$

$x=\log_4(11)$

Now using the change of base:

$x=\frac{\log(11)}{\log(4)}$ .

If we assume the equation is $4^{x-5}=6$ , then we use the following process:

$4^{x-5}=6$

Write an equivalent logarithm form:

$\log_4(6)=x-5$

$x-5=\log_4(6)$

Add 5 on both sides:

$x=\log_4(6)+5$

Use change of base formula:

$x=\frac{\log(6)}{\log(4)}+5$

6 0

3 years ago

Solve for x using zeros of function method<br>-x³+2x²+x-2=0

Naya [18.7K]

Answer:

x = - 1, x = 1, x = 2

Step-by-step explanation:

The coefficients of the polynomial sum to zero, that is

- 1 + 2 + 1 - 2 = 0

This indicates that x = 1 is a zero

let x = - 1, then

- (- 1)³ + 2(- 1)² + (- 1) - 2 = 1 + 2 - 1 - 2 = 0

Thus x = - 1 is a zero

let x = 2

- (2)³ + 2(2)² + 2 - 2 = - 8 + 8 + 2 - 2 = 0

Thus x = 2 is a zero

The 3 zeros are x = - 1, x = 1, x = 2

3 0

3 years ago

Given that (-5,-6) is on the graph of f(x), find the corresponding point for this function -1/3f(x).

masya89 [10]

<h3>Answer: (-5, 2)</h3>

Explanation:

We multiply the y coordinate by -1/3 because of the notation (-1/3)*f(x). Recall that y = f(x). The x coordinate stays the same.

5 0

2 years ago

Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

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