How far will the feather have fallen if it reaches the surface in 9.00 seconds? Given: g on moon = -1.63 meters/second2

Answers

Answer 1

Answer: -1.63 times 9.00 = -6.57 meters in 9.00 seconds

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A baseball player had 4 hits in 8 games. At this rafe, how many hits will the baseball player have in the next 28 games?

Answers

Answer: About 14 hits

Which of the following is the graph of f(x) = x2 − 5x + 4?

Answers

Answer:

refer attachment for the graph.

Step-by-step explanation:

Given: The equation $f(x)=x^2-5x+4$

We have to draw the the graph for the given equation.

Consider the given equation $f(x)=x^2-5x+4$

The vertex of the parabola of the form $f(x)=ax^2+bx+c$ is given by $x=-(b)/(2a)$

Here, a = 1 , b = -5 and c = 4

Thus, vertex is

$x_v=-(\left(-5\right))/(2\cdot \:1)=(5)/(2)$

Also, the y coordinate at $x=(5)/(2)$ is

$y_v=\left((5)/(2)\right)^2-5\cdot (5)/(2)+4$

Simplify, we get,

$y_v=-(9)/(4)$

Thus, The vertex of parabola is $\left((5)/(2),\:-(9)/(4)\right)$

y - intercept is the point where x = 0

Plug x = 0 in given equation $f(x)=x^2-5x+4$

$f(0)=0^2-5(0)+4=4$

Thus, y - intercept is (0,4)

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

$x^2-5x+4=0$

Solving the given quadratic equation using quadratic formula ,we have

$x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)$

we have a = 1 , b = -5 and c = 4

$x_(1,\:2)=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:1\cdot \:4))/(2\cdot \:1)$

Simplify, we have,

$x_(1,2)=(5\pm√(9))/(2)$

Thus, $x_1=4, x_2=1$

Thus, The x - intercept are (4,0) and (0,1)

Plot the graph and we obtain as shown below.

I made a graph of the equation hope this helps.

Prove that $cos 3 x =4 cos ^(3)x-3 cos x$

Answers

$cos3x=4cos^3x-3cosx\n\nL=cos(2x+x)=cos2xcosx-sin2xsinx\n\n=(cos^2x-sin^2x)cosx-2sinxcosxsinx\n\n=cos^3x-sin^2xcosx-2sin^2xcosx\n\n=cos^3x-3sin^2xcosx\n\n=cos^3x-3cosx(1-cos^2x)\n\n=cos^3x-3cosx+3cos^3x\n\n=4cos^3x-3cosx=R$

$cos(a+b)=cosa\ cosb-sina\ sinb\n\nsin^2a+cos^2b=1\to sin^2a=1-cos^2b\n\ncos2a=cos^2a-sin^2a\n\nsin2a=2sina\ cosa$

Convert the following to a fraction:

0.363636

Answers

0.363636 = 90909
250000
as a fraction
To convert the decimal 0.363636 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
0.363636 = 0.363636
1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 6 numbers after the decimal point, we multiply both numerator and denominator by 1000000. So,
0.363636
1
= (0.363636 × 1000000)
(1 × 1000000)
= 363636
1000000
.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(363636,1000000) = 4. So,
(363636÷4)
(1000000÷4)
= 90909
250000
when reduced to the simplest form.

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Hope it works!

Need help solving this proportion....
x\4 = 5\7