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4 years ago

Which transformation are needed to change the parent cosine function to y=3cos(10(x-pi))

Mathematics

2 answers:

BlackZzzverrR [31]4 years ago

6 0

Answer:

Step-by-step explanation:

First, we can transform y = cos(x) to y = 3*cos(x) by stretching the graph vertically by a factor of 3. At x = 0, the y value would now be 3 * 1 = 3 instead of 1 (the stretching would cause all new y-values to be 3 times their original values for any given x).

Now transforming y = 3*cos(x) to y = 3*cos(10*x) will stretch the graph horizontally by a factor of 10 (for any given y value, the new x value corresponding to it is 10 times the original x value).

Finally, to transform y = 3*cos(10*x) to y = 3*cos(10(x-pi)), shift the graph to the right by pi.

tensa zangetsu [6.8K]4 years ago

3 0

Answer:

It's B or C

Step-by-step explanation:

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The relative locations of a swing set, a garden, and a sandbox in Gina's backyard are shown in the diagram.

Archy [21]

Let us suppose the distance between the sandbox and garden is x feet.

Apply the sine law in the given triangle, we have

$\frac{x}{\sin 65^{\circ}}=\frac{36}{\sin 104^{\circ}}\\
\\
\text{On coss multiplying, we get}\\
x\sin 104^{\circ}=36\sin 65^{\circ}\\
\\
x=\frac{36\sin 65^{\circ}}{\sin 104^{\circ}}\\
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x\approx 33.6$

Therefore, in the nearest foot, the distance between the sandbox and garden is 34 foot.

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4 years ago

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Which expressions represent the distance between 1.8 and 9.4 on the number line?

sergiy2304 [10]

9.4 - 1.8 will tell you the distance between them

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3 years ago

Jason has a bar of chocolate he gives his friend 2/5 of his chocolate bar.what percentage of his bar of chocolate does he have l

ddd [48]

Answer:

60%

Step-by-step explanation:

he gave away 2/5 which is 40%. 100%-40% is 60%

8 0

3 years ago

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The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.

tatuchka [14]

Answer:

$y=\dfrac{7}{5}x-\dfrac{67}{5}$

Step-by-step explanation:

Slope-intercept form of a linear equation:

$y=mx+b$

where:

m is the slope.
b is the y-intercept.

Rearrange the given equation so that it is in slope-intercept form:

$\implies -5x-7y=-17$

$\implies -7y=5x-17$

$\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}$

Therefore, the slope of the given equation is -⁵/₇.

If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1. Therefore, their slopes will be negative reciprocals of each other.

Therefore, the slope of the line perpendicular to the given equation is:

$\sf m=\dfrac{7}{5}$

Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:

$\implies -5=\dfrac{7}{5}(6)+b$

$\implies -5=\dfrac{42}{5}+b$

$\implies b=-\dfrac{67}{5}$

Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:

$\implies y=\dfrac{7}{5}x-\dfrac{67}{5}$

Learn more about slope-intercept form here:

brainly.com/question/27317293

brainly.com/question/27926846

8 0

2 years ago

Mrs. Welch and her 5 children are shopping at a local grocery store. Each of the children will be allowed to select one box of c

lara [203]

<h3>Answer: 462</h3>

==================================================

Explanation:

Let's call the children A, B, C, D, E for the sake of simplicity. Also, let's have the children select in alphabetical order.

Child A has 11 choices to pick from.
Child B has 10 choices to pick from
Child C has 9 choices to pick from
Child D has 8 choices to pick from
Child E has 7 choices to pick from

We started at 11 and counted down by 1 until we had all the children selecting.

Multiply out these values: 11*10*9*8*7 = 55440

There are 55440 different permutations possible. If order mattered, then we would stop here. However, order does not matter because the cereals aren't ranked and their position doesn't matter. All that matters is what fills the grocery cart. In other words, imagine the kids jumbling up the boxes as they push around the cart, so the order would be irrelevant.

Consider a group of 5 items. There are 5! = 5*4*3*2*1 = 120 different ways to arrange the five items in this group. So for any 5 cereals picked, there are 120 ways to order them. But again, order doesn't matter, so we have to correct for this over-counting. We do this by dividing by 120

55440/120 = 462

------------------

If you want to use a formula, then plug n = 11 and r = 5 into the combination formula below and simplify.

n C r = (n!)/(r!(n-r)!)

11 C 5 = (11!)/(5!*(11-5)!)

11 C 5 = (11!)/(5!*6!)

11 C 5 = (11*10*9*8*7*6!)/(5!*6!)

11 C 5 = (11*10*9*8*7)/(5!)

11 C 5 = (11*10*9*8*7)/(5*4*3*2*1)

11 C 5 = 55440/120

11 C 5 = 462

We get the same answer.

8 0

3 years ago