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1 year ago

5

The graph of f(x)=cos(x) is transformed to a new function, g(x), by stretching it horizontally by a factor of 4 and shifting it

1 unit up.
What is the equation of the new function g(x)?

1 answer:

pshichka [43]1 year ago

4 0

I hope this helps you :)

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A jogger runs around a circular track of radius 55 ft. Let (x,y) be her coordinates, where the origin is the center of the track

bagirrra123 [75]

Answer:

11.25 ft/sec

Step-by-step explanation:

Given that a jogger runs around a circular track of radius 55 ft.

. Let (x,y) be her coordinates, where the origin is the center of the track.

Then we know x,y satisfies the equation of the circle as

$x^2+y^2 = 55^2$

Let us differentiate this implicit function with respect to t

$2x \frac{dx}{dt} +2y \frac{dy}{dt} =0$

At this point, dx/dt 15 and x=33. y =44

Substitute to have

$2(33)(15) +2(44) \frac{dy}{dt}\\=0\\\frac{dy}{dt}=11.25$

dy/dt = 11.25 ft /s

6 0

2 years ago

30 points if correct. Select all the are true.

ivann1987 [24]

Answer:

Options B,C and E are correct choices.

Step-by-step explanation:

We are asked to find correct answers for the given box and whisker plots.

Let us our options one by one.

A. This option is false as lowest value for children's cereals is 30 and highest value for adults is 35.

B. This option is correct. We can see our upper value for combined range will be 60 and lower value will be 5 and range is upper value- lower value.

$60-5=55$

C. Since we know that we can find spread of data by its range.

$\text{Range for children's cereals}=60-30=30$

$\text{Range for adult's cereals}=60-30=30$

So option C is correct indeed.

D. This options is false because for adults mean and median are different while for children mean and median are same.

E. We can see that median for children's cereals is 45 and it is about 12 for adults.

We can see that $12*3$ . So median amount of sugar in children's cereals is 3 times as much as the median amount of sugar in adult's cereals.

Therefore, options B,C and E are correct choices.

4 0

2 years ago

Solve the system by substitution.<br> 3x + y = 20<br> -7y=x<br><br> Please help

alisha [4.7K]

9514 1404 393

Answer:

(x, y) = (7, -1)

Step-by-step explanation:

The expression for x makes it easy to use that for substitution.

3(-7y) +y = 20

-20y = 20 . . . . . collect terms

y = -1 . . . . . . . . . divide by -20

-7(-1) = x = 7 . . . use y in the second equation to find x

The solution is (x, y) = (7, -1).

8 0

2 years ago

Describe this translation.

Jet001 [13]

Answer:

D(4 units right, 2 up)

Step-by-step explanation:

You must pick a point which does not have an apostrophe. Then you see how which direction is goes (e.g left or right) and then you see the height (up and down) and combining all this the answer would be 4 units right, 2 up

3 0

2 years ago

Stefan sells Jim a bicycle for $175 and a helmet for $17. The total cost for Jim is 160% of what Stefan spent originally to buy

Nady [450]

Answer:

Stefan spend $120 originally.

Stefan made $72 by selling bicycle and helmet to Jim.

Step-by-step explanation:

Given:

Cost of bicycle = $175

Cost of Helmet = $17

Percent of total cost of Jim = 160% of original cost of Stefan

We need to find the Amount Stefan spend originally and money he made by selling the bicycle and helmet to Jim.

Solution:

Let the Amount Stefan spend originally be 'x'.

Total Cost of Jim is equal to sum of Cost of bicycle and Cost of Helmet.

framing in equation form we get;

Total Cost of Jim = $175+17 =\$192$

Now we know that;

Total Cost of Jim is equal to 160% of Amount Stefan spend originally.

framing in equation form we get;

$192 = \frac{160}{100}\times x\\\\192 =1.6x$

Dividing both side by 1.6 we get;

$\frac{192}{1.6}=\frac{1.6x}{1.6}\\\\x= \$120$

Hence Stefan spend $120 originally.

Now we can say that;

Money Stefan made is equal to Money Stefan spend originally minus Total Cost of Jim.

framing in equation form we get;

Money Stefan made = $192-120 =\$72$

Hence Stefan made $72 by selling bicycle and helmet to Jim.

7 0

2 years ago