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4 years ago

Why are domain restrictions for inverse trigonometric functions necessary?

1 answer:

8 0

A function must be one-to-one for it to have an inverse. As we are sure you know, the trig functions are not one-to-one and in fact they are periodic (i.e. their values repeat themselves periodically). So in order to define inverse functions weneed to restrict the.

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Rosita earns money by walking dogs after school and on weekends.She walks Madeline every other day,buddy every fourth day,and er

leonid [27]

On 12th day Rosita will walk all three dogs

Solution:

Given that Rosita earns money by walking dogs after school and on weekends

She walks Madeline every other day,buddy every fourth day,and ernie every third day

Today she walked all three dogs

To find: the day when she walked all three dogs

From given question,

Madeline is walked every other day means every two days: 2

Buddy is walked every fourth day: 4

Ernie is walked every third day: 3

To find the day when she walked all three dogs, we have to find the least common multiple (LCM) of 2, 4, 3

L.C.M of 2, 4, 3:

List all prime factors for each number

Prime Factorization of 2 shows:

2 is prime => $2^1$

Prime Factorization of 3 shows:

3 is prime => $3^1$

Prime Factorization of 4 is:

$2 \times 2 = 2^2$

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 = 12

Thus on 12th day Rosita will walk all three dogs

4 0

4 years ago

Describe two different sequences of transformations that will map ABCD to EFGH.

Harlamova29_29 [7]

The orientation of the figure has been changed by 90°, but the points are not all rotated around the same center. Translation is involved.

Translation before rotation:
.. translate down 5 units
.. rotate counterclockwise 90° about the origin

Translation after rotation:
.. rotate counterclockwise 90° about the origin
.. translate right 5 units

This can also be accomplished by a double reflection.
.. reflect across the line y=x
.. reflect across the line x=2.5

Or,
.. reflect across the line y=2.5
.. reflect across the line y=x

3 0

4 years ago

What is the equation of the graphed line in point-slope form? y – 1 = 2/3 (x + 3), y – 1 = 2/3 (x – 3), y + 1 = 2/3 (x – 3), y +

saul85 [17]

Slope = 4/6= 2/3
Intercept is -1 (I think just check with gradient on graph in doing in my head)

Y=MX+B
Y=2/3X-1 ( if my calculations add up

3 0

3 years ago

Income East and West of the Mississippi

dolphi86 [110]

Answer:

H0: μ1 = μ2

H1: μ1 ≠ μ2 ;

xbar1 - xbar2

Step-by-step explanation:

The Null hypothesis should state that there is no difference in average household income between those located east and west of the Mississippi

H0: μ1 = μ2

H1: μ1 ≠ μ2

Statistic from the sample that would be used to estimate difference

Statistic refers to the numerical characteristic derived from the sample.

To estimate the difference in the average household income between those located east and west of the Mississippi, we take the sample mean of the two groups

Group 1, East of Mississippi = xbar 1

Group 2, West of Mississippi River = xbar 2

xbar1 - xbar2

6 0

3 years ago

The price of an item has been reduced by $3.45. The new price is $22.36. What was the original price?

Anna11 [10]

Answer:

$25.81 is the original price

Step-by-step explanation:

All you would have to do is add the two numbers together to find the original price.

5 0

3 years ago