MATHEMATICS
COLLEGE

D(t) =

(b) Using the expression obtained in part (a), find the distance between the two ships 4 hr after leaving the port. (Round your answer to two decimal places.)

mi

Answer:

Answer:

a) D(t) =

b) 178.885 miles

Step-by-step explanation:

Ship A travels north at the rate of 20 mph.

Ship B travels east at the rate of 40 mph.

After t hours, Ship A is at a distance of 20t miles from the origin.

Similarly, Ship B is at a distance of 40t miles from the origin.

(a) Distance D(t) =

=

=

=

(b) Distance between the two ships when t = 4,

=

= miles

= 80 * 2.236

= 178.885 miles

HIGH SCHOOL

What is the square root of negative 100?

The square root of negative 100 can be dissected step by step. The square root of 100 is 10 however there is no such thing as square root of something negative, thus the imaginary notion is applied. square root of -1 is equal to i .Hence the answer to this problem is 10 i.

Answer:

0 + 10i

Step-by-step explanation:

HIGH SCHOOL

William is reading a book for class. The book is 94 pages long. For the first assignment, William read 25 pages. For the second assignment, he read 37 pages. For the last assignment, he has to finish the book. How many pages does he have left to read?

The book has 94 pages. The following is a break down of the word problem:

94 - 25 = 69

69 - 37 = 32

He reads 32 pages for the last assignment.

94 - 25 = 69

69 - 37 = 32

He reads 32 pages for the last assignment.

Based on the question, we can found that :

25 + 37 + x = 94

62 + x = 94

x = 94 - 62

x = 32 Pages

hope this helps

25 + 37 + x = 94

62 + x = 94

x = 94 - 62

x = 32 Pages

hope this helps

MIDDLE SCHOOL

Fred peeled 9 carrots. Nancy peeled 6 carrot. how many fewer carrots did Nancy peeled than fred

9-6=3 she peeled 3 less than fred Or fred peeled 3 more than Nancy

MIDDLE SCHOOL

A lawn sprinkler spins in a circle. The sprinkler covers a radius of 4 feet. Which choice is the closest to the area of lawn that the sprinkler can cover?

Answer:

The correct answer is 50 feet

Step-by-step explanation:

Area= r^2*π = 4^2*π= 16π.

The final answer is 16π ft^2~

The final answer is 16π ft^2~

HIGH SCHOOL

Eduardo counted ten seconds between swing lightning and hearing thunder, and he knew that the lighting was about 2 miles away.if he counted four seconds between the next flash of lighting and thunder, about how far away was the lightning?

The Lightning was about 1/2 mile away from Eduardo.

MIDDLE SCHOOL

Consider this function. f(x) = |x – 4| + 6

If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

1.Since the domain of the original function is limited to x> 6, the range of the inverse function is y ≤ 6.

2.Since the domain of the original function is limited to x> 4, the range of the inverse function is y ≤ 1.

3.Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

4.Since the range of the original function is limited to y> 4, the domain of the inverse function is x ≥ 1.

Answer:

3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.

__

Comment on the answer choice:

The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.

Answer:

3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

Given absolute function,.

f(x) = |x-4|+6,

Since, an absolute function is defined for all real numbers,

So, the domain of f(x) is the set of all real numbers,

∴ Options (1) and (2) can not be true.

Now, for any real number,

|x-4| ≥ 0,

That is, f(x) ≥ 6,

Hence, the range ( possible value of output of a function ) of f(x) would be all real numbers greater than equal to 6,

I.e. Range of f(x) is, f(x) ≥ 6,

⇒ if y = f(x) ⇒ the range of the original function is limited to y > 6

∴ Option (4) can not be true,

Also, range of = Domain of

Hence, domain of is x ≥ 6.

HIGH SCHOOL

A spotlight is mounted on the eaves of a house 3030 feet above the ground. a flower bed runs between the house and the sidewalk, so the closest the ladder can be placed to the house is 1616 feet. how long a ladder is needed so that an electrician can reach the place where the light is mounted?

For this case we can model the problem as a rectangle triangle.

We have two sides.

We want to find the hypotenuse of the triangle.

We have then:

h = root ((30) ^ 2 + (16) ^ 2)

h = 34 feet

Answer:

is needed a ladder of 34 feet long so that an electrician can reach the place where the light is mounted

We have two sides.

We want to find the hypotenuse of the triangle.

We have then:

h = root ((30) ^ 2 + (16) ^ 2)

h = 34 feet

Answer:

is needed a ladder of 34 feet long so that an electrician can reach the place where the light is mounted

HIGH SCHOOL

tina is ordering a pair of shoes that cost 123.99 if the sales tax is 8% and the shipping is 19.99 what is the total cost

$153.82 is the total cost

256.99 have a nice day sir/maam

MIDDLE SCHOOL

A worker has four different job offers, each with a contract for seven years. Assuming the job descriptions are identical, which offer will allow the worker to earn the least over seven years? a starting salary of $125,000 with a 2% increase each year a starting salary of $110,000 with a 3% increase each year a starting salary of $98,000 with a 8% increase each year a starting salary of $105,000 with a 4% increase each year

Answer:

The answer is C

Step-by-step explanation:

I took the test

Answer:

The Answer is D) a starting salary of $105,000 with a 4% increase each year.

Step-by-step explanation: