If you stand on a ship in a calm sea, then your height x (in feet) above sea level is related to the farthest distance y (in miles) that you can see by the equation: y=sqrt (1.5x+(x/5280)^2) how high up do you have to be to be able to see 10mi?

Answers

Answer 1

We are given the relation between the height (in feet) and the distance (in miles) as follows:
y = sqrt(1.5x + (x/5280)^2).

We want to know the height (x) that makes the distance (y) = 10 miles

So, we will simply substitute in the above equation with y = 10 and calculate x as follows:
10 = sqrt(1.5x + (x/5280)^2)
we will square both sides to get rid of the root:
100 = 1.5x + (x/5280)^2
1.5x + (x/5280)^2 - 100 = 0
(x-66.11475)(x+7986.1147) = zero
either x = 66.11475 feet (accepted solution)
or x = -7986.1147 feet (rejected solution as no height is in negative)

Answer 2

Final answer:

To see 10 miles into the distance, one must be approximately 593.4 feet above sea level. This is calculated by substituting y = 10 into the given formula and solving for x.

Explanation:

The student's question involves finding how high above sea level they must be to see a distance of 10 miles. We begin with the equation given:

y = sqrt(1.5x + (x/5280)^2)

We need to solve this equation for x when y is 10 miles. First, we substitute 10 for y and square both sides of the equation to eliminate the square root:

10^2 = 1.5x + (x/5280)^2100 = 1.5x + x^2/(5280^2)

Multiply through by 5280^2 to simplify:

100(5280^2) = 1.5x(5280^2) + x^2100(5280^2) = 7920x^2 + x^2100(5280^2) = 7921x^2

Now, we solve for x:

x^2 = 100(5280^2) / 7921x = sqrt(100(5280^2) / 7921)x ≈ sqrt(2787840000 / 7921)x ≈ sqrt(352000)x ≈ 593.4 feet

Therefore, a person needs to be approximately 593.4 feet above sea level to see 10 miles into the distance.

Related Questions

Which number is equivalent to 35 %

Answers

0.35 is equivalent to 35%

0.35 and the number 35 is equivalent

Alex earns an allowance of $6 per week. He also received $35 as a birthday gift from his grandmother. How many weeks (w) will it take for Alex to save $110?

Answers

35+6x[tex] \geq [/tex]110
6x[tex] \geq [/tex]75
x[tex] \geq [/tex]12.5

between which two square roots can u find 3.14

Answers

The square root of 9 is 3
The square root of 16 is 4

Between those square roots lies 3.14

how do you solve for
-40=-2(3n-4)

Answers

-40 = -2(3n-4)

-40 = -6n +8

-40 - 8 = -6n +8 - 8

-48/-6 = -6n/ -6

8 = n

n = 8

hope this helps

34/5 less than y is -51/10

Answers

y - 34/5 = -51/10

I'm not sure if you wanted me to solve this but I will anyways

y = -51/10 +34/5
y = -51/10 + 68/10
y = 17/10

Hope this helps!

Y-(34/5)=-(51/10) ,
Y - (34/5) + (34/5) =-(51/10) +(34/5),
Y= -(51/10) +(68/10) (found common denominator),
Y=(17/10)

To have a batting averages over .500,how many hits in 45 times at bat would Rail and Karen need?

Answers

A batting average is simply the ratio of hits/at-bats. So if Karen were up to bat 1,000 times and she got a hit 444 times, that makes her batting average 444/1,000=.444 or another way to solve this problem is to multiply 0.500(0.5)to 45 and you would get 22.5. Hope I helped!

Travis has a savings account that his parents opened for him. It pays 6% annual interest. His uncle also opened an account for him, but it pays 8% annual interest. If there is $500 more in the account that pays 6%, and the total interest from both accounts is $100, how much money is in each of the accounts?

Answers

so let's say the amounts are "a" and "b", at 6% and 8% respectively.

how much is 6% of a? well (6/100) * a, or 0.06a.
how much is 8% of b? well (8/100) * b, or 0.08b.

so hmm whatever "a" and "b" amounts are, we know that their yield is $100, thus 0.06a + 0.08b = 100.

now, there's more money in "a" than in "b", 500 bucks more, so whatever "b" is, we know that a = b + 500.

[tex]\bf \begin{cases} 0.06a+0.08b=100\\ \boxed{a}=b+500\\ ----------\\ 0.06\left( \boxed{b+500} \right)+0.08b=100 \end{cases} \\\\\\ 0.06b+0.08b+30=100\implies 0.02b=70\implies b=\cfrac{70}{0.02} \\\\\\ b=3500[/tex]

how much was deposited in the 6% one? well, a = b + 500.

Get confused with all the powers??? Answer??

Answers

Hello There!

The rules with powers or exponents are:
If you multiply, you add them
If you divide, you subtract them
And if you multiply with brackets, you multiply the numbers.
Therefore this is what you get:
49[tex] d^{16} [/tex]

Hope This Helps You!
Good Luck :)

(7d^8)²

7 x 7 = 49

(d^8)² = d^64

d^64 + 49 is your answer

hope this helps

Explain how to use grouping symbols to organize information appropriately.

Answers

The use of grouping symbols in math shows us which part of the problem or expression should be done first. Brackets, braces and parentheses are common grouping symbols used in mathematics. If no symbol is shown between brackets, forexample, (3+7)(8+1) it means that you should multiply after simplifying the operations inside the brackets.

Final answer:

Using grouping symbols helps organize and clarify information in mathematical expressions.

Explanation:

Grouping symbols are essential in organizing information effectively. By using grouping symbols like parentheses, brackets, or braces, you can prioritize operations, clarify relationships, and maintain accuracy in mathematical expressions. For example, in the expression 2 x (3 + 5), the grouping symbols clarify that the addition inside the parentheses should be done first before multiplying the result by 2.

in order to lose 1 pounds one, must burn off 3500 calories. To burn off 100 calories you must bicycle at 9 mph for 15 minutes. How long do you have to bicycle at 9 mph to lose 7 ponds?

Answers

To burn off one pound,
100 cal * x = 3500
x= 35
You'll need 35 15 minutes to burn off one pound so, 525 minutes per pound, and you need to lose 7 pounds so,
525*7 = 3675 minutes OR 61.25 hours

Final answer:

The student needs to bicycle for a total of 61.25 hours at 9 mph to lose 7 pounds.

Explanation:

The subject of the question is Mathematics, and it relates to calculating the amount of exercise needed to achieve a certain weight loss goal. The student wants to know how long they must bicycle at 9 mph to lose 7 pounds.

First, we know that to lose 1 pound, one must burn off 3,500 calories. Since 15 minutes of bicycling at 9 mph burns 100 calories, we calculate the time required to burn 3,500 calories (for 1 pound) and then multiply by 7 for the 7 pounds.

To lose 1 pound:
3,500 (calories per pound) / 100 (calories per 15 minutes) = 35 (15 minute sessions to lose 1 pound).

35 sessions * 15 minutes = 525 minutes.

To lose 7 pounds:
525 minutes (to lose 1 pound) * 7 = 3,675 minutes.

3,675 minutes can be converted into hours by dividing by 60 minutes per hour:

3,675 minutes / 60 = 61.25 hours.

Therefore, the student needs to bicycle for a total of 61.25 hours at 9 mph to lose 7 pounds.

You mow your lawn in 5 hours and earn $45. What is your hourly wage?

Answers

first you divide the total with the amount of hours you worked

45/5 = 9

9 is the amount of money you earn per hour

so your answer is $9 per hour

hope this helps

Angles θ and Φ are complementary, and θ = pi/12 Find the measure of Φ.

Answers

sum of complement angles = a right angle = π/2
so
measure of Φ = π/2 - π/12
measure of Φ = 6π/12 - π/12
measure of Φ = 5π/12

answer
5π/12

Answer:

sum of complement angles = a right angle = π/2

measure of Φ = π/2 - π/12

measure of Φ = 5π/12 + π/12

measure of Φ = 6π/12

6π/12 = π/2

answer

π/2

In the 1st generation, there are 4 monkeys on the island.....

Answers

General explicit formula:
[tex]a_n = a_1 (r^{n-1})[/tex]

You are given initial value of 4.
a1 = 4

The rate of growth is it doubles every generation or multiplies by 2.
r = 2

Answer:
[tex]a_n = 4 (2^{n-1})[/tex]

Answer:

you're answer is letter D.

Step-by-step explanation:

"a man drove 10 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work. if a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?"

Answers

Answer:

11.2 miles

Step-by-step explanation:

We can create a triangle from the information given.

We can call the starting point (0,0) in the coordinate system.

10 mi east - 10 miles to the right. then,5 mi north - 5 miles above

See the attached picture. The direct distance is labeled as x.

Now we need to find x using pythagorean theorem.

Pythagorean Theorem = leg²+leg²=hypotenuse²

Solving for x:

[tex]10^2+5^2=x^2\\100+25=x^2\\125=x^2\\x=\sqrt{125}\\x=11.18[/tex]

Rounding to nearest tenth, we have 11.2 miles

We have that the distance is mathematically given as

AB=11.2miles

From the question we are told

"a man drove 10 mi directly east from his home, made a left turn at an intersection, and then traveled 5 mi north to his place of work.if a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?"

Distance

Generally the equation for the Pythagoras Theorem is mathematically given as

AB^2=AC^2+BC^2

Therefore

AB^2=10^2+5^2

AB=11.2miles

For more information on distance visit

https://brainly.com/question/989117

At
Euclid Middle School, of the 30 girls who tried out for the lacrosse team, 12
were selected and of the 40 boys who tried out, 16 were selected. Are the ratios of number of students on the
team to number of student trying out the same for both boys and girls? How do you know?

Answers

Since the ratio of girls who tried out to the girls that were accepted is 30/12=2.5 and the ratio of boys who tried out to the boys that were accepted is 40/16=2.5, we know that they are the same because 2.5=2.5

The amount of interest earned by $6000 invested by a certain rate is $220 less than $13000 would earn at a 1% lower rate. At what rate is,the $6000 invested?

Answers

let's recall that I = Prt

so... hmm we're assuming here, it doesn't say there, but this is for 1 year period.

ok... so... let's use two quantities for such interest, say "a" is the Interest for the Principal of 6000, and let's use "b" is the Interest for the Principal of 13000.

[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$6000\\ r=rate\to r\%\to& \frac{r}{100}\\ t=years\to &1 \end{cases} \\\\\\ a=6000\left( \frac{r}{100} \right)1\implies \stackrel{\textit{P=6000}}{a=60r}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\to& \$13000\\ r=rate\to (r-1)\%\to &\frac{r-1}{100}\\ t=years\to &1 \end{cases} \\\\\\ b=13000\left( \frac{r-1}{100} \right)1\implies \stackrel{\textit{P=13000}}{b=130(r-1)}[/tex]

now, we know that, whatever the interest amount of "a" is, is 220 less than whatever "b" is.

we know what "b" is, b = 130(r-1), and 220 less than that is just b - 220, or 130(r-1) - 220.

[tex]\bf a=60r\qquad \boxed{a=130(r-1) - 220}\implies 130(r-1)-220=60r \\\\\\ 130r-130-220=60r\implies 70r=350\implies r=\cfrac{350}{70}\implies r=5[/tex]

The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass?

F = 16.1m
F =
F = 32.2m
F =

Answers

F = 32.2m

Explanation:

The equation that represents the force on an object due to gravity is

[tex]F=mg[/tex]

where

m is the mass of the object

g is the acceleration due to gravity

In this problem, the acceleration due to gravity is [tex]g=32.2 ft[/tex], so if we substitute this value into the previous equation, we obtain

[tex]F=m(32.2)=32.2 m[/tex]

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Constant of variation due to gravity = 32.2 feet per sec².

As we know that "The fore of gravity on an object varies with its mass".

So, According to statement,

[tex]F=mg\\\\\text{ here, m denotes object's mass and g denotes gravity }\\\\\text{ F denotes the force on an object due to gravity according to m}[/tex]

Substituting the value of g , we get,

[tex]F=32.2m[/tex]

Hence, Third option is correct.

Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters of wsilutawsiluta be arranged? identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.

Answers

The letters wsilutawsiluta have 87178291200 unique combinations. Which we can find via the factorial rule (14x13x12... ect). There are no 14 letter words in english that contain this combination of letters (we can narrow the search by looking for 14 letter words with two W's of which none contain the same combination of letters). Ergo we can conclude the correct unscrambling is more than one word. The letters unscramble to spell 'lawsuit' twice. this is the only correct unscrambling (unless we allow the archaic word williwau). Thus there is a 1 in 87178291200 possibility of randomly unscrambling the letters

If a tire rotates through 250 degrees in 15 seconds, how many degrees does it rotate in 45 seconds?

Answers

Multiply it by three. Look for patterns. 45/15 is 3 therefore the x amount of degrees must be multiplied by three

How much of a 60% saline solution would you need to add to pure water to create 10 L of a 50% saline solution ?

Answers

so say, we add "x" of the 60% saline solution, now, how much salt is in that solution? now 60% is salt but the rest is something else, but only salt is 60% of "x", or (60/100) * x, or 0.6x.

likewise, for the 10 Liters, if only 50% is salt, then is just (50/100) * 10 or 5.

now... let's check the water whilst we add "y" amount, the water has no salt at all, freshwater for that matter, so, salinity is 0%. or (0/100) * y or 0.

[tex]\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{\textit{\% of salt}}{quantity}&\stackrel{\textit{total salt}}{quantity}\\ &------&------&------\\ \textit{60\% sol'n}&x&0.60&0.6x\\ \textit{pure water}&y&0.00&0y\\ ------&------&------&------\\ mixture&10&0.50&5 \end{array}[/tex]

[tex]\bf \begin{cases} x+y=10\\ 0.6x+0y=5 \end{cases} \\\\\\ 0.6x=5\implies x=\cfrac{5}{0.6}\implies x=\cfrac{25}{3}\implies x=8\frac{1}{3}[/tex]

integral of cot^4/cot^2x

Answers

[tex]\bf 1+cot^2(\theta)=csc^2(\theta)\implies cot^2(\theta)=csc^2(\theta)-1\\\\ -------------------------------\\\\ \displaystyle \int~\cfrac{cot^4(x)}{cot^2(x)}\cdot dx\implies \int~\cfrac{[cot(x)]^4}{[cot(x)]^2}\cdot dx\implies \int~[cot(x)]^2\cdot dx \\\\\\ \displaystyle \int~cot^2(x)dx\implies \int~[csc^2(x)-1]dx\implies \int~csc^2(x)dx-\int1\cdot dx \\\\\\ -cot(x)-x+C[/tex]

[tex]\int \frac{\cot^4x}{\cot^2x}dx = \int \cot^2x dx [/tex]

using the identity: [tex]1+\cot^2x = \csc^2x[/tex]
[tex]\int \cot^2x dx = \int( \csc^2x - 1 )dx[/tex]
[tex]=-\cot x-x +c[/tex]

What is 83.45 rounded to the nearest tenth?

Answers

83.45 rounded to the nearest tenth would be 83.5 because the hundredths place is a number of 5 and above (the number in the hundredths place is 5) which means you move the tenths place value up by 1.

83.45
Tenth is the first number after the decimal.
So if the number after the tenth (the hundredths) is 0-4 the tenth doest change. If it's 5-9 you add one to the tenth.
Since it is a 5 you add one to the 4 making it 83.5 :)

Involves 6 suspects, 6 weapons and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. how many solutions are possible?

Answers

their would be 21 different solutions for this problem

Answer:

Step-by-step explanation:

If 100 poster printing machines printed 10,000 art posters in 100 days, how many days will take one machine to print one poster?

Answers

10,000 posters in 100 days, means 10,000/100 posters per day, that is 100/1 posters/day.

that simply means, the 100 machines print 100 posters in 1 day then.

now, if 100 machines, in 1 day they print 100 posters, that means 1 machine alone, is printing, the obvious :).

One machine would take one day to print one poster, calculated by dividing the total posters by the number of machines and days.

If 100 poster printing machines printed 10,000 art posters in 100 days, we first need to find out how many posters a single machine can print in one day. This can be done by dividing the total number of posters by the number of machines and then by the number of days.

Step-by-step calculation:

Determine the total number of posters one machine can print in 100 days: 10,000 posters / 100 machines = 100 posters.

Next, determine the number of posters one machine can print in one day: 100 posters / 100 days = 1 poster.

Therefore, it would take one machine one day to print one poster.

4 times a number cubed decreased by 7

Answers

Ok, so we first need to set this up in variable form. You should have "4n³³-7" Are they asking you to solve this equation as well?

Marietta was given a raise of $0.75 per hour, which gave her a new wage of $12.25 per hour. Write and solve an equation to determine Marietta’s hourly wage before her raise. Show that your answer is reasonable.

Answers

12.25-.75=11.50
The answer is reasonable because .75 is around a dollar and the final answer is about a dollar off new wage

Me Kirk drove 164 miles in the morning and 219 miles in the afternoon.esttimate the total number of smiles she drove?

Answers

You can estimate 164 to 165 and 219 to 220
Then add 165+220 which is 385 approximately

385 would it be I guess

The Cunninghams are moving across the country. Mr. Cunningham leaves 3 hours before Mrs. Cunningham. If he averages 40mph and she averages 80mph, how long will it take Mrs. Cunningham to overtake Mr. Cunningham?

Answers

recall your d = rt, distance = rate * time

now, if say, by the time they meet, Mr Cunningham has travelled "d" miles, that means Mrs Cunningham must also had travelled "d" miles as well.

However, he left 3 hours earlier, so by the time he travelled "d" miles, and took say "t" hours, for her it took 3 hour less, because she started driving 3 hours later, so, she's been on the road 3 hours less than Mr Cunningham, so by the time they meet, Mrs Cunningham has travelled then "t - 3" hours.

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Mr Cunningham}&d&40&t\\ \textit{Mrs Cunningham}&d&80&t-3 \end{array} \\\\\\ \begin{cases} \boxed{d}=40t\\ d=80(t-3)\\ ----------\\ \boxed{40t}=80(t-3) \end{cases} \\\\\\ \cfrac{40t}{80}=t-3\implies \cfrac{t}{2}=t-3\implies t=2t-6\implies 6=2t-t \\\\\\ 6=t[/tex]

How can you make 100?
1 2 3 4 5 6 7 8 9 = 100

Fill in the gaps with suitable operations (+,-,×,÷,) to make 100

I NEED TWO WAYS TO MAKE 100! HELP ME PLEASE! 15 POINTS!

Answers

Hey there!

1+2+3+4+5+6+7+8×9
1 + 2 = 3
3 +3 = 6
6 +4 = 10
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
28 + 8 (9) = 100

Good luck on your assignment and enjoy your day

~MeIsKaitlyn

Note: Just go through all of your operations (+, - , × , ÷ )

Final answer:

Two ways to make the number 100 by inserting operations between the sequence 123456789 are 1+2+3-4+5+6+78+9=100 and 123-45-67+89=100.

Explanation:

To create the number 100 by inserting mathematical operations (+, -, ×, ÷) between the numbers 1 to 9 sequenced as 123456789, we can approach the problem in several ways. Here are two solutions:

1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100123 - 45 - 67 + 89 = 100

In the first solution, we primarily use addition, with a single subtraction to adjust the total to 100. The second solution uses both subtraction and addition, combining smaller numbers to form larger numbers that eventually add up to 100.

round 499,553 near thousand

Answers

The nearest hundred thousand would be 500,000

It would be rounded to [tex]500,000[/tex] because the [tex]499[/tex] would [tex]round[/tex] up to [tex]500[/tex] and the [tex]553 [/tex] would be going [tex]downward [/tex] so, that's how we found out that it was [tex]rounded [/tex] to [tex]500,000[/tex]

Good luck on your assignment
and enjoy your day

~[tex]MeIsKaitlyn :)[/tex]

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