A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is pi/6, and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?

Answers

Answer 1

Answer:

0.533 miles/min

Step-by-step explanation:

Calculate how fast  the balloon is rising at the moment : dy /dt

location from the lift-off point = 4 miles

angle between the observer's line-of-sight and the horizontal ( ∅ )  = [tex]\frac{\pi }{6}[/tex]

d∅ / dt = 0.1 rad/min

tan ∅ = y / 4

derivate

sec^2 ∅ . d∅ / dt  = 1/4 . dy/dt

= sec^2 [tex]\frac{\pi }{6}[/tex] . 0.1 = 1/4 . dy/dt

= ( sec^2 0.5238 * 0.1 ) * 4 = dy/dt

dy/dt = 8 / 15  miles/min


Related Questions

which line segment shows the height that corresponds to the given base of the triangle? ​

Answers

Answer:

is this full question

Step-by-step explanation:

there is no line segment or triangle

Rewrite the equationy−2=−2/3 (x+6) in standard form.

Answers

Answer:

y=-2/3x-2

Step-by-step explanation:

Help ASAP please!!
Which congruence theorems can be used to prove ABR is congruent toACR? Select three options.
•HL
•SAS
•SSS
•ASA
•AAS

Answers

Answer:

SAS, HL, and something else

Answer: HL SAS SSS

Step-by-step explanation:

The equivalent ratios show how many teaspoons there are in 5 cups. What method can be used to convert 1 cup to teaspoons? multiply 1,200 by 5 divide 1,200 by 5 multiply 5 by 1 divide 5 by 1,200

Answers

The correct answer is Option B.

Divide 1,200 by 5.

What is equivalent ratio?Equivalent ratios are those that are the same when compared. Two or more ratios can be compared to determine whether or not they are equivalent.Equivalent ratios are two ratios that have the same value. Multiply or divide both quantities by the same number to find an equivalent ratio. It is the same as determining equivalent fractions. Equivalent equations are algebraic equations with the same solution or root. An equivalent equation is created by adding or subtracting the same number or expression from both sides of an equation.

Here = 1200tsp / 5c = ?tsp/1c

        = 1200 / 5

       = 240 tsp

To learn more about equivalent ratio refer to :

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Find PM pls help fast​

Answers

Answer:

I think it is 4 but, im not sure

a movie theater charges $8 for adults and $5 for children. If there were 40 people altogether and theater collected $272

Answers

Answer: You can put this solution on YOUR website!

let's call the number of adults a and the number of children c.

so the total adults plus the total children equals 40 or a+c=40 or c=40-a

also we know that 8a+5c=272

substituting c's value in the 1st equation into the 2nd equation we get

8a+5(40-a)=272---->lets distribute that left side---->8a+200-5a=272

now let's combine like terms on either side of the equals sign.

3a=72 a=24

so we have highlight%2824-adults%29

and c=40-a(24)=highlight%2816-children%29

a portion of the quadratic formula proof is shown. fill in the missing reason.

ax^2+bx+c=0 —— Given
ax^2+bx=-c ——subtract c from both sides of the equation
x^2+b/a x=-c/a —— divide both sides of the equation by a
x^2+ b/a x+(b/2a)^2=-c/a+(b/2a)^2 —— complete the square and add (b/2a)^2 to both sides.
x^2+ b/a x+(b/2a)^2=-c/a+b^2/4a^2 —— square (b/2a) on the right side of the equation.
x^2+ b/a x+(b/2a)^2=-4ac/4a+b^2/4a^2—— find a common denominator on the right side of the equation.
x^2+ b/a x+(b/2a)^2=b^2-4ac/4a^2 —— ?????

A-multiply the fractions together on the right side of the equation
B- subtract 4ac on the right side of the equation
C- add 4ac to both sides of the equation
D- add the fractions together on the right side of the equation

Answers

9514 1404 393

Answer:

  D- add the fractions together on the right side of the equation

Step-by-step explanation:

In the previous step, the fractions are written with a common denominator. In the last step, the two fractions are combined (added together).

The best description of those provided is ...

  D- add the fractions together on the right side of the equation

of a car for $40,300 at 2.5% add on rate for 5 years. What is the APR?

Answers

Like 55k bs snanbdndhdmd

Answer:

$45,337.5

Step-by-step explanation:

1. 2.5 * 5 = 12.5

2. $40,300 + 12.5%

Hope This Helps :)

Convert 10010001 from binary to hexadecimal.

Someone pls quickly answer this only if you're sure it's right.

Answers

10010001 is 91 in hexadecimal

Answer:

its 91

Step-by-step explanation:

Jessica hiked 5 miles in 2 hours. At this same rate, what is the total number of miles Jessica could hike in 14 hours?

Answers

Answer: 35

so in one hour she'd do 2.5 hours

so in 14 she'd do 2.5*14=35

35!!!!!!!!!!!!!!!!!!!

CAN SOMEONE PLEASE HELP ME ON THE TOP ONE !!!!!!

Answers

the linear equation is
slope-intercept form y=-3x+18
standard form 3x+y=18

slope is -3

y intercept is (0,18)

Answer:

[tex]the \: slope \: is \to \boxed{-3} \\ the \: y \: intercept \to \boxed{18}[/tex]

Step-by-step explanation:

[tex]the \: solpe \: \boxed{m} = \frac{9 -1 2}{3 - 2} = -3 \\ y = mx + c \\ 12 = (-3)(2) + c \\ c = 12 + 6 = 18[/tex]

Graph the greatest integer, f(x) = [x]

Answers

Answer:

Step-by-step explanation:

What is 65658 divided by 706? SHOW YOUR WORK!!

Answers

Answer:

the answer is 93

Step-by-step explanation:

i dont know how to explain it but just use a calculator.

URGENT!!!!!

3sin^2θ-17sinθ+10=0
Determine the θ

Answers

Let sin be a
3a^2-17a+10=o
A =5 or 2/3
Sin =5rej
Sun=2/3 = 41.8 or138

Elena is going to mow lawns for the summer to make some extra money. She will charge $20 for every lawn she mows and plans on mowing several lawns each week.
Let n = the number of lawn she mows.
Write an expression for the total amount she will charge for all of the lawns she mows.
will brainlist

Answers

Answer:

Kx20=N

Step-by-step explanation:

k with be the number multiplied by 20 and then N will be the answer  

The expression for the total amount she charged can be represented as A = 20n.

What is an expression?

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

For example 2x = 54

An expression is a mathematical proof of the equality of two mathematical expressions.

Given that,

She will charge $20 for every lawn

Number of lawns she mows = n

Total charge let's represent by A

Then,

A = 20n will be the correct expression.

Hence "The expression for the total amount she charged can be represented as A = 20n".

To learn more about expression,

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elena receives $200 for a birthday present, which she deposited in a bank account. Every month she withdraws $25. how much will she have left in her bank?

Answers

Answer:

8 months

Step-by-step explanation:

for every 100 four 25s and these two 100s so 8

hope this helps

Before her hike, Lara filled her water bottle with 4 cups of water. During the hike, she drank about 10 fluid ounces every hour. Afterward, she had about 12 fluid ounces left. How many hours did she hike?

Answers

Answer:

Lara hiked for 2 hours.

Step-by-step explanation:

1 cup = 8 ounces

4 cups = 32 ounces

32 - 10h = 12

10h = 20

h = 2

Lara hiked for 2 hours.

A cup contains 8 fluid ounces so the total number of ounces that Lara had before the hike was:

= Number of cups x fluid ounces per cup

= 4 x 8

= 32 fluid ounces

After the hike, Lara was left with 12 fluid ounces which means that she consumed:

= 32 - 12

= 20 fluid ounces

She drank 10 fluid ounces per hour so the total number of hours she hiked were:

= Number of fluid ounces consumed / Fluid ounces per hour

= 20 / 10

= 2 hours

Find out more at https://brainly.com/question/11719641.

Which of the following values is a zero of the expression x²+9x²-x-105

Answers

Answer:

x=7

x=5

x=−3

Step-by-step explanation:

0-(x^3-9*x^2-x+105)=0  

Step by step solution :

STEP

1

:

Equation at the end of step 1

 0 -  ((((x3) -  32x2) -  x) +  105)  = 0  

STEP

2

:

Checking for a perfect cube

2.1    -x3+9x2+x-105  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  -x3+9x2+x-105  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x-105  

Group 2:  -x3+9x2  

Pull out from each group separately :

Group 1:   (x-105) • (1)

Group 2:   (x-9) • (-x2)

help⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️⁉️​

Answers

Answer:

$1017.19

Step-by-step explanation:

First find the fraction of how much of Paulo's money is spent on his rent and car. Add 1/4 and 1/8, which is 3/8 because 1/4 = 2/8. Then multiply 3/8 by Paulo's monthly spending, which is $2712.50. Multiplying those numbers will get you $1017.1875. which you have to round up to $1017.19 because you can't spend three quarters of a cent.

Answer:

Asumming that you are rounding to the nearest hundreth:

1,017.19

Step-by-step explanation:

Find [tex]\frac{1}{8}[/tex] of 2,712.5 to find how much money Paulo spends on his car.

[tex]\frac{1}{8}[/tex] = .125

Multiply 2,712.5 by .125

2,712.5 × .125 = 339.0625 ≈ 339.06

Now, find [tex]\frac{1}{4}[/tex] of 2,712.5 to find how much paulo spends on his rent.

[tex]\frac{1}{4}[/tex] = .25

Multiply 2,712.5 by .25

2,712.5 × .25 = 678.125 ≈ 678.13

Add the two values together to get your answer

339.09 +

678.13

----------

1,017.19

(Another way to dolve this problem would be to find [tex]\frac{5}{8}[/tex] of 2,712.5 and subtract it from the origional value, 2,712.5)

Which of the following represents a molecule?
Cu

Ca
CO
Cu
Co

Answers

Answer:

CO

Step-by-step explanation: C for: corbin (I probably spelt that wrong)  and O for: oxygen

|2x + 7| >7

what are the boundary points?

Answers

Answer:

the answer is  [tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x<-7\quad \mathrm{or}\quad \:x>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-7\right)\cup \left(0,\:\infty \:\right)\end{bmatrix}[/tex]

Step-by-step explanation:

i hope this helps :)

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations (I use it all the time).

Answer:

absolute value

Step-by-step explanation:

If your talking about the two lines by the 7 and the 2.

there used to find the absolute value of a number.

lets say you have this  |-2| your answer would be 2.

|1| =1

-|1|= -1

I hope you get the point

the question would be 2x=7>7 its that easy

The area of a rectangular pool is 7719m2. If the width of the pool is 83m, what is its length?

Answers

Answer:

The answer is 93 m

Step-by-step explanation:

Area of a rectangle = l × w

l is the length

w is the width

From the question

Area = 7719 m²

width = 83 m

We have

[tex]7719 = 83l \\ \frac{83l}{83} = \frac{7719}{83} [/tex]

We have the final answer as

length = 93 m

Hope this helps you

In your own words how do you graph an equation that is in slope-intercept form?​

Answers

Step-by-step explanation:

find the y intercept then graph using your slope

What is the equation in slope-intercept form of the line that passes through the points (-4, 2) and (12, 6) ?

The possible answers are
y=0.25x +3
y=0.25x - 4.5
y=4x + 18
y=4x - 42

Answers

it would be y=0.25x+3 :)

HELP ME ASAP

graph f(x)=3x+4 and h(x)=f(x+3)

Answers

sorry if it’s the wrong answer

The standard form for expressing the equation of a straight line is

y = mx + b

Given the functions from the question f(x)  = 3x + 4

If h(x) = f(x+3)

Replace x with x+3 in the function f(x) to have;

h(x) = 3(x+3) + 4

h(x) = 3x + 9 + 4

h(x) = 3x + 13

Hence the required graph for both functions are attached below;

Learn more here: https://brainly.com/question/17003809

Please just give me a good explanation on how to reflect the x-axis and y-axis so I can learn it on my own as well as answering the question in the picture.

Answers

Answer:

Alright! BTW, the answer to the question is D :)

Step-by-step explanation:

Reflecting across the x-axis, the x-coordinate ALWAYS remains the same, but the y-coordinate is transformed into its opposite. If you forget this, fold along the x line, and you should be able to figure it out. Reflecting across the y-axis, the y-coordinate ALWAYS remains the same, but the x-coordinate is transformed into its opposite. If you forget this, fold along the y line, and you should be able to figure it out.

Hope I helped!

What is the least common denominator of 5/6 and 3/8?​

Answers

Answer:

Step-by-step explanation:

5/6 and 3/8  LCD is 24

(8.2k - 6) - (4.5 - 9k)

Answers

Answer: -5.3k-6

Step-by-step explanation: I dont know if its correct but this is what i got (i hope this helps:)

p-25=16
[tex]its \: pretty \: easy \: n \\ boys[/tex]
thank you for helping
SHOW WORK​

Answers

Hi there! The answer would be:

P=41

Explanation:
We can figure out what P equals by adding 25+16, which equals 41. So, we now know that 41-25=16!!

Stephen and Diana are traveling towards each other from points that are 276 miles apart. If Diana is traveling 4 mph faster than and they meet after 6 hours, how fast was each traveling?
Stephen is traveling______mph.
Diana is traveling_____ mph.​

Answers

Answer:

Step-by-step explanation:

let speed of Stephen=x mph

speed of Diana=x+4

then

6x+6(x+4)=276

divide by 6

x+x+4=276/6=46

2x=46-4=42

x=42/2=21

Stephen is traveling at  21 mph.

Diana is traveling at 21+4=25 mph.

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