A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π4 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
Answer:
Step-by-step explanation:
aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:
tanθ = opp/adj = y/x
y = xtanθ
What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):
dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)
We need to find out values for all of the variables:
The observer is not moving, therefore dx/dt = 0.
The observer is standing 4 miles away from the lift-off point, so x = 4.
The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.
The rate of change for the angle, dθ/dt, is 0.1.
Just plug all the numbers in:
dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)
dy/dt = 0 + 1.6
dy/dt = 1.6 mi/min
What is the quotient if 2/4 of 40 is divided by 4/5 of 5/7?
Answer:
2/4 * 40 4/5 * 5/7 = 102/
7
= 14 4/
7
≅ 14.5714286
Step-by-step explanation:
To find a new numerator:
a) Multiply the whole number 40 by the denominator 5. Whole number 40 equally 40 * 5/
5
= 200/
5
b) Add the answer from previous step 200 to the numerator 4. New numerator is 200 + 4 = 204
c) Write a previous answer (new numerator 204) over the denominator 5.
Forty and four fifths is two hundred four fifths
Multiple: 2/
4
* 204/
5
= 2 · 204/
4 · 5
= 408/
20
= 102 · 4/
5 · 4
= 102/
5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(408, 20) = 4. In the following intermediate step, cancel by a common factor of 4 gives 102/
5
.
In other words - two quarters multiplied by two hundred four fifths = one hundred two fifths.
Multiple: the result of step No. 2 * 5/
7
= 102/
5
* 5/
7
= 102 · 5/
5 · 7
= 510/
35
= 102 · 5/
7 · 5
= 102/
7
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(510, 35) = 5. In the following intermediate step, cancel by a common factor of 5 gives 102/
7
.
In other words - one hundred two fifths multiplied by five sevenths = one hundred two sevenths.
The cost of 3 scarves is $71.25. What is the unit price?
The unit price is $
per scarf.
Answer:
unit price= $23.75
Step-by-step explanation:
$71.25/ 3
unit price means the price of 1
Find the values of x, y, and z.
Please help!!
Answer:
x=20
y and z=160
Step-by-step explanation:
the arc of the circle is congruent to the central angle therfore x is also 20
next for y and z we can tell they are congruent now to find the measure. we can tell A is 180 so we do 360-180-20=160
third time posting this question pls help. it's 7 grade maths.pls help i need it I give brainlist
Answer:
Step-by-step explanation:
7) m + 6 > 17
m > 17- 6
8. 500 + p > 1500
9. Let cost of pencil be 'x' and it is 5 less than y
x < y -5
Cost of pencil and ruler is less than $ 30.
x + y < 30
10. r + 5 > 17
r > 17 - 5
r > 12
12.She is spending $ x. So, we have to subtract from $10.
10 -x < 5
The perimeter of the surface
of a workbook is 36 inches. The
area is 80 square inches. What
are the dimensions of the
workbook?
Answer:
10 inches by 8 inches
The length and with would be half the perimeter: 36/2 = 18
find 2 numbers when added together equal 18 and when multiplied together equal 80.
8 + 10 = 18
8 x 10 = 80
How could you correctly rewrite the equation 4(10 + 5) = 6 (12 - 2) using the distributive property?
Answer:
40+20 = 72-12 is the simplified version.
Step-by-step explanation:
Your equations
4(10+5) = 6(12-2)
Multiply 4 by 10 and 5 for the "4(10+5)"
Multiply 6 by 12 and -2 for the "6(12-2)"
40+20 = 72-12 is the simplified version.
If you want to solve/verify:
40+20 = 72-12
60 = 60
The nanswer is correct.
Answer:
40 + 20 = 72 - 12
Step-by-step explanation:
The number outside the parenthesis will be multiplied to both numbers inside the parenthesis, making the equation
(4 * 10) + (4 * 5) = (6 * 12) + (6 * (-2))
simplifying the equation...
40 + 20 = 72 - 12
The train station clock runs too fast and gains 8 minutes every 5 days. How many minutes and seconds will it have gained at the end of 8 days?
When 58,511 is divided by 21, the quotient is 2,786 R ___.
Numerical Answers Expected!
Answer for Blank
If you take the answer, 2786 and multiple by 21
You get 58,506
Which if you subtract from 58,511 you would get 5
Which is r
Let w = width and 4 + w = length. Which equation represents the situation?
Answer:
Depends on whether you're looking for area or perimeter. Follow the equations below
Step-by-step explanation:
This depends on whether you're being asked to find perimeter of area
Perimeter is equal to 2(length) + 2(width)
In which case perimeter would be 2(4 + w) + 2(w)
Which can be simplified to 8 + 2w + 2w = 4w + 8
However, Area is equal to length times width
Which would be (4 + w) * w = 4w + w^2
Answer:
Step-by-step explanation:
✔ w(4 +w) = 60
?? im so confused please help
Answer:
y = 5.5 ·x
Step-by-step explanation:
x= pounds purchased
y = cost in $
Given:
4 pounds for $22
x pounds for $ y
Find unit price so will know how much will pay for 1 pound
22/4 = 11/2 = $ 5.5 for 1 pound
Make a general formula :
y = 5.5 ·x
a) Work out
41/7 + 1 1/2
Answer:
11 5/4
Step-by-step explanation:
make the denominator the same then add.the common factor of 2 and 7 is 14 so make all the denominator to 14 then u can add.thus having the answer
Bob swam a total of 250 meters on Monday and Tuesday. On Tuesday, the numbers of meters he swam was 30 less than 3 times the amount he swam on Monday. How many meters did Bob swim on Monday?
Answer:
Bob swam 70 meters on Monday
Step-by-step explanation:
Let x = Meters swam on Monday
and y = Meters swam on Tuesday
x + y = 250
y = 250 - x
y = 3x - 30
250 - x = 3x - 30
4x = 280
x = 70
y = 180
Math Correct answers only please!!
Put question number with correct letter (ex: 1:a, 2:c, 3:d....etc)
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Rewrite and add each vector:
[tex]p=\langle40cos70^\circ,40sin70^\circ\rangle\\q=\langle50cos270^\circ,50sin270^\circ\rangle\\r=\langle60cos235^\circ,60sin235^\circ\rangle\\p+q+r=\langle40cos70^\circ+50cos270^\circ+60cos235^\circ,40sin70^\circ+50sin270^\circ+60sin235^\circ\rangle\\p+q+r\approx\langle-20.73,-61.56\rangle[/tex]
Find the magnitude of the resulting vector:
[tex]||p+q+r||=\sqrt{x^2+y^2}\\||p+q+r||=\sqrt{(-20.73)^2+(-61.56)^2}\\||p+q+r||\approx64.96[/tex]
Therefore, the best answer is D) 64.959
Problem 2
Think of the vectors like this:
[tex]t=\langle7cos240^\circ,7sin240^\circ\rangle\\u=\langle10cos30^\circ,10sin30^\circ\rangle\\v=\langle15cos310^\circ,15sin310^\circ\rangle[/tex]
By adding the vectors, we have:
[tex]t+u+v=\langle7cos240^\circ+10cos30^\circ+15cos310^\circ,7sin240^\circ+10sin30^\circ+15sin310^\circ\rangle\\t+u+v\approx\langle14.8,-12.55\rangle[/tex]
Since the direction of a vector is [tex]\theta=tan^{-1}(\frac{y}{x})[/tex], we have:
[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{-12.55}{14.8})\\\theta\approx-40.3^\circ[/tex]
Don't forget to take into account that the resulting vector is in Quadrant IV since the horizontal component is positive and the vertical component is negative, so we will add 360° to our angle to get the result:
[tex]\theta=360^\circ+(-40.3)^\circ\\\theta=319.7^\circ[/tex]
Therefore, the best answer is D) 320°
Problem 3
Again, rewrite the vectors and add them:
[tex]u=\langle30cos70^\circ,30sin70^\circ\rangle\\v=\langle40cos220^\circ,40sin220^\circ\rangle\\u+v=\langle30cos70^\circ+40cos220^\circ,30sin70^\circ+40sin220^\circ\rangle\\u+v\approx\langle-20.38,2.48\rangle[/tex]
Using the direction formula:
[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{2.48}{-20.38})\\\theta\approx-6.94^\circ[/tex]
As the vector is located in Quadrant II, we need to add 180° to our angle:
[tex]\theta=180^\circ+(-6.94)^\circ\\\theta=173.06^\circ[/tex]
Therefore, the best answer is D) 173°
Problem 4
Using scalar multiplication:
[tex]-3u=-3\langle35,-12\rangle=\langle-105,36\rangle[/tex]
Find the magnitude of the resulting vector:
[tex]||-3u||=\sqrt{x^2+y^2}\\||-3u||=\sqrt{(-105)^2+(36)^2}\\||-3u||=111[/tex]
Find the direction of the resulting vector:
[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{36}{-105})\\\theta\approx-18.92^\circ[/tex]
As the vector is located in Quadrant II, we need to add 180° to our angle:
[tex]\theta=180^\circ+(-18.92)^\circ\\\theta=161.08^\circ[/tex]
Therefore, the best answer is C) 111; 161°
Problem 5
Using scalar multiplication:
[tex]5v=5\langle25cos40^\circ,25sin40^\circ\rangle=\langle125cos40^\circ,125sin40^\circ\rangle[/tex]
Since the direction of the angle doesn't change in scalar multiplication, it only affects the magnitude, so the magnitude of the resulting vector would be [tex]||5v||=125[/tex], making the correct answer C) 125; 200°
What is the value of the expression 25 ÷ 5 + (6 x 2) − 4?
7
9
12
13
Answer: 13
Step-by-step explanation:
Answer:
Hey Dude....
Step-by-step explanation:
This is ur answer.....
25 ÷ 5 + (6 x 2) − 4= 5 + 12 - 4= 5 + 8 = 13Hope it helps!
Brainliest pls!
Follow me! :)
what value makes 3k– 6 < 12 true?
Answer: Any number smaller than 6
3k - 6 < 12
(Add six to both sides)
= 3k < 18
(Divide by 3 on both sides)
= k < 6
Also a side note that may be helpful in other similar problems: If you are dividing or multiplying by a negative number you have to flip the inequality sign.
Determine where the given function is concave up and where it is concave down.
q(x) = 8x3 + 2x + 8
Answer:
concave up
Step-by-step explanation:
there is no negatives in the equation (in front of x-value)
Find the value of x.
Answer:x.
Step-by-step explanation:
Use interval notation to express the following: The set of all numbers less than or equal to −5.
Answer:
(- infinitysymbol,-5]
see image.
Step-by-step explanation:
Interval notation uses parenthesis or square brackets in the format:
( or [ begin , end )or]
Always use parenthesis around the infinity or negative infinity symbol. Square brackets are for when the number is included. Like in this case where it says "or equal to -5"
see image.
Work out the highest common factor (HCF) of 18 and 30
[tex]18 = 2\times 3 \times 3\\\\30 = 2 \times 3 \times 5\\\\\text{HCF}~ = 2\times 3 = 6[/tex]
A trapezoid has sides of length 16.7 centimeters, 12.9 centimeters, 16.7 centimeters, and 18.9 centimeters. What is the perimeter? centimeters
Answer:
65.2 cm
Step-by-step explanation:
P = a + b + c + d
P = 16.7 cm + 12.9 cm + 16.7 cm + 18.9 cm
P = 65.2 cm
The perimeter of the trapezoid is 65.2 cm.
Answer:
To find the perimeter of this trapezoid, simply add all four sides (since there are only four sides to a trapezoid):-
16.7 + 12.9 + 16.7 + 18.9
= 65.2 centimetres is the perimeter.
You can picture it like this;
Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle. The length of K M is 6 and the length of M J is 3.
What is the length of line segment LJ?
9 units
12 units
15 units
18 units
Answer:
I think 9 units is the correct answer
Answer:
its 15 units
Step-by-step explanation:
momma told me it was right
The following list gives the number of pets for each of 14 students.
2
,
0
,
2
,
4
,
4
,
4
,
3
,
2
,
3
,
4
,
1
,
3
,
3
,
2
Find the modes of this data set.
If there is more than one mode, write them separated by commas.
If there is no mode, click on "No mode."
Answer:
2,3,4
Step-by-step explanation:
Given data:
2,0,2,4,4,4,3,2,3,4,1,3,3,2
Solution:
Mode = Most often number
There are
4 = two's
1 = zero's
4 = four's
4 = Three's
1 = ones's
Hence the mode is:
2,3,4
~lenvy~
pls i need help asap
what's the area of this figure?
Answer:
35
area of traingle b xh/2 5x4/2 - 10
area of square lxl - 5x5 -25
add- 35
Answer:
The answer would be 35.
Step-by-step explanation:
The area of the shape would be 35 square centimeters because if we divide the shape into 3 different shapes, a square on the bottom and 2 triangles at the top, we can multiply the square's length and width to get an area of 25. Next, we'll multiply the 2 triangles length of 4 with the width of 5 to get a total area of 20 from both of them, we'll then divide the area of 20 by 2 to get 10. Now add 20 and 10 to get 35.
What is the area of a circle with the diameter of 10
In a simple economy (assume there are no taxes, thus, Y is disposable income), the consumption function is:
C = 200+ 0.80Y
00
The current level of real GDP is $4000.
At this level of real GDP, consumption will be $, and savings will be $1. If GDP were to increase by $1000, consumption would increase by $(Round your
responses to the nearest dollar.)
Using linear function concepts, it is found that consumption would increase by $800.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the function is given by:
C = 200 + 0.8Y.
Which means that the slope is of m = 0.8 per unit of Y.
For 1000 units:
0.8 x 1000 = 800.
Consumption would increase by $800.
More can be learned about linear function concepts at https://brainly.com/question/24808124
Select the most appropriate unit for the situation
Rate of filling a buck with water
Feet / minute
Square feet /minute
Cubic feet / minute
Answer: Is Square feet/minute if there is two of them the second one is Cubic feet/minute
Step-by-step explanation: feet/minute would cover anything linear {forward, backward, left, right}
square feet/minute would cover two-dimensional areas {walls, floors, sides of buildings, etc.}
cubic feet/minute would cover three dimensional situations {swimming pools, buckets, containers, etc.}
There are caterpillars in two greenhouses. Greenhouse A has 4 times the number of caterpillars Greenhouse B has. A bird came into the two greenhouses and devoured many caterpillars. After the bird ate 41 caterpillars in Greenhouse A and 5 caterpillars in Greenhouse B, both greenhouses have the same number of caterpillars. How many caterpillars did Greenhouse A have in the first place?
there will be your 1000 caterpillars
Answer:
12
Step-by-step explanation:
4a = b and A-41=b-5
a-41+5=b
a-36 =b
which means a+36 =4a
so 3a=36 and a=12
Three times a number x is more than 18.
Answer:
3x>18
Step-by-step explanation:
Three times the number x will be called 3x. If an expression is more or greater than a number, we use the greater symbol: >
So, we can write,
3x>18
Please help me just a and d
C = 2 x pi x r
if r = 5 cm
C = 2 x pi x 5 = 10 x pi
≈ 10 x 3,14 ≈ 31,4 cm
C = 2 x pi x r = pi x d
if d = 2 m
C = pi x 2
≈ 3,14 x 2 ≈ 6,28 m
Hello!
a)
C = 2πr C= 2*π *5 31,4cm
= 2*3,14* 5
d)
r =2/2 => 1m
C= 2πr C= 2*π*1 6,28m
= 2 *3,14*1