When the balloon, rising at 10 ft/sec, rises to 100 feet, the rate of change of the angle of elevation is 0.05 rad/sec
How can the rate of change of the angle of elevation be found?The rate at which the balloon rises = 10 ft/sec
Horizontal distance of the balloon from the observer, d = 100 feet
Therefore;
[tex] \frac{dy}{dt} = 10[/tex]
The angle of elevation can be presented as follows;
[tex] tan(\theta) = \frac{y}{100} [/tex]
[tex] y = 100 \times tan(\theta) [/tex]
Therefore;
[tex] \frac{dy}{dt} = \mathbf{ 100\cdot sec^2 \frac{d \theta}{dt}} [/tex]
Which gives;
[tex] \frac{d \theta}{dt}= \frac{ \frac{d y}{dt}}{100} \times cos^2 \theta [/tex]
[tex] \mathbf{ \frac{d \theta}{dt}} = \frac{ 10}{100} \times cos^2 \theta [/tex]
When the balloon is 100 ft. from the ground, we have;
cos(theta) = 100/(√(100²+100²) = 1/(√2)Therefore;
[tex] \frac{d \theta}{dt}= \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 [/tex]
[tex] \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 = \frac{ 1}{20} [/tex]
Which gives;
[tex] \frac{d \theta}{dt}=\frac{ 1}{20} = 0.05 [/tex]
The rate of change of the angle of elevation when the balloon is 100 feet from the ground is 0.05 rad/secLearn more about finding the rate of change of a function here:
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Graph the image of rectangle EFGH after a reflection over the line x= –1
Answer:
G (1,7)
H (2,7)
F (1,-1)
E (2,-1)
Step-by-step explanation:
The image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
What is a translation?The process of changing the location of the image on the coordinate system will be known as the translation. A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that graph the image of rectangle EFGH after a reflection over the line x= –1. Translated image of the points is attached with the answer below. The translated points are G (1,7), H (2,7), F (1,-1), and E (2,-1).
Therefore, the image of rectangle EFGH after a reflection over the line x = –1 will cover the points G (1,7), H (2,7), F (1,-1), and E (2,-1).
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In ΔJKL, l = 920 inches, j = 880 inches and ∠K=157°. Find the length of k, to the nearest inch.
Answer:
1764
Step-by-step explanation:
Answer:
1764
Step-by-step explanation:
Delta Math
Help me plsssssssssssssssssssssssssssssssssss
Answer:
One inch would represent 100 miles
Answer: 1 inch is 100 miles
Step-by-step explanation:
1/4 times 4 is 1 right so 25*4=100
Need help ASAP giving 55 points and a branlist
Answer:
There are 54 squares on a rubix cube
Step-by-step explanation:
each side has 9 squares, and there are 6 sides, so you multiply 9x6 wich equals 54, so your answer would be
54 squares
Hope this helps! :)
PLEASE HELP ASAP! What is the slope of the line graphed below?
Answer:
6/3 simply so 2 your slope is 2
Step-by-step explanation:
A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 2 tables is $22. The total cost to rent 3 chairs and 8 tables is $71. What is the cost to rent each chair and each table?
Answer:
The cost to rent each chair is $1.25 and the cost to rent each table is $8.50
Step by step:
A party rental company has chairs and tables for rent. The total cost to rent
A party rental company has chairs and tables for rent. The total cost to rent 4
chairs and 8
tables is $73
. The total cost to rent 2
chairs and 3
tables is $28
. What is the cost to rent each chair and each table?
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Edward C. answered • 02/10/15
TUTOR 5.0 (377)
Caltech Grad for math tutoring: Algebra through Calculus
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Let C = cost to rent each chair
Let T = cost to rent each table
4C + 8T = 73
2C + 3T = 28
Multiply the 2nd equation by (-2) and then add the equations together
4C + 8T = 73
-4C - 6T = -56
2T = 17
T = 17/2 = 8.5
Plug this in to the 1st equation to solve for C
4C + 8(17/2) = 73
4C + 68 = 73
4C = 5
C = 5/4 = 1.25
So the cost to rent each chair is $1.25 and the cost to rent each table is $8.50
The cost to rent each chair and each table are $1 and $8.5 respectively.
Suppose the price of one chair =x
The price of one table =y
What is a linear equation?Any equation of the form ax+by+c=0 is called a linear equation where a, b, c∈ R.
According to the question, the total cost to rent 5 chairs and 2 tables is $22.
5x+2y=22
Multiplying it by 4 on both sides
20x+8y=88.......(1)
The total cost to rent 3 chairs and 8 tables is $71.
3x+8y=71.........(2)
Subtracting (2) from (1)
17x=17
x=1
So, y=8.5
So, the price of 1 chair =$1
the price of 1 table =$8.5
Hence, the cost to rent each chair and each table are $1 and $8.5 respectively.
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yo 20 points! pls help me out
Answer:
the top one would be -40x+24, bottom one is x=12
Step-by-step explanation:
uwu
Answer:
a. -40x + 24
b. x = 4
Step-by-step explanation:
-8 * 5x = 40x, -8 * -3 = 24
-5 * -x = 5x
-5 * 4 = -20
40 - 20 = 20
20/5 = 4
Whos your favorite character from Miraculous Ladybug?! mines Alya and of course cat noir he kinda cute
Answer:
CAT NOIR
He's cool and my cousin's fav characters LOL
Step-by-step explanation:
um, he's cool i guess?
Answer:
I like Mari and Luca bc he is rlly cute for me
Please answer please.
Answer:
Triangles are not similar.
Step-by-step explanation:
Properties of the similarity of two triangles,
1). Corresponding angles of two triangles are equal in measure.
2). Corresponding sides of the similar triangles are proportional.
From the given triangles,
- Corresponding angles of the given triangles are not equal in measure.
- Ratios of the corresponding sides,
[tex]\frac{KM}{XY}=\frac{CM}{RY}= \frac{KC}{XR}[/tex]
[tex]\frac{53}{53}= \frac{54}{53}= \frac{64}{53}[/tex]
But these ratios are not equal.
Therefore, both the triangles are not similar.
Taylor is decorating for a party. She cuts 5 equal-length streamers from a strip of yellow paper that is 9 feet long.?
Answer: 1 4/5 feet
Step-by-step explanation:
Here's the complete question:
Taylor is decorating for a party. She cuts 5 equal-length streamers from a strip of yellow paper that is 9 feet long. How long is each streamer in fraction form?
The length of each streamer will be gotten by dividing the length of the strip of yellow paper by the number of streamers. This will be:
= 9 feet / 5
= 1 4/5 feet
Therefore, the length of each streamer is 1 4/5 feet.
Ron purchases $32,000 worth of stock on his brokers advice and pays his broker a 1.25% broker fee. How much did he pay his broker! Show work please !!
factor the expression below
x^2-49
Answer:
(x+7)(x-7)
Mark my answer as Brainlist.
Two learners are planning to make baskets to raise money for the honors society at their school. Marcia will make baskets out of palms. Norma plans to make baskets out of pine straw. Together, they have $100 to spend on supplies.
The palm baskets cost $4 to make and will sell for $20.
The pine straw baskets cost $3 to make and will sell for $17.
The learners agree that they will each make at least 14 items. Let x represent the number of palm baskets and let y represent the number of pine straw baskets.
Answer:
3
Step-by-step explanation:
Pretty sure it is the third but sorry if im incorrect
Need help!!!! ahaaaaaa
Answer:
Not sure if I am right but this is what I did. I have attached a picture of me solving the equation. Hope this helps, thank you !!
Please help me with this
Answer:
1) equation is set up to determine when the cost of printing at home is the same as the cost of printing at the office
2) p = 500 means that, at printing 500 pages, the costs of home versus office printing are the same
Step-by-step explanation:
Answer:
1) No, it does not represent the story.
2) It represents the number of pages.
Step-By-Step Explanation:
1) It has nothing to do with the story.
2) It says: Let p represent the number of pages
6 Work out the sizes of the angles labelled rº, sº and tº.
Plzzzz help I suck at geometry
Answer:
t = 30
s = 25
r = 55
Step-by-step explanation:
Let's begin by r
r is angle in quadlitral shape, so the sum of the interior angles = 360
r = 360 - (95 +100+110) = 55
Then Now it's time for ( t )
Look at the triangle whose angles are r, 95 and t. The sum of the measures of the interior angles of triangle is 180
so t = 180 - ( 95 + r) = 180 - (95 + 55) = 30
Similarly, look at the triangle whose angles are r, s and 100
s = 180 - (100 + r) = 180 - (100 + 55) = 25
I hope you find this helpful! If you have any questions, please feel free to ask them in the comments
please simplify √16bx⁴
Answer: 4bx^2
Step-by-step explanation:
Answer:
Hey there!
I got the answer
4bx^4
Step-by-step explanation:
All you have to do is simplify the radicand up into a product of known factors , assuming positive real numbers.
5 years ago, john was half the age he will be in 8 years. How old is he?
Answer: John is now 18 years old
Step-by-step explanation:
Let, John's age is now x years.
5 years ago, he was (x - 5) years old
In 8 years, he will be (x + 8) years old
By the given condition,
x - 5 = 1/2 (x + 8)
⇒ 2 (x - 5) = x + 8
⇒ 2x - 10 = x + 8
⇒ 2x - x = 8 + 10
⇒ x = 18
what is the error in this polynomial x²+9=(x+3)(x+3)?
Answer:
(x + 3i)(x - 3i)
Step-by-step explanation:
Wrong statement: x² + 9 = (x + 3)(x + 3)
Correct statement: x² + 9 = x² - (3i)² = (x + 3i)(x - 3i)
Divide 600 kg into 2 boxes so that one box has twice as much in it as the other box. How
much is in the heavier box?
Help please
Answer:
200 box 1 / 400 box 2
box 2 Step-by-step explanation:
200 + 400 = 600
Answer:
Hello asuna here
600 would be your answer
Step-by-step explanation:
Hope this helps
A water tank holds 1,088 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds
1,360 gallons but is leaking at a rate of 9 gallons per week. After how many weeks will the amount of
water in the two tanks be the same?
The amount of water in the two tanks will be the same in
weeks.
The first tank hold 1088 - 5t gallons of water after t weeks, while the seocnd tank holds 1360 - 9t gallons after t weeks.
Both tanks hold the same amount of water when
1088 - 5t = 1360 - 9t
Solve for t :
4t = 272
t = 68
So the tanks will hold the same amount of water after 68 weeks.
Answer the photo below thanks
Answer:
C. 36 degrees
Step-by-step explanation:
90 + 54 = 144
180 - 144 = 36
you were correct
What is the answer to 10x2x5%20
Answer:
ITS 0
Step-by-step explanation:
Help a dum person out?
Answer:
150 i think i dont really understand this question either sorryyy <3
Step-by-step explanation:
bc it has to be less than 150 but the answer also has to be more than 138 so i hope that helped more than the answer i put :)
Answer:
I think It was 123
Step-by-step explanation:
Because i try to add it all four then divide it unto 5 so it was the result but I'm not sure about my answer maybe it will help :)
The shadows of two vertical poles were measured at the same time to be 6m and 15m long. If the first pole is 8cm long, find the height of the second pole
Answer:
20 cm
Step-by-step explanation:
Shadow of vertical poles : 6m ; 15m
Length of poles : 8cm ; h
8cm long pole = shadow length, 6m
h cm long pole = shadow length, 15 m
Using cross multiplication :
8cm * 15 m = h cm * 6m
120 = 6h
h = 120 / 6
h = 20 cm
Height of second pole = 20cm
Four students are reading books with different numbers of pages. The table shows the number of pages each student has read. Drag each name to order the students from the lowest percentage of their book read to the highest percentage of their book read. Pages Read Total Number of Pages Elliot 105 175 = Elliot Frankie 165 300 Hayden 88 220 = Frankie Ruth 117 260 = Hayden = Ruth
Answer:
i think is 434.54
Step-by-step explanation:
Answer:
434.54
Step-by-step explanation:
7x< 21 Im on khan academy so i need help
Answer:
x< 3
7x<21
Divide each term in 7x<21 by 7.
Cancel the common factor of 7.
Divide 21 by 7.
The result can be shown in multiple forms.
Inequality Form:
x< 3
Interval Notation:
(−∞, 3)
I need help with math here is the problem 3(2x+6)
Answer:
6x+18
Step-by-step explanation:
Step-by-step explanation:
Distribute the 3 to the 2X and 6:
3 x 2X + 6 x 3 = (3 x 2)X + 18 = 6X +18
Convert 64°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C= 5 (F-32)
P=C+32
3. Use distributive property to simplify
a. (-6) * [(-12) + (25)]
C. (+6) * [(-17) + (+28)]
e. (+7) * [(-12) – (+6)]
Solve this answer with solution please
Answer:
see the answersStep-by-step explanation:
to understand thisyou need to know about:PEMDAStips and formulas:orders of PEMDAS:
parenthesesexponentmultiplication ordivisionaddition orsubstractionleft to rightlet's solve:a)
remove first parentheses and add: -6×[-12+26] =-6×[14]remove third parentheses and multiply:-6×14=-84c)
remove first parentheses and add:(6)×[-17+28]=6×[11]remove third parentheses and multiply: 6×11=66e)
remove first parentheses and substract:7×[-12-(6)]=7×[-12+(-6)]=7×[-18] multiply:7×[-18]=-126