Answer:
The equation in slope intercept form is y= 2 - 4x
Calculus Application
2. A ladder 20 feet long leans a vertical building. If the bottom of the ladder slides away from the building
horizontally at a rate of 2 ft/sec, how fast is the ladder sliding down the building when the top of the
ladder is 12 feet above the ground?
-8/3 ft/s
Step-by-step explanation:We are given:
distance of the top of the ladder from the ground (h) = 12 ft
height of the ladder = 20 ft
rate of change of the distance of the base of ladder from the wall (dx/dt):
2 ft/s
Finding the distance of the base of the ladder from the wall:
From the Pythagoras's Theorem, we know that:
hypotenuse² = height² + base²
replacing the given values
20² = 12² + x²
400 = 144 + x²
x² = 256 [subtracting 144 from both sides]
x = 16 ft [taking the square root of both sides]
The rate of change of the height of the Ladder from the ground:
We know that:
h = 12 ft
([tex]\frac{dh}{dt}[/tex]) = ?
x = 16 ft
([tex]\frac{dx}{dt}[/tex]) = 2 ft/s
According to the Pythagoras's Theorem:
20² = x² + h²
differentiating both sides with respect to time
[tex]\frac{d(400)}{dt} = \frac{d(x^{2} + h^{2})}{dt}[/tex]
[tex]0 = \frac{d(x^{2})}{dt} + \frac{d(h^{2})}{dt}[/tex]
[tex]0 = \frac{d(x^{2})}{dx}(\frac{dx}{dt}) + \frac{d(h^{2})}{dh}(\frac{dh}{dt})[/tex]
[tex]0 = 2x(\frac{dx}{dt}) + 2h(\frac{dh}{dt})[/tex]
replacing the variables
[tex]0 = 2(16)(2) + 2(12)(\frac{dh}{dt})[/tex]
[tex]0 = 64 + 32(\frac{dh}{dt})[/tex]
[tex]-64 =32(\frac{dh}{dt})[/tex] [subtracting 64 from both sides]
[tex]\frac{-64}{32} =(\frac{dh}{dt})[/tex] [dividing both sides by 32]
[tex]\frac{dh}{dt} = \frac{-8}{3} ft/s[/tex]
Hence, the ladder will slide down at a speed of 8/3 feet per second
30 POINTS PLEASE HELP Solve 2 (e)^3t =10 for t. Round to three decimal places
Answer:
t = 0.768Step-by-step explanation:
2 (e)^3t =10(e)^3t = 5ln (e)^3t = ln 103t ln e = ln 103t = 2.303 t = 2.303/3t = 0.768Please help me im having trouble answering this question
Answer:
I'm not 100 percent sure but I think the area is 12.
Solve the equation n/10 + 8 = 11
Answer: I think 7
Step-by-step explanation:
Alex is ordering his girlfriend a bouquet of flowers for their anniversary. Roses cost $5 each and carnations cost $2 each. He would like to include at least 3 flowers.To stay in his budget, he must not spend more than $36.
1) Identify the combinations of roses or carnations Alex could purchase for his girlfriend.
A) 3 roses and 8 carnations
B) 6 roses and 6 carnations
C) 6 roses and 1 carnation
D) 4 roses and 11 carnations
E) 2 roses and 6 carnations
2) Norah graphed the system above.
Did she graph the system correctly?
O) No, Norah did not graph correctly.
O) Yes, Norah is correct.
Answer:
Y=2x+ 5y
Y<(less than or equal to) 36
X+y>( greater than or equal to) 3
Step-by-step explanation:
So to find one variable in the equation such as finding the amount of roses or carnations, you would have to do system of equations. Some ways of using system of equations is to use substitution, elimination, or graphing.
PLS HELP DUE VERY SOON
Write an equation that represents the green line
Answer: The answer is
Step-by-step explanation:so are u asking fo X,Y?
Answer:
The green line represents the true relationship between the variables. ... this is an overfit model, and I'll show you how to detect it shortly . Fitted line ... Calculates the regression equation.
Helppppppppppppppppppppppp meeeeeeee
Answer:
A I think
Step-by-step explanation:
GIVING BRAINLIST ASAP
A basketball that sold for $65 is marked up to $70.20. What is the percent of the markup?
Answer:
8%
Step-by-step explanation:
70.20−65.00=5.20
(5.20/65.00)×100=8
Answer:
8% markup
Step-by-step explanation:
65x=70.20
x = 70.20/65
x = 1.08
to get it as a percentage, you multiply 1.08*100=108%
this means that there is an 8% markup
3. n X 721 = 72.1
n =
Answer:
n would be 0.10
Step-by-step explanation:
the only way to get 72.1 is to multplay something below it like 0.10 so that why it makes since
Last Friday Cicely had $22.50. Over the weekend she received some money for
cleaning out the attic. She now has $32. Which equation represents how much
money she received?
Answer:
It should be $32 - $22.50.
Step-by-step explanation:
This is because we're trying to find out the amount she received. So we will subtract the amount she already has from how much she now has to figure out how much she received. 32 - 22.50 = 9.50.
Hope this helps:)!
largest two digit prime natural number
Answer:
97
Step-by-step explanation:
Answer:
97 97 97
Step-by-step explanation:
its 97........
PLEASE HELP! I WILL GIVE BRAINLIST AND THANKS list three physical properties of matter
Answer:
mean,range,and mode.
I learned this just last Thursday, duh ;)
Step-by-step explanation:
What is the value place in 5 in 56.13
Answer:
It is Tens if that is what you are asking.
Step-by-step explanation:
1 is ones 10 is tens 100 is hundreds and so on
A sofa is on sale for 29% off. The sale price is $213. What is the regular price?
Answer:
$151.23
Step-by-step explanation:
29/100*213=61.77
213-61.77=151.23
HELP ASAP 5/6b- 3/4=6
Answer:
b= 8 1/10 i think
Step-by-step explanation:
you might want to test it out tho. I really hope this helps
A seagull ate exactly 12 anchovies everyday for one week,How many ancovies did it eat in all?
Answer:
Step-by-step explanation:
7 days in a week so 12 times 7, which is 84 anchovies
PLEASE ANSWER THIS MY BRAIN IS EXPLODING!!!! I NEED YOUR HELP!!!! SAVE ME FROM THESE MATH PROBLEMS!!!
(1)
This table shows the minutes students spent studying for their math exam and the scores they received.
Study time (min) 15 10 30 12 17 43 61 20 8 25 31 40
Exam score 80 78 92 72 75 85 99 83 68 88 86 90
Use a graphing calculator to model the data using a linear function.
What is the correlation coefficient of the data?
−0.75
−0.40
0.49
0.87
2)
A group of people tried joining a gym to see if it would help them to lose weight. This table shows the relationship between the number of weeks since each person joined the gym and the number of pounds they have lost.
Weeks 10 8 6 2 1 5 9 8
Pounds Lost (lb) 4 2.5 0 1 0.5 3 3.5 1.5
Which function best models the data?
y = 0.31x + 0.12
y=−0.43x+2.5
y=−1.5x+5.5
y=0.75x−3.5
(3)
What is the strength of the association between the two variables in the scatter plot?
The strength of association is?
A. Weak
B. Strong
Answer:
0.49
Step-by-step explanation:
This is what I would put. If my work isn't correct I am so sorry.
helppppppppppppppppp
Answer: 1
Step-by-step explanation:
Y intercept is when x=0 so the answer is 1
The ___ is located at (-4, 3.5).
The Brooklyn Bridge is located at ___.
Answer:
Statue of Liberty,(-5,-4.5)
Step-by-step explanation:
Answer:
third one for both
Step-by-step explanation:
What is f(3) if f(x) = -4x + 1 ?
f(3)=10 I think this is it
Answer:
f(3) = -11
Step-by-step explanation:
should be lol
There are 550 people at the school
carnival.
Part A
If 385 of the people are students, what
percentage of the people at the school
carnival are students?
Part B
If 30% of all the people at the carnival are
on a ride, how many people are on a ride?
Helppppp me I have 30 minutes
Answer: part A is 20%
Part B is 165
Step-by-step explanation:
Part B: 30% x 550= 165
The percentage of people who are students will be 70%. And the number of people who are on the ride will be 165.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
There are 550 people at the school carnival. If 385 of the people are students, then the percentage is calculated as,
P = (385 / 550) x 100
P = 70%
If 30% of all the people at the carnival are on a ride. Then the number of people on a ride will be given as,
⇒ 30% of 550
⇒ 0.30 x 550
⇒ 165 people
The percentage of people who are students will be 70%. And the number of people who are on the ride will be 165.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
pls help! will give brainliest!
Answer:
192 and 288
Step-by-step explanation:
What is 67.98 ÷ 100000000
Answer:
0.00000067
Step-by-step explanation:
PLEASE HELP!!!!!!!!! WILL MARK BRAINLIEST!!!!!!!!
1. For a field trip, the school bought 47 sandwiches for $4.60 each and 39 bags of chips for $1.25 each. How much did the school spend on sandwiches? Fill in the blank with the numerical answer only. The school spent $_______ on sandwiches.
2. For a field trip, the school bought 47 sandwiches for $4.60 each and 39 bags of chips for $1.25 each. How much did the school spend on chips? Fill in the blank. The school spent $_______ on chips
3. For a field trip, the school bought 47 sandwiches for $4.60 each and 39 bags of chips for $1.25 each. How much did the school spend in all? Fill in the blank. The school spent $_______ in all.
Answer:
1. $216.2
2.48.75
3.264.95
Step-by-step explanation:
1. 4.60x47=216.2
2. 1.25x39=48.75
3. 216.2+48.75=264.95
The explicit formula for an arithmetic sequence is an = 20 + (n − 1)(2). What is the 200th term?
Answer:
[tex]a_{200}=418[/tex]
Step-by-step explanation:
The explicit formula for an arithmetic sequence is given by :
[tex]a_n=20+(n-1)2[/tex] ...(1)
We need to find the 200th term of the sequence.
Put n = 200 in equation (1)
[tex]a_{200}=20+(200-1)2\\\\=20+199\times 2\\\\=418[/tex]
So, the 200th term of the sequence is 418.
Jo estimated the quotient of –41.71 divided by –6.03 by rounding each to the nearest integer. What is Jo’s error?
Negative 42 divided by negative 7 = 6
Jo should have rounded the dividend to –40.
Jo should have rounded the divisor to –6.
Jo should have divided –7 by –42.
Jo should have divided –7 by –7.
Answer:b
Step-by-step explanation:
Answer:
b
Step-by-step explanation: i took the test and got it right
Arrow is planning to bake approximately 305 cookies. If 3 pounds of cookie dough make 96 cookies, how many pounds of cookie dough should he make? HELP.
Answer:
32
Step-by-step explanation:
96÷3=32 biscuits from 1 pound of dough. 305÷32=9.5 pounds of dough for 305 biscuits.
Answer:
96÷3=32 biscuits from 1 pound of dough. 305÷32=9.5 pounds of dough for 305 biscuits. so yeah and no i did not copy and past!
Step-by-step explanation:
On a local sports team, 30 % of 50 players are -handed. How many left -handed players are there?
Answer:
35 players are left-handed
Step-by-step explanation:
50% of 50 is 25
40% of 50 is 20
30% of 50 is 15
50 - 15 = 35
does the y axis only contain ordered paris with y coordinates of 0
Answer:
no
Step-by-step explanation:
the the y axis is just the top and the line is to symbolize where the dots can be
Answer:
nope
Step-by-step explanation:
help
Michelle and her friends wondered who had the most pop albums in their music collection. She recorded the information below:
Music Collection Survey
Name Number of Pop Albums Total Number of Albums in the collection
Michelle 33 60
Sasha 36 78
Kat 40 89
Monica 24 59
Based on the survey, which friend had the greatest percentage of pop albums? (5 points)
a
Michelle
b
Sasha
c
Kat
d
Monica
Answer:
Michelle (A)
Step-by-step explanation:
cause I ligit took the test