A ladder 20 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 16 feet from the wall.
Answer:
0.17 °/s
Step-by-step explanation:
Since the ladder is leaning against the wall and has a length, L and is at a distance, D from the wall. If θ is the angle between the ladder and the wall, then sinθ = D/L.
We differentiate the above expression with respect to time to have
dsinθ/dt = d(D/L)/dt
cosθdθ/dt = (1/L)dD/dt
dθ/dt = (1/Lcosθ)dD/dt where dD/dt = rate at which the ladder is being pulled away from the wall = 2 ft/s and dθ/dt = rate at which angle between wall and ladder is increasing.
We now find dθ/dt when D = 16 ft, dD/dt = + 2 ft/s, and L = 20 ft
We know from trigonometric ratios, sin²θ + cos²θ = 1. So, cosθ = √(1 - sin²θ) = √[1 - (D/L)²]
dθ/dt = (1/Lcosθ)dD/dt
dθ/dt = (1/L√[1 - (D/L)²])dD/dt
dθ/dt = (1/√[L² - D²])dD/dt
Substituting the values of the variables, we have
dθ/dt = (1/√[20² - 16²]) 2 ft/s
dθ/dt = (1/√[400 - 256]) 2 ft/s
dθ/dt = (1/√144) 2 ft/s
dθ/dt = (1/12) 2 ft/s
dθ/dt = 1/6 °/s
dθ/dt = 0.17 °/s
Find the volume of a right circular cone that has a height of 11.4 in and a base with a radius of 5.1 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
Step-by-step explanation:
h=11.4 in
r=5.1 in
v=3.14*r^2*(h/3)
V=3.14*5.1^2*(11.4/3)=3.14*26.01*3.8=310.35
Question
20 pts
There are 600 6th grade students who attend Falcon Cove Middle School. 17% of them
believe that Mr. Too Much should be fired for being the silliest teacher they have ever known.
How many 6th graders at Falcon Cove believe Mr. Too Much should be fired?
6th graders at Falcon Cove believe Mr. Too Much should be fired.
Question 2
20 pt
Answer:
u can ask the tutor and he or she will help u in real time and explain
can u pls help me with this question
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
We know that the artist can complete [tex]\frac{1}{4}[/tex] of a painting in 2 weeks. So, we just have to find half of [tex]\frac{1}{4}[/tex] to find how much of a painting the artist can do in a week, which is [tex]\frac{1}{8}[/tex] because half of [tex]\frac{1}{4}[/tex] is [tex]\frac{1}{8}[/tex].
Hope this helps! :)
You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground, y after x seconds.
Find the quadratic function y=ax^2+bx+c whose graph passes through the given points.
1 -> 339
3 -> 271
4 -> 189
Answer:
1
Step-by-step explanation:
PLEASE I NEED HELPPPP
Answer:
r=3
Step-by-step explanation:
12 times 3 is 36
18 times 3 is 54
25 times 3 is 75
what you are doing is plugging in X and seeing what X is multiplied to get Y
r•x=y
Answer:
I really don't know
which grade math is this Caz bro
Which of the sets of ordered pairs represents a function? (4 points)
A = {(-5,5), (-2, 2), (2, -2), (5, -5)}
B = {(4,2), (3,-2), (9,4), (11, -3)}
Only A
Only B
Ο Ο Ο
Both A and B
Neither A nor B
Answer:
A if i'm not mistaking
Step-by-step explanation:
Can someone please help me if you know! Thank you
Answer:
D
Step-by-step explanation:
the equation for Josh is 500 + 40x while the equation for Vanessa is only 60x
if josh's account balance is greater than it would be josh > vanessa or vanessa < josh
which of the following statement about the point (5,3 and ( 5,-3) is true?
Answer:
I think it's A
Step-by-step explanation:
Jordan bought an all-in-one printer that regularly sells for $249.99 at the markdown rate of 32%.
Answer: 167
Step-by-step explanation: 249.99 - 32% is 167
What is the value of x?
x =
( number only )
Answer:
9
Step-by-step explanation:
90+(9x5)+9= 90+
the picture is linked here
Answer:
A.
Step-by-step explanation:
In a Linear Function, the changes between x and y should remain constant.
A: x increases by 2 while y increases by 2 steadily so it is a linear function.
B: x increases by 1 and then zooms up to increasing in double (2) while y increases by 2 and then zooms up to increasing to more than double (5) so B is not a linear function.
C: x increases by 3, then one-third of 3 (1), then two-third of 3 (2). y decreases by 6, then one-third of 6 (2), then one-third (2) again when it should have decreased by two-third of 6 (4). Notice that the last decrease was different from x.
D: x increases by 6, then one-third of 6 (2), then half of 6 (3). y decreases by 3, then one-third of 3 (1), then two-third of 3 (2) when it should have decreased by half of 3 (1.5). Notice the last decrease was different from x.
Answer:
pick the answer a
Step-by-step explanation:
a bow bear could watch 44 in 4 seconds at this rate how far can a brown bear run in 20 seconds
Answer:
111 is a great place to be your friend
Step-by-step explanation:
I am not it to 3rd or 3rd to be friends
Answer:
220
Step-by-step explanation:
44 divided by 4 = 11
11 times 20 = 220 so that's the answer
BRAINLIEST PLEASE
2x
+1 = 7
-Z | -1
= [?]
=
2x
3
Answer: nop
Step-by-step explanation:
A polynomial function has a root of -6 with multiplicity 1, a root of -2 with multiplicity 3, a root of 0 with multiplicity 2 and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?
The graph of the function is positive on (-6, -2). The graph of the function is negative on (-∞, 0). The graph of the function is positive on (-2, 4). The graph of the function is negative on (4,∞)
9514 1404 393
Answer:
(a) The graph of the function is positive on (-6, -2)
Step-by-step explanation:
A function of odd degree and positive leading coefficient will be negative from -∞ to the left-most zero. Here, that zero is -6. The multiplicity of that zeros is odd (1), so the sign changes to positive at that point, and remains positive until the next odd-multiplicity zero, which is -2, with multiplicity 3.
Hence the function is positive on the interval (-6, -2), matching choice A.
Answer:
a
Step-by-step explanation:
An example of statistical inference is a. a population mean b. hypothesis testing c. calculating the size of a sample d. descriptive statistics
Answer:
B
Step-by-step explanation:
Statistical inference is the process of making use of analytics to determine the characteristics of a population using its sample.
The two types of statistical inference are:
Hypothesis testing. Confidence interval estimation.answer this correctly please
Answer:
8x-25
Step-by-step explanation:
14) The value of y varies directly with x, and y = 3.6 when x = 6. Find y when x= 48.
Please and thank you. I needed now. Please help
Answer: y = 28.8
Step-by-step explanation:
By using ratios
if the values vary with each other, then they will increase the same amount. 6x8 is 48. So 3.6 x 8 is your answer, 28.8
4 × 22 + 16 ÷ 4 - (4.9 + 5.5)
Answer:
81.6
Step-by-step explanation:
4 × 22 + 16 ÷ 4 - (4.9 + 5.5)
88 + 4 - (10.4)
81.6
Please!!!!! help me fill the blanks. I really need it!!! It due tomorrow!!!!
Answer:
The first blank which is in the first row would be 9
The second blank under the 5 is 100
The third blank below the 8 is 160
And the last blank is 240
Step-by-step explanation:
It you do 60 divided by 3, it would be 20, meaning each sweater costs $20.
Answer:
5 shirts=100. 8 shirts=160. 12 shirts.=240. 180$=9
Step-by-step explanation:
1 sweatshirt is 20. 60 divided by 3.
multiply 20 by the sweatshirt numbers for answers
how to give points
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Answer: answer questions
Step-by-step explanation:
Answer:
tyyyy hope you have a good holiday !!!!!!!
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HELP ME WITH THIS. FOR 10 POINTS
Answer: B. 49 1 hour
Step-by-step explanation: hope this helps
Answer:
49 miles for 1 hour
Step-by-step explanation:
x axis is for hours, y axis is for miles the y axis is up to 49, and x is to 1 so it is B.
10)
3
7
(Click on the picture)
Answer:
What’s the questio???
Step-by-step explanation:
I need help with this I’ll mark you
Answer:
The answer is C
Need help with geometry.
Answer:
x = 23
Step-by-step explanation:
m<1 and m<3 will be the same because they are vertical
m<3 and m<5 will be the same (I forgot their relationship)
which means m<5 and m<7 will be the same
which ALSO means that m<1 =7
So you know that m<1 = m<7 (4x -6 = 2x +40)
x = 23
Shahwhehehehdjdjendbxbsnenenen
Answer:
Shahwhehehehdjdjendbxbsnenenen
Y=-1/4x +9 what is the slope and y - intercept
Answer:
The slope is -1/4 and the y intercept is at (0, 9)
Step-by-step explanation:
In the equation y = mx + b, m is the slope and b is the y intercept.
Since -1/4 is the coefficient to x in the equation, the slope is -1/4.
Since there is a +9 at the end of the equation, the y intercept is (0, 9).
So, the slope is -1/4 and the y intercept is at (0, 9)
What is the slope of line M.
What is a?
What is B?
Answer: A 2,2
Step-by-step explanation: 1 - 1 something
The domain of function f(x) is the set of all integers from 0 to 15, and the range of f(x) is the set of all multiples of 5 from 0 to 75. Part A: Which of the following points might be on the graph of(f(x)? O (5, 1) 0 (7, 15) 0 (10, 80) (20, 10) Part B: Which of the following statements must be false about f(x)? Select all that apply. f(0) = 0 $(2) = 1 O O O O O. f(5) = 5 Of(10) = 75 of(15) = 100
Answer:
pt1 = d and pt 2= c and d
Step-by-step explanation:
Answer:
I know for fact part A is correct but I’m iyffy abt part B
Step-by-step explanation:
Hope it helps
At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. What is the probability that a randomly selected student studies for a test and gets a B or higher?
0.08
0.11
0.33
0.55
Answer:
.33
Step-by-step explanation: