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
Two airplanes leave the same airport heading different directions. After 2 hours, one airplane has traveled 710 miles and the other has traveled 640 miles. Describe the range of distances that represents how far apart the two airplanes can be at this time
Answer:
Step-by-step explanation:
710 + 640 = 1350m
Simplify the expression. (Use the Distributive Property)
4(2c - 2)
Answer:
4(2-2c)
Step-by-step explanation:
because you switch it around
Answer:
-1
Step-by-step explanation:
times 4 by 2c and 4 by -2
8c and -8 then you divide by each other and get -1
Help me with this please
Answer:
It would be -13
Step-by-step explanation:
Answer:
-13
Step-by-step explanation:
You need to separate the 8 from each side of the equation. Picture it like this:
-104= 8 (multiplied by) x
To separate 8 from the variable, you need to divide that side by 8. Similarly, you need to do the same thing to the other side.
-104/8=8x/8
-13=x
write an equation that reflects this relationship using X to represent the amount of grams in fish and y to represent the number of calories
Answer:
[tex] y = \frac{3}{2}x [/tex]
Step-by-step explanation:
The graph shows there is a proportional relationship between amount of grams of fish (x) and number of calories (y).
A original relationship can be represented by An equation as [tex] y = kx [/tex], where, k = constant of proportionality (y/x).
The constant of proportionality using any point, let's say (200, 300), would be:
k = y/x = 300/200 = ³/2
Plug in the value of k into [tex] y = kx [/tex].
Thus, the equation that reflects the relationship would be:
[tex] y = \frac{3}{2}x [/tex]
The equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories is (2y = 3x) and this can be determined by using the point-slope form of a line.
Given :
A graph where the x-axis represents the number of fish in grams and the y-axis represents the number of calories.Points - (100,150) and (200,300)The point-slope form can be used to determine the equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories.
The point-slope form is given by the equation:
[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex] ----- (1)
where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.
Now, put the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the equation (1).
[tex]\dfrac{y-150}{x-100}=\dfrac{300-150}{200-100}[/tex]
[tex]2(y-150)=3(x-100)[/tex]
2y - 300 = 3x - 300
2y - 3x = 0
2y = 3x
The equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories is (2y = 3x).
For more information, refer to the link given below:
https://brainly.com/question/14022834
In last Quiz, Ahmed answered 24 out of 30 questions correctly. In this quiz he answered 20 out of 24 questions correctly. On which quiz did Ahmed have better results?
Answer:
He scored better on the second test by a margin of 3%.
Step-by-step explanation:
Find the percentage of each one by dividing Ahmed's score / Total possible score
24/30 = 0.8 > move the decimal place over twice for % > 80%
20/24 = 0.83333 > move the decimal place over twice for % > 83%
He scored 3% better on the second test.
What is the slope and the y-intercept of the line on the graph below?
b=
m=
Write an equation for this line in slope-
intercept form (y=mx+b).
Answer:
b=1
m=1/4
y=1/4x+1
Step-by-step explanation:
m is the slope, b is the y-intercept
Can someone help me please
Answer:
krkk4k4k
Step-by-st man this really is an annoying question
A roof rises 15 feet vertically and 12 feet horizontally. What is the slope of the roof?
Answer: 15/12 or in simplest form its 5/4
Step-by-step explanation:
Slope is rise/run
Answer:
Do you know rise over run?? The roof goes up 15 feet and to the left or right 12 feet... the slope would be 15/12 or it would be 1.25 (when divided). Hope it helps!
Step-by-step explanation:
What is the total cost for a ten-day trip
Answer:
omgggg I ready. the nostalgia .... The answers 250
$239 television; 10% discount
Step-by-step explanation:
cost of television-$239
discount-10%
239÷10
Answer:
$215.10
Step-by-step explanation:
I believe this is correct.
Hope this helps!
Plz help will name brainiest and 100 points
Answer:
51
Step-by-step explanation:
Multiply 3 2/5 by 15
Change the mixed number to an improper fraction
3 2/5 = (5 * 3 + 2) /5 = 17/5
17/5 * 15
17 * 15/5
17 * 3
51
Answer:
Hey bby <3 i would have to say it's E
Step-by-step explanation:
Rewrite in simpliest terms-
−0.2(3p−0.9)+0.4(−0.9p−5)
Answer:
-0.96p - 1.82
Step-by-step explanation:
Rewrite the linear equation x+3y=2.
Answer:
y=-1/3x + 2/3
Step-by-step explanation:
Write in slope-intercept form:
3y=-x+2
Divide by 3
y=-1/3x + 2/3
Determine wether the relation is a function (4,0),(2,0),(1,2),(2,4),(4,4),(5,2)
Answer:
This is not a function
Step-by-step explanation:
Hope this helps
Please answer i will brainliest:D
Jeremy is training for a race.When he trains,He runs on a path that is 1.25 miles long.Last week,Jeremy ran on the path 5 times,plus an extra 1.37 miles.How many miles did Jeremy run on the path last week
A.6.255
B.6.38
C.7.62
D.19.95
This is Lesson 4.5 5th grade go math book
Answer:
c.
Step-by-step explanation:
1.25x5=6.25
6.25+1.37=7.62
C) 7.62 miles
We can make an equation out of this.
5(1.25)+1.37=6.25+1.37=7.62
Pls helpppppppp......... :( :( :(
Answer:
Step-by-step explanation:
a: is not proportional
because you cant divide any of the tope numbers by the bottom numbers so u can leave the thing blanc.
b: is proportional
becuase you can divide the top and bottom by 30 so the answer is 30
hope this help :)
Answer: 30 for b
Step-by-step explanation:
Log_10 x =2 what does x equal???? Plz help
Answer:
x = 100
Step-by-step explanation:
[tex]Log_{10} x =2 \\ \\ x = {10}^{2} \\ \\ x = 100[/tex]
A meal has 408 calories in 8 serving find the unit rate. ANSWER PLEASE DUE TONIGHT
Answer:
51
Step-by-step explanation:
408/8= 51
(its that simple)
Jennifer wants to buy a new television set that regularly sells for $900. Because she works at the store, Jennifer will receive an employee discount of 30% off the regular price, but she will have to pay 6% sales tax on the adjusted price. What will be Jennifer's final cost to buy the television?
Answer:
$667.80
Step-by-step explanation:
30% of 900 is 270, so the price of the TV would be 630 without the tax. 6% of 630 is 37.8, so in total, the price would be $667.80
-25 - (-100) + 62.3 *
Answer:
137.3
Step-by-step explanation:
I really need help!
Write the equation of the line with the given slope which passes through the given point.Please show work.
m = 3 (2, -3)
graph y=|x|-5
a b c d
Answer:
Sorry, I don't exactly know what you mean by a b c d, however the graph of y=|x|-5 should be two rays with slopes of 1 and -1, meeting at the point (0,-5)
find the product (-5) (-6) (-2) (-1)
Answer:
60
Step-by-step explanation:
If you multiply -5 and -6 which is 30 and if you multiply -2 and -1, you get 2. If you multiply both 30 and 2, you get 60.
Answer:
Easy it's 60
Step-by-step explanation:
First solve step by step:
-5*-6
=30
30*-2
= - 60
-60* -1
= - 60Hopes This Helps!:)Trey needs to invest to help with his child's college fund. How much would he have to invest to have $89,600 after 14 years, assuming an interest rate
of 2.15% compounded monthly?
Do not round any intermediate computations, and round your final answer to the nearest dollar.
Answer:
final value:116.57
interest:26.97
2+2/4+7-9x(-5).
Please help me
Answer:
109/2 is the answer of your question . Use PEMDAS rule
NEED HELP IMAGE ATTACHED!!!
Answer:
A.
[tex] \frac{ {7x}^{2} - 5x + 1}{4x + 1} [/tex]
Step-by-step explanation:
Since the denominators are the same we just have to combine the top.
[tex] {x}^{2} - 5x + {6x}^{2} + 1[/tex]
Combine alike terms.
[tex] {7x}^{2} - 5x + 1[/tex]
put that over our denominator.
[tex] \frac{ {7x}^{2} - 5x + 1 }{4x + 1} [/tex]
Find the product of 11/12 (-2.4)
Answer:
-1.961666666666
Step-by-step explanation:
The highest level of PEMDAS here is multiplication/division which is done left to right. So do 11/12 first.
11/12 (-2.4)
.916 (-2.4)
Then multiply to get an answer of -1.961666666 ( the six repeats forever)
In a recent survey of 79 heads of household, 46 said they did online banking on their cell phones. Find the standard error for the sample proportion of heads of household who do online banking on their cell phones. Enter your answer as a decimal rounded to three decimal places.
Answer:
[tex]SE_p = 0.055[/tex]
Step-by-step explanation:
Given
[tex]n = 79[/tex] --- Heads
Proportion, p = 46 out of 79
Required
Determine the standard error for sample proportion (SEp)
This is calculated using the following formula
[tex]SE_p = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this case:
[tex]p = \frac{46}{79}[/tex]
[tex]p = 0.5823[/tex]
Substitute values for p and n in:
[tex]SE_p = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]SE_p = \sqrt{\frac{0.5823 * (1-0.5823)}{79}}[/tex]
[tex]SE_p = \sqrt{\frac{0.5823 * 0.4177}{79}}[/tex]
[tex]SE_p = \sqrt{\frac{0.24322671}{79}}[/tex]
[tex]SE_p = \sqrt{0.00307881911}[/tex]
[tex]SE_p = 0.0554871076[/tex]
[tex]SE_p = 0.055[/tex] ---- Approximated
58 = k + 6 show work if u can
Answer:
[tex]k = 52[/tex]
Step-by-step explanation:
Isolate k:
[tex]58 - 6 = k + 6 - 6[/tex]
solve for k:
[tex]k = 52[/tex]
Answer:
The answer is 52. Like it says move everything to one side
Stefan sells Jin a bicycle for $116 and a helmet for $16. The total cost for Jin is 110% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
He originally spent 120$
He made 12 extra dollars.
Step-by-step explanation:
To solve this I turned the 110% into a decimal.
So I divided 110 by 100 and got 1.1
In order to find the original number you would then need to divide the total cost of the bicycle and helmet together by 1.1
So, 116 + 16 = 132
132/1.1= 120
Hope this helps