Answer:
The area is changing at 15.75 square feet per second.
Step-by-step explanation:
The triangle between the wall, the ground, and the ladder has the following dimensions:
H: is the length of the ladder (hypotenuse) = 10 ft
B: is the distance between the wall and the ladder (base) = 6 ft
L: the length of the wall (height of the triangle) =?
dB/dt = is the variation of the base of the triangle = 9 ft/s
First, we need to find the other side of the triangle:
[tex]H^{2} = B^{2} + L^{2}[/tex]
[tex] L = \sqrt{H^{2} - B^{2}} = \sqrt{(10)^{2} - B^{2}} = \sqrt{100 - B^{2}} [/tex]
Now, the area (A) of the triangle is:
[tex] A = \frac{BL}{2} [/tex]
Hence, the rate of change of the area is given by:
[tex] \frac{dA}{dt} = \frac{1}{2}[L*\frac{dB}{dt} + B\frac{dL}{dt}] [/tex]
[tex] \frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} + B\frac{d(\sqrt{100 - B^{2}})}{dt}] [/tex]
[tex]\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} - \frac{B^{2}}{(\sqrt{100 - B^{2}})}*\frac{dB}{dt}][/tex]
[tex]\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - 6^{2}}*9 - \frac{6^{2}}{\sqrt{100 - 6^{2}}}*9][/tex]
[tex]\frac{dA}{dt} = 15.75 ft^{2}/s[/tex]
Therefore, the area is changing at 15.75 square feet per second.
I hope it helps you!
The rate of change (ROC) of the area with respect to (w.r.t.) time can be
found from the ROC of the area w.r.t. x and the ROC of x w.r.t. time.
At the time the ladder is 6 feet from the wall, the area is increasing at 15.75 ft.²/sec.Reasons:
The length pf the ladder = 10 feet
Rate at which the ladder is pulled from the wall, [tex]\displaystyle \frac{dx}{dt}[/tex] = 9 feet per second
Required:
The rate at which the area of the triangle formed by the ladder, the wall
and the ground, is changing at the instant the ladder is 6 feet from the wall.
Solution:
The area the triangle, A = 0.5·x·y
Where;
x = The distance of the ladder from the wall
y = The height of the ladder on the wall
By Pythagoras's theorem, we have;
10² = x² + y²
Which gives;
y = √(10² - x²)
Therefore;
The area the triangle, A = 0.5 × x × √(10² - x²)
By chain rule, we have;
[tex]\displaystyle \frac{dA}{dt} = \mathbf{\frac{dA}{dx} \times \frac{dx}{dt}}[/tex]
[tex]\displaystyle \frac{dA}{dx} = \frac{d\left(0.5 \cdot x \cdot \sqrt{10^2 - x^2} }{dx} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}}[/tex]
[tex]\displaystyle \frac{dA}{dx} = \frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}[/tex]
Therefore;
[tex]\displaystyle \frac{dA}{dt} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100} \times 9}[/tex]
When the ladder is 6 feet from the wall, we have;
x = 6
[tex]\displaystyle \frac{dA}{dt} = \frac{\left(6^2 - 50\right) \cdot \sqrt{100-6^2} }{6^2-100} \times 9 = \mathbf{15.75}[/tex]
At the time the ladder is 6 feet from the wall, the area is increasing at 15.75 ft.²/sec.
Learn more about chain rule of differentiation here:
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There are between 25 and 35 students in a class.
The ratio of boys to girls is 4:7.
How many students are in the class?
Answer:
33
Step-by-step explanation:
ratio is 4:7 multiple of 2 its 8:14 which sum up to 22(below range) multiple of 3; it is 12:21 which sum up to 33 students(within range)
for multiple of 4; 16:28 which sum up to 44(above range)
PLZ HELP I WILL GIVE BRAINLIEST FOR THE 1ST PERSON TO ANSWER!!
there are 15 peices of fruit in a bowl and 6 of them are apples what percentage of the peices of fruit are apples
Answer:
40%
Step-by-step explanation:
6/15 = 0.4
0.4x100 = 40%
Question 4
12 marks
4.1 a. In each case find the unit cost and then state which is the better buy.
4 marks
6kg of potatoes for $2.45 or
15 kg of potatoes for $5.9 or
10 kg of potatoes for $3.92?
Answer:
The better buy is to buy 10 kilograms of potatoes at $ 3.92, since each kilogram costs $ 0.392.
Step-by-step explanation:
To find the cost per unit in each case and then state which is the better buy, the following calculations must be performed:
6kg of potatoes for $ 2.45:
2.45 / 6 = 0.408
15 kg of potatoes for $ 5.9:
5.90 / 15 = 0.393
10 kg of potatoes for $ 3.92:
3.92 / 10 = 0.392
Thus, the better buy is to buy 10 kilograms of potatoes at $ 3.92, since each kilogram costs $ 0.392.
Sean took 6 tests and currently has an average of a 90. His range of his scores was 18 and the mode of the test scores is 89.
Answer:
what is the question?
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
Total scores = 6*90 = 540.
He had more than one 89 ( mode) and max score - min score = 18.
Let max score = x then min = x-18.
Lets say he has 3 89's then
x + x - 18 + 3*89 + y = 540 where y is another score then:
2x + 249 + y = 540
2x + y = 291
x = 98 and y = 95 will fit this so the 6 scores could be
80, 89, 89, 89, 95, 98.
If a cookie recipe calls for ¾ cup of sugar and you have 9 ½ cups of sugar, how many whole batches of cookies can you make?
Answer:
c
Step-by-step explanation:
i just did t
Answer:
12
Step-by-step explanation
A ranch hand herded his cattle to some grazing land. Then he began riding back to the ranch,
which is due west, at 7 miles per hour. Simultaneously, the cows began moving away from
him, too, headed due east at 3 miles per hour. How long did it take for the herd and the
ranch hand to be 2 miles apart? (Please help me !!)
Answer:
1/5 hr or 12 min
Step-by-step explanation:
We are going to use the formula D = RT
Let t = the time for them to be 2 mi. apart
Then 7t = the distance the ranch hand traveled
and 3t = the distance the cows traveled
Since they traveled in opposite directions, the sum of their distances will give us how far they are apart.
So, 7t + 3t = 2
10t = 2
t = 2/10 = 1/5 hr. = 12 min.
Justin has $7.50 more than Eva, and Emma has $12 less than Justin. Together, they have a total of $63.00. How much money does each person have?
i only have 5 min help fast
Answer:
To make it easier, lets say Justin = J, Eva = E, and Emma = M. Then, J = E + 7.50 M = J -12 J + E + M = 63 You can substitute for M in the third equation using the second equation, and you get: J + E + J - 12 = 63 Clean it up a little bit and you get: 2J + E = 75 You know J = E + 7.50, so substitute that for J and you get: 2(E + 7.50) + E = 75 2E + 15 + E = 75 3E + 15 = 75 3E = 60 E = 20 ; meaning that Eva has $20. Justin has $7.50 more than Eva, so he has $27.50. Emma has $12 less than Justin, so Emma has $15.50. Double check your answer by making sure they all add up to 63, which they do.
Find the slope of a line perpendicular to the equation: 3x – 2y = 6
Answer:
3/2x
Step-by-step explanation:
I need help please help
Answer:
137
Step-by-step explanation:
Scientists conducting a study on global climate change want to determine if there has been an increase in the number of days per year that the temperature in El Paso rises above 100 degrees. In 1981, there were 21 days (5.75%) where the temperature was in the triple digits. The scientists want to know whether this percentage has increased. Which pairs of hypotheses is the most appropriate for addressing this question?
Answer:
The percentage maybe went up because of air pollution, and global warming
Step-by-step explanation:
What is the standard form equivalent of this quadratic expression in factored form? (2x-3)(3x-4)
Answer: 6x^2 -17x +12
Step-by-step explanation:
Cameron has a mask collection. He keeps 267 of the masks on his wall, which is 89%
of his entire collection. What is the total number of masks in Cameron's collection?
Answer:
300 masks
Step-by-step explanation:
If 267 is 89% of the whole amount, we can set up the following proportion:
[tex]\frac{89}{100} =\frac{267}{x}[/tex], where x is the total amount of masks we need to find.
If we cross-multiply, we get 26700=89x. Divide both sides by 89, and we get 300. So, Cameron has a total of 300 masks in his collection.
I hope this helped.
Answer:
300 masks
Step-by-step explanation:
89% = 0.89
( / ) = divided by
267/total amount of masks = 0.89
267/0.89 = 300
300 masks in total
HELP PLEASE THIS IS DUE IN 5 MINUTES
Answer:
Part A:
Since Jasmine has more cousins rhan Brenda, who has 4 cousins, then the amount of cousins that Jasmine has (j) is greater than 4 so j > 4
Part B:
We have a number line and we draw an arrow starting from 4 and going to the right.
Hope this helped!
Answer:
4.8h - 2.3d - 14
Step-by-step explanation:
When the football play started,
Tony ran forward 20 yards,
then turned around and ran 5 yards back.
He stood in that spot for 3 seconds,
then walked back to where he began.
The two tables below show the amount of tip, y, included on a bill charging x dollars. Restaurant B Restaurant A 10 20 30 10 25 50 75 1 2 3 EN Which compares the slopes of the lines created by the tables? 1. O The slope of the line for Restaurant B is 5 times greater than the slope of the line for Restaurant A. O The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A. O The slope of the line for Restaurant B is 5 times greater than the slope of the line for Restaurant A. O The slope of the line for Restaurant B is 10 times greater than the slope of the line for Restaurant A.
Answer:
The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.
Step-by-step explanation:
5 cakes shared between 3 people. what does each person recieved
Answer:
Each person recieves 1.6 of the cakes.
Step-by-step explanation:
5 divided by 3 equals to 1.6.
Find the missing exponent.
100
10,000
Submit
Answer: 1000
Step-by-step explanation:
You just simply add a 0!
Answer: The missing exponent is [tex]100^{2}[/tex]
Step-by-step explanation: When you multiply 100 x 100 you get 10,000.
90 boxes of fruit sold 72, what percentage did I sell
(90 - 72)/90 = P/100
Let P = percentage
18/90 = P/100
90P = 100(18)
90P = 1,800
P = 1,800/90
P = 20
Now 100% - 20%
You sold 80% of the boxes of fruits.
What is the equation of the line that passes through the point (-1, -5) and has a slope of -2?
Answer:
2x+y=-7
Step-by-step explanation:
y-y1=m(x-x1)
y-(-5)=-2(x-(-1))
y+5=-2(x+1)
y=-2x-2-5
y=-2x-7
-2x-y=7
2x+y=-7
Find the value (5x2 - 6x) = 3x
Answer:
x=0, 1+4/5
Step-by-step explanation:
do you need a Step-by-step explanation?
The ratio of blue paint to yellow paint in a green paint mixture is 2:3. If you use 16 ounces of blue paint how much ounces of yellow paint. Use tape diagram
Answer:
Step-by-step explanation:
2 in 2:3 is the amount of blue paint
3 in 2:3 is the amount of yellow paint
Figure out how many times to multiply 2 to get 16:
16/2=8
Now, multiply 3 by 8, which would be equal to 24.
Ratio: 16:24
A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $31.the total cost to rent 2 chairs and 6 tables is $22.what is the cost to rent each chairs and each table?
Answer:
$1.25 & $10.25
Step-by-step explanation:
Let c be the cost of renting one chair and t be the cost of renting table. We're given two equations:
#1. 5c + 3t = 37
#2. 2c + 6t =64
We have a system of equations. Using our system of equations calculator, we can solve this problem any of 3 ways below:
Chairs (c) cost $1.25Tables (t) cost $10.25Which linear inequality represents the graph
OW!
(-2, 3)
-5
(0, -2)
Answer:
It has a negative slope, so B and C are eliminated. The graph also has a solid line instead of a dashed line. This means D is eliminated because it is only greater than. If the graph had a dashed line, then D would be correct, but it does not. So then the answer is A
Alex needs 36 boxes in the carton above.
Answer:
1 stack of 36
Step-by-step explanation:
First find how much one carton can hold
length is 45
width is 20
height is 40
40 * 20 * 45 = 36,000
Then find how much volume each box has
length is 20
width is 10
height is 5
5 * 10 * 20 = 1000
so each box is 1000 volume
1 stack of 36 is good
Please help! :( If AJKL = ARST, which congruences are true by CPCTC? Check all that apply.
A. ZL ZR
B. KL: ST
C. KZS
D. JK = RS
E. JL - RS
F. LJ2S
Step-by-step explanation:
I just got it on a pex. JK=RS. KL=ST. K=S. those are the answers
The congruences that are true by CPCTC are:
∠L = ∠R
KL ≅ ST
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
If ΔJKL = ΔRST, then the corresponding parts of the triangles are congruent.
CPCTC stands for "corresponding parts of congruent triangles are congruent,"
So we can use this property to determine which congruences are true.
∠L = ∠R:
This is true by CPCTC because they are corresponding angles in congruent triangles.
JK ≅ RS:
This is not true by CPCTC because they are not corresponding sides in congruent triangles.
KL ≅ ST:
This is true by CPCTC because they are corresponding sides in congruent triangles.
JL ≅ RS:
This is not true by CPCTC because they are not corresponding sides in congruent triangles.
∠L = ∠S:
This is not necessarily true just by the fact that ΔJKL = ΔRST.
It could be true in some cases, but it is not guaranteed by CPCTC.
Therefore,
The congruences that are true by CPCTC are:
∠L = ∠R
KL ≅ ST
Learn more about triangles here:
https://brainly.com/question/25950519
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What is the radius of the cone in the diagram? Round your answer to the nearest whole number.
Answer:
r = 4 units
Step-by-step explanation:
Volume of cone = 201.06 cubic units
Height (h) = 12 units
Radius (r) = ?
Thus, formula for volume of cone = ⅓*πr²h
Plug in the values and solve for r
⅓*π*r²*12 = 201.06
r²*4*π = 201.06
r²*12.57 = 201.06
Divide both sides by 12.57
r² = 201.06/12.57
r² = 15.9952267
r = √15.9952267
r ≈ 4 units
Answer:
Sample answer
like and Rate!!!
Leah spins each spinner one time what is the probali
After completing this activity, what is your initial explanation of how the populations of predators and prey are related? plz help
Answer:
prey and predators depends in each other .in the absence of one another is useless or meaning less. predators is responsible for population of prey.if less predators more prey and more predators means less prey.
Answer:
A predator-prey relationship tends to keep the populations of both species in balance. ... As the prey population increases, there is more food for predators. So, after a slight lag, the predator population increases as well. As the number of predators increases, more prey are captured.
Step-by-step explanation:
is 0.8 larger than 0.83
Answer:
no, 0.83 is larger.
Step-by-step explanation:
it says I need at least 20 characters so I'm typing this:) have a good day
