Answers
Answer:
[tex]\left.\dfrac{\text{d}x}{\text{d}t}\right|_{h=2}\approx0.184\; \sf m/s[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Given variables:
a = length of the ladder.h = height of the ladder's top at time t.x = distance of the ladder from the wall at time t.Given a = 8.9, use Pythagoras Theorem to create an equation for x² in terms of h²:
[tex]\implies x^2+h^2=a^2[/tex]
[tex]\implies x^2+h^2=8.9^2[/tex]
[tex]\implies x^2+h^2=79.21[/tex]
[tex]\implies x^2=79.21-h^2[/tex]
Differentiate with respect to h:
[tex]\implies 2x\dfrac{\text{d}x}{\text{d}h}=0-2h[/tex]
[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{2h}{2x}[/tex]
[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{h}{x}[/tex]
Given:
[tex]\dfrac{\text{d}h}{\text{d}t}=-0.8\; \sf m/s[/tex]
Therefore:
[tex]\begin{aligned} \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}h}\times \dfrac{\text{d}h}{\text{d}t}}\\\\ \implies &=-\dfrac{h}{x} \times -0.8\\\\ &=\dfrac{0.8h}{x} \end{aligned}[/tex]
Calculate x when h = 2:
[tex]\implies x^2=79.21-2^2[/tex]
[tex]\implies x^2=79.21-4[/tex]
[tex]\implies x^2=75.21[/tex]
[tex]\implies x=\sqrt{75.21}[/tex]
Substitute the values of h and x into the equation for dx/dt:
[tex]\implies \dfrac{\text{d}x}{\text{d}t}=\dfrac{0.8 \times 2}{\sqrt{75.21}}=0.1844939751[/tex]
Therefore, the rate of the ladder's distance from the wall is 0.184 m/s (3 d.p.)
Related Questions
Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Answers
It will take 25 minutes for the two containers to have the same amount of water .
In the question ,
it is given that ,
water present in container A = 200L
water present in container B = 500L
rate at which the water is filling in container A= 6 liter/minute
rate at which the water is draining in container B = 6 liter/minute
let the time taken = m minutes ,
So , According to the question ,
the equation representing the situation is
200 + 6m = 500 - 6m
Simplifying further , we get
6m + 6m = 500 - 200
12m = 300
m = 300/12
m = 25
Therefore , It will take 25 minutes for the two containers to have the same amount of water .
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L, M and N are points on a circle, centre O.
QMT is the tangent at M
(1) find LNOM
(2) find LNMQ
Please help me guys it urgent it would really make my day.
Answers
The size if the angle NOM is 54.
What is angle?
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
What is tangent of circle?
A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet.
Given,
M and N are points on a circle.
QMT is the tangent
O is the center.
angle NOM = 2 angle NLM
NOM = 2(27)
= 54.
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Please help with slope question
Answers
choose any 2 points on the graph
To calculate the slope use the formula:
slope = y (point 2)-y (point 1)/x (point 2)-x (point1)
substitute the choses points in
calculate your awnser
help help help help help help
Answers
When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
What are graph equations?Equations with graphs as unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory.Different graph equations may be used to express the aforementioned graphs.So, the equations are graphs are:
Given equation: f(x) = 3x + 4Which is transform to equation: h(x) = f(x + 3)Now, graph both equations as follows:
Both equations are parallel to each other.(Refer to the graph attached below)Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.
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HELP ITS DUE IN A LITTLE BIT!!!
Answers
Answer:
Step-by-step explanation:
Yes it does
10 and 15
Answer:
A. the independent and dependent variables are the number of miles and total fee (y = 2.8 + 3.5x)
B. the domain is 0 <= x <= 20 and range is 2.8≤x≤20
Step-by-step explanation:
SOLVE FOR X Help please
Answers
Answer:
x = 20
Step-by-step explanation:
Comment
If you follow the angles down, you discover 2 things
There are only 2 answers
One is the supplement of the other.
In this case, both angles can be shown to be the same. The process is accomplished by two vertically opposite angles and 2 supplements. I can't show you how this is done because there are no letters on the lines.
It turns out that 3x + 10 = 4x - 10
Solution
3x + 10 = 4x - 10 Add 10 to both sides
3x + 10 + 10 = 4x - 10 + 10 Combine
3x + 20 = 4x Subtract 3x from both sides.
3x-3x + 20 = 4x-3x Combine
20 = x
What is the total volume of both boxes if s equals 8 inches
Answers
The total volume of both cubed boxes, combined, is of:
612 cubic inches.
What is the volume of a cube?The volume of a cube of side length s is given by the side length s cubed, as shown by the formula presented as follows:
V = s³.
In this problem, the boxes are given as follows:
Cubed box with side length of s = 8 inches.Cubed box with a volume of 100 cubic inches.The volume of the box with side length 8 inches is given as follows:
V = 8³ = 512 cubic inches.
(measure is in inches, hence the cubed measure is in cubic inches).
The total volume is given by the sum of the volumes of the two boxes, hence:
Total volume = 512 cubic inches + 100 cubic inches = 612 cubic inches.
Missing InformationThe image showing the cubes is given at the end of the answer.
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Solve x² + 5x - 14 = 0
Answers
By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
Given,
In the question:
To solve the equation:
x² + 5x - 14 = 0
Now, According to the question:
x² + 5x - 14 = 0
Split the middle term into two terms :
x² - 2x + 7x - 14 = 0
Factor the first two terms and the last two terms separately
x(x - 2) + 7 (x -2) = 0
Factor out
(x - 2) (x + 7) = 0
Apply Zero Product Property
x - 2 = 0 or x + 7 = 0
x = 2 or x = -7
Hence, By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
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Sandy bought an outboard motor for a total selling price of $420 in Maine, which has a 7% sales tax rate. Calculate the sales tax.
Answers
Answer
you do 420x0.7= 29.40
Answer:
The sales tax is 29.4
Step-by-step explanation:
Just divide in half until you reach 5 and then calculate the other 2 percent of it and add the 2 percent back onto it.
A goat is tied by a rope 2.5 m to a peg
in some grass. The goat eats 1 m² of
grass in
28 min. How long does it take to eat all that
it can reach?
Answers
Time taken to eat all = 549.5 minutes.
What is unitary method?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
The goat can rototate in a circule the radius of the curcle is 2.5 mSo the area of circle is;A=(pi) (r^2)A=(3.14)(2.5)^2A=19.625 m^2As 28 minutes for 1 m^2 so;Time taken to eat all = (28)(19.625)=549.5 minutesHence,Time taken to eat all = 549.5 minutes.
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wilma can mow a lawn in 40 minutes. vanessa can mow the same lawn in 120 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?
Answers
It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.
A lawn can be mowed by Wilma in 40 minutes. In one hour, Vanessa can cut the same lawn in 120 minutes.
1/120 + 1/40 = 1/T
multiply by 40T;
3T = 40
T = 40/3
= 13 1/3 minutes
= 13 minutes 20 seconds
It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.
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what is the smallest positive integer $n$ such that the rightmost three digits of $n!$ and $(n 1)!$ are the same?
Answers
The smallest positive integer n will be 10 .
To find : the smallest positive integer n such that the rightmost digits of n ! and ( n + 1 ) ! are same .
Since ,
putting n = 10 gives
n ! = 10 ! = 3628800
and ( n + 1 ) ! = 39916800
Last three digits ( rightmost digits ) ie. 800 are same .
Hence , n = 10 is the required answer ,
Therefore , the smallest positive integer is n = 10 such that the rightmost digits of n ! and ( n + 1 ) ! are same .
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f(x) = x + 2
g(x) = 3x
Work out the value of gf (4).
Answers
The value of gf(4) is 18
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given,
f(x) = x + 2
g(x) = 3x
Now we need Function of a function
i.e. g[f(x)]
Then on g(x) we have to replace the x with f(x)
Thus,
g[f(x)] = 3(x + 2)
= 3x + 6
Now by evaluating at
x = 4 i.e.
gf(4) = 3(4) + 6
gf(4) = 12 + 6
gf(4) = 18
Hence, The value of gf(4) = 18
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The sum of two numbers is 12. The difference of the same two numbers is -4. Wht is the smaller number?
Answers
Answer:
The smaller number is 4.
Step-by-step explanation:
X and Y are the two numbers
x+y=12
x-y=-4
Subtract these two equations
(x+y=12)
-(x-y=-4)
—————-
2y=16
y=8
Plug it in to any equation:
x+y=12
x+8=12
x=4
If x²y - 3x = y³ – 3, then at the point (-1,2), dy/dx=
Answers
now, the assumption in this implicit differentiation is that "y" is really a function in x-terms, whilst "x" is just a simple variable
[tex]x^2y-3x=y^3-3\implies \stackrel{product~rule}{\left( 2xy + x^2\cdot \cfrac{dy}{dx} \right)}-3=\stackrel{chain~rule}{3y^2\cdot \cfrac{dy}{dx}} \\\\\\ 2xy-3=3y^2\cdot \cfrac{dy}{dx}-x^2\cdot \cfrac{dy}{dx}\implies 2xy-3=\cfrac{dy}{dx}(3y^2-x^2) \\\\\\ \left. \cfrac{2xy-3}{3y^2-x^2}=\cfrac{dy}{dx} \right|_{(-1,2)}\implies \cfrac{2(-1)(2)-3}{3(2)^2-(-1)^2}\implies -\cfrac{7}{11}[/tex]
Given g(x)=-x-4g(x)=−x−4, solve for xx when g(x)=10g(x)=10.
Answers
The solution for x in the function when the function g(x) = 10 is 4
How to determine the solution for x in the function?From the question, we have the following equation that can be used in our computation:
g(x)=x-4
To make the equation legible, we need to rewrite it
So, we have the following representation
g(x) = x - 4
Also from the question, we have
g(x) = 10
This means that we calculate x when g(x) = 10
Substitute the known values in the above equation, so, we have the following representation
10 = x - 4
So, we have the following equation
x - 4 = 10
Add 4 to both sides of the equation
So, we have the following representation
x - 4 + 4 = 10 + 4
Evaluate the equation
x = 14
Hence, the solution is 14
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The sum of the ages of pam,dion, and their three children, in years, is 5x - 99. where x is dion's age. pam is five years younger than dion. what is the usm of the ages of their children?
Answers
The sum of the ages of the children would be 3x - 94 years.
We have the total sum of the ages of pam ,dion and their children
as 5x - 99
here , x is the age of Dion .
we see , pam is five years younger than Dion , so
age of Pam = x - 5
Now as the sum of all the ages = 5x - 99
therefore ,
Age of Dion + Age of Pan + Age of children = 5x - 99
x + x - 5 + Age of children = 5x - 99
2x - 5 + Age of children = 5x - 99
therefore ,
Age of children = 3x - 94
So the age of their children would be 3x - 94 years
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sam rolls 3 standard fair dice. that probability that the three numbers rolled on the dice are the sides of a triangle is , where are relatively prime positive integers. what is the value of ?
Answers
The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.
Here,
When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).
Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.
As a result, 186 outcomes or triplets are possible and satisfy this property.
Hence, the required probability is 186/216=31/36.
The required probability is 31/36 for three dice rolls to produce triangle sides.
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Which of the following equations have infinitely many solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-6x+35=-6x-35−6x+35=−6x−35minus, 6, x, plus, 35, equals, minus, 6, x, minus, 35
(Choice B)
B
-6x+35=-6x+35−6x+35=−6x+35minus, 6, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice C)
C
6x+35=-6x+356x+35=−6x+356, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice D)
D
6x+35=-6x-356x+35=−6x−356, x, plus, 35, equals, minus, 6, x, minus, 35
Answers
The equation which has infinitely many solutions include the following: B. -6x + 35 = -6x + 35
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal.
This ultimately implies that, an equation would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and intercept for the two lines are the same.
In this scenario, we can reasonably and logically deduce that the following equations satisfy the condition for an equation which has infinitely many solutions:
-6x + 35 = -6x - 35 (False).
-6x + 35 = -6x + 35 (True).
6x + 35 = -6x + 35 (False).
6x + 35 = -6x - 35 (False).
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Complete Question:
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A. -6x + 35 = -6x - 35
B. -6x + 35 = -6x + 35
C. 6x + 35 = -6x + 35
D. 6x + 35 = -6x - 35
please help. ill give brainliest
Answers
Answer:
X=30
Step-by-step explanation:
[tex](4x + 30) + (2x - 30) = 180 \\ 4x + 2x + 30 - 30 = 180 \\ 6x = 180 \\ x = 30[/tex]
Answer:
x = 30
Step-by-step explanation:
We are told that:
• m∠A = (4x + 30)°
• m∠B = (2x - 30)°,
and that these two angles are supplementary to each other.
When two angles are supplementary to each other, it means that they add up to 180°.
Therefore:
∠A + ∠B = 180°
⇒ (4x + 30)° + (2x - 30)° = 180°
⇒ 4x + 30 + 2x - 30 = 180
⇒ 4x + 2x + 30 - 30 = 180 [Combining like terms]
⇒ 6x = 180
⇒ [tex]\frac{6}{6}x = \frac{180}{6}[/tex] [Dividing both sides of the equation by 6]
⇒ x = 30
Solve for X:
1/2x + 1/3x = 10
Answers
Answer:
Step-by-step explanation:
weknr f not sure
Answer:
12
Step-by-step explanation:
1/2x+1/3x=10
We simplify by making common denominator and adding them (if you don’t know how to do that please tell me)
3/6x+2/6x=10
5/6x=10
Now divide 5/6 on both sides
5/6x=10
/5/6. /5/6
x=10*6/5
x=60/5
x=12
Hopes this helps please mark brainliest
Which is not true about a direct porprtion
Answers
The equation of the line in slope - intercept form will be -
y = (4/5)x + 5
Writ the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
At [c] = 0 -
y = mx
We have a directly proportional relation.
The general equation of a straight line is -
[y] = [m]x + [c]
At [c] = 0, y = mx
m = y/x
where [m] acts as a constant of proportionality.
So -
y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.
Therefore, y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.
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Simplify the expression:
2(2f+5) =
Answers
Answer:
4f+10
Step-by-step explanation:
multiply the 2 to both the numbers in the parenthesis. 2 times 2f is 4f and 2 times 5 is 10
Solve for an angle in right triangles
I just need the answer :)
Answers
Answer:
19.47
Step-by-step explanation:
Answer:
[tex]m\angle A \approx 19.47 \textdegree[/tex]
Step-by-step explanation:
Utilize the trigonometric ratio sine.
[tex]\sin(m\angle A) = \dfrac{2}{6}[/tex]
[tex]\sin(m\angle A) = \dfrac{1}{3}[/tex]
[tex]m\angle A = \sin^{-1}\left( \dfrac{1}{3} \right)[/tex]
[tex]m\angle A \approx 19.47 \textdegree[/tex]
Can anyone write the equation of this graph?
Answers
The equation of the graph in the figure is f(x) = |x - 3| + 5
How to find the equation of the graph line?Given that the graph is an absolute value graph
We start by calculating the vertex of the graph
In this case, the graph has it minimum point located at the coordinate (3, 5)
This coordinate can then be interpreted as
(h, k) = (3, 5)
As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = |x - 3| + 5
Hence, the equation of the graph is f(x) = |x - 3| + 5
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a license plate consists of 2 letters followed by 4 digits. how many license plates are possible if the 1st digit cannot be 0, and letters and digits may repeat? a) 4,100,625 b) 6,760,000 c) 4,435,236 d) 5,625,000 e) 6,084,000 f) none of the above.
Answers
The possible number of license plates is 6084000 .
We have to make a 6 word license plate in which first two are letters and remaining four are digits.
conditions are :
1. letters and digits can repeat themselves
2. 1st digit can't be 0.
taking into account these conditions
we know total letters are 26 and total digits are 10 ( 0,1,2,3,4,5,6,7,8,9)
Now if we divide number plate in 6 columns where first two are filler by letters and rest four by digits so
1st column can be filled in ways = 26
2nd column can be filled in ways = 26
3rd column can be filled in ways = 9 ( as zero is not allowed )
4th column can be filled in ways = 10
5th column can be filled in ways = 10
6th column can be filled in ways = 10
therefore, total number of ways = 26x26x9x10x10x10
= 6084000 ways
The possible number of license plates is 6084000 .
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How do you find the x for both of these problems?
Answers
Considering the figure the required angle is solved using the vertical angle theorem. The values are
14. 42 degrees and 16. 20 degreesHow to determine the required angleThe problem is solved considering this theorems
vertical angle theorem
According to this theorem, when two straight lines cross, they create two sets of linear pairs and the vertical opposite angles are equal.
solution for the missing angle
x + 70 + 60 = 180 sum of angles of a triangle
x = 50
Using vertical angle theorem
? + 88 + 50 = 180 sum of angles of a triangle
? = 180 - 88 - 50
? = 42
solution for the missing angle
x + 75 + 30 = 180 sum of angles of a triangle
x = 75
Using vertical angle theorem
? + 88 + 75 = 180 sum of angles of a triangle
? = 180 - 85 - 75
? = 20
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What is the value sine?
5/12
5/13
12/13
13/5
Answers
Answer:
(C.) 5/13
Step-by-step explanation:
The sine proportion is opposite / hypotenuse
Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse
Thus, sine is 5/13
Describe in words where cube root of 24 would be plotted on a number line.
100 points and brainliest
Answers
Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.
Step-by-step explanation:
after collecting the historical data from a process of filling coca-cola bottles, it was found that the variance in the filling process is constant. however, clogs in the machine often affect the average volume. the historical standard deviation is 5 ml. in filling 250 ml bottles, a sample of 20 bottles found an average of volume of 246 ml. create a 95% confidence interval for the average volume of coca-cola in a bottle. can you conclude from your results that the manufacturer needs to adjust the equipment to meet the standard?
Answers
The manufacturer needs to adjust the equipment to meet the standard with the margin of error of 2.34.
Define the term margin of error?The calculated number known as the margin of error is added to and removed from the mean value to get the resulting confidence interval. The confidence interval expands as the margin of error does.
Alpha value = 0.05Standard deviation = 5Sample size = 20Sample average = 246Calculate the 95% confidence interval's margin of error based on the aforementioned data.
α = 0.05
n = 20
s = 5
The following is the formula to determine the margin of error:
E = T(n-1) ×s/√n
The t-distribution table is used to determine the value of tn-1 at 19 degrees of freedom.
Replace the values in the formula above.
E = 2.093 ×5/√20
Thus, its margin of error is 2.34 as a result.
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