5) Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s. With dimension as in Figure 5:
(a) Find a formula for the speed of the wagon in terms of q and the variable x in the figure.
(b) Find the speed of the wagon when x=0.6 if q=0.5 m/s.
Answers
The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.
[tex](a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.
Reasons:
(a) The distance from the cart to the pulley, r is given by Pythagoras's
theorem as follows;
r = √((3 - 0.6)² + x²) = √(2.4² + x²)
The speed of the wagon = [tex]\mathbf{\dfrac{dx}{dt}}[/tex]
The speed of the rope, q = [tex]\mathbf{\dfrac{dr}{dt}}[/tex]
By chain rule, we have;
[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}[/tex]
[tex]\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
Therefore;
[tex]\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}[/tex]
[tex]\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}[/tex]
(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;
[tex]\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243[/tex]
The speed of the wagon when x = 0.6 and q = 0.5 m/s, [tex]\dfrac{dx}{dt}[/tex] ≈ 0.243 m/s
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Related Questions
Progressions A person borrowed a sum of Rs. 3400 from his provident fund account on the condition to repay in 22 monthly installment of Rs. 150 and last installment of Rs. 100. Calculate the S.I. at the rate of 4.5% pa, which he , has to pay as the 24th installment?
Answers
question but I am solving four questions, Please try to
understand me and its my humble request to create
separate post for each question.
In a class of 60 students, 38 are Democrats, 12 are business majors, and 8 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of
choosing a Democrat or a business major.
P(Democrat or business major) =
(Simplify your answer. Type an integer or a simplified fraction.)
Answers
Answer:
7/10 or
0.7 or
70 percent
Step-by-step explanation:
[tex]p (democrat \: or \: business \: major \: ) = \frac{30 + 4 + 8}{60} [/tex]
[tex] = \frac{42}{60} [/tex]
[tex] = 7/10[/tex]
Therefore, the probability is 7/10, 0.7 or 70 °/•
Please help me :0
What is the order of this matrix?
Answers
============================================================
Explanation:
The order of a matrix is a way of describing its size. Specifically, the order is represented in the form [tex]m \times n[/tex], where,
m = number of rowsn = number of columnsThe rows are laid out horizontally, and the columns are vertical.
In this case, we have 5 rows and 3 columns. Therefore, the answer is 5 x 3. The order is important because a 5 x 3 matrix is different from a 3 x 5 matrix.
can find anything to answer this
Answers
Answer:
where?
Step-by-step explanation:
maybe I can help to your question
Explain bc MN is not midsegment
Find the area (A) of the figure below: 166) 6cm A) 18 square cm B) 35 square cm 12cm C) 72 square cm D) 144 square cm 167) 12 in A) 37.68 square inches B) 72.52 square inches C) 108.12 square inches D) 113.09 square inches
Answers
Answer:
166) C. 72 square cm 167) D. 113.09 square inches
Step-by-step explanation:
166) Parallelogram area formula is A=Base x height
A= 6 x 12
A= 72
167) Circle area formula A=πr²
r= half of diameter (12)
A=π(6)²
A=112.09
The sum of two numbers is 17 and their product is 66 what are the two numbers.
Answers
Answer:
11 and 6
Step-by-step explanation:
Let the numbers be X and Y
Then their sum: X+Y=17 equation 1
Product: X×Y=66 equation 2
X+Y=17. X =17-Y
XY=66.
(17-Y)Y=66 -Y²+17Y-66=0
Y=6 or 11
X=17-Y. X=17–6=11 or X=17–11=6
Therefore you can conclude that the numbers are 11&6
Answer:
11 and 6
Step-by-step explanation:
x + y = 17
x × y = 66
First, solve for y
x + y = 17
x + y - x = 17 - x
y = 17 - x
Then substitute y to x × y = 66
x × y = 66
x(17 - x) = 66
17x - [tex]x^{2}[/tex] - 66 = 66 - 66
- [tex]x^{2}[/tex] + 17x - 66 = 0
(- [tex]x^{2}[/tex] + 17x - 66) = 0
(-x + 6)(x - 11) = 0
-x + 6 = 0
-x + x +6 = 0 + x
6 = x or x = 6
x - 11 = 0
x - 11 +11 = 0 + 11
x = 11
Then the numbers are 11 and 6
Select whether the equation has a solution or not.
√5-7
no roots
O roots
Answers
[tex] \sqrt{x} = 7[/tex]
[tex]x = {7}^{2} [/tex]
[tex]x = 49[/tex]
Root.
Solve for x:
Spam: WHSIYWsugwediywedw
Answers
Answer:
um whats m or y?
Step-by-step explanation:
Answer:
[tex]x=3m+y[/tex]
Step-by-step explanation:
Let's solve for [tex]x[/tex].
[tex]m=\frac{x-y}{3}[/tex]
Step 1: Flip the equation.
[tex]\frac{1}{3}x+\frac{-1}{3}y=m[/tex]
Step 2: Add [tex]\frac{1}{3}y[/tex] to both sides.
[tex]\frac{1}{3}x+\frac{-1}{3}y+\frac{1}{3}y=m+\frac{1}{3}y[/tex]
[tex]\frac{1}{3}x=m+\frac{1}{3}y[/tex]
Step 3: Divide both sides by [tex]\frac{1}{3}[/tex].
[tex]\frac{\frac{1}{3}x }{\frac{1}{3} } ={\frac{m+\frac{1}{3}y }{\frac{1}{3} }[/tex]
[tex]x=3m+y[/tex]
Answer:
[tex]x=3m+y[/tex]
Four movie tickets cost $48. At this rate, what is the cost of...
a. 5 movie tickets? Show your work.
b. 11 movie tickets? Show your work.
Answers
5 movie tickets will cost $60 because 5 times 12 is 60.
11 movie tickets will cost us $121 because 11 times 12 is 121!
Hope this helps!! :)
Let be an angle in quadrant I such that sin +10 Find the exact values of sec 0 and tan 0.
Answers
Answer:
just look at picture's That's the answer
Circles C and C′ are similar. State the translation rule and the scale factor of dilation.
Question 12 options:
A) To obtain C′, circle C is translated to the right four units and down three units and is dilated with a scale factor of one.
B) To obtain C′, circle C is translated to the left three units and up two units and is dilated with a scale factor of 1∕2.
C) To obtain C′, circle C is translated to the right three units and down two units and is dilated with a scale factor of one.
D) To obtain C′, circle C is translated to the right three units and down two units and is dilated with a scale factor of two.
Answers
The average of 5 consecutive whole numbers is 2021. What is the average of the first 3 of these numbers?
Answers
Answer:
2020
Step-by-step explanation:
if it is 5 consecutive numbers, it means it needs to be 2019, 2020, 2021, 2022, 2023
it is the number in the middle.
for the first 3 numbers, it is 2019, 2020, 2021
the middle number is 2020
What is the algebraic expression for the following word phrase: "the product of x and the sum of 2 and y"?
Answers
Answer:
x(2+y)
Step-by-step explanation:
sum of 2 and y=2+y
product of x=x times expression
:. Answer =x(2+y)
James made $85.00 in 2 weeks mowing yards. He spent 20% of that buying new tools. How much did he spend on tools? *
10 points
A $15
B $20
C $17
D $14
Answer asap please!
Answers
Answer: c 17
Step-by-step explanation:
Easy
Answer:
C. $17
Step-by-step explanation:
85 x (1/5) = 17
Which of the following scatterplots do not show a clear relationship and would not have a trend line?
Answers
Hope this helps!
Answer:
B
Step-by-step explanation:
Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation . You may use either an explicit or parametric description of the surface across the slanted face of the tetrahedron x in the first octant ; normal vectors point upward . F= langle0,0,-1 rangle; z = 4-x - y
Answers
Step-by-step explanation:
Surface integrals of vector fields Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or a parametric description of the surface. F =( 0,0,-1) across the slanted face of the tetrahedron Z=4-x-y in the first octant; normal vectors point upward
how many prime numbers are multiples of 5 please
Answers
Answer:
the only number would be 5
Step-by-step explanation:
5 is the first and only prime multiple of 5
There are only ''one'' prime number are multiples of 5.
What is Prime number?
Prime numbers are number that have only two factors, 1 and themselves.
Given that;
The prime numbers multiples of 5.
Now,
The multiples of 5 = 5, 10, 15, 20, 25, ...
But there are only one prime number (that is; 5) which are multiple of 5.
Thus, There are only ''one'' prime number are multiples of 5.
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is 1/4 to the 0 power bigger then 1
Answers
Answer:
1/4 to the 0 power is equal to 1. Therefore, it is not bigger than 1
You make $5000 per morth. If you spend 50% on necessitles, 30% on stuff you want and 20% of it you end up saving, how much money do you save per month?
Answers
Answer:
$1000 per month
Step-by-step explanation:
5000 dollars is 100 percent so we put 5000 over 100
5000/100
then since we need to find 20 percent of something, we put x over 20
x/20
Then we cross multiply
5000 times x
100 20
so 100x = 100000
and x = 1000
Good luck, and hope I did this correctly
Answer:
1000
Step-by-step explanation:
NECESSITIES
$2,500
WANTS
$1,500
SAVINGS AND DEBT REPAYMENT
$1,000
Please help me answer this question!!!
Answers
Answer:
19
Step-by-step explanation:
The triangle is an isosceles and so angle SRT and angle STR are equal
also:
Angle SRT and angle STU are supplementary so their sum is equal to 180
7x + 2x + 9 = 180 add like terms
9x + 9 = 180 subtract 9 from both sides
9x = 171 divide both sides by 9
x = 19
Given log 102 = 0.3010 and log 103= 0.4771, find log 1049 without using a calculator.
Answers
Bearing in mind that when the base is omitted, base 10 is assumed, or namely log(x) = log₁₀(x).
[tex]\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\log_{10}(2)=0.3010\qquad \qquad \log_{10}(3)=0.4771 \\\\[-0.35em] ~\dotfill\\\\ \log_{10}\left( \cfrac{4}{9} \right)\implies \log\left( \cfrac{4}{9} \right)\implies \log\left[ \cfrac{2^2}{3^2} \right]\implies \log\left[ \left( \cfrac{2}{3} \right)^2 \right]\implies 2\log\left[ \cfrac{2}{3}\right] \\\\\\ 2[\log(2)-\log(3)]\implies 2[0.3010~~ - ~~0.4771]\implies -0.3522[/tex]
Solve
-46 + - 4
A. 50
B. 42
C. -42
D. -50
Answers
The correct alternative that, matches the correct value of this expression is the letter D. That is, the answer will be -50.
Step-by-step explanation:To find the value of this expression, let's eliminate the parentheses and extract the numbers.
To find the value of this expression, let's eliminate the parentheses, and add the numbers, where the signs are equal.
_ When the signs are the same: just add them up.
_ When the signs are different: just subtract.
Resolution:[tex]\large \sf =-46 + (- 4)[/tex]
[tex]\large \sf =-46-4[/tex]
[tex]\boxed{\boxed{\large \sf -50 }}[/tex]
So, the numeric value of this numeric expression will be -50.
a company blends 1000 bushels of two types of apples to make a beverage that contains 12% real-juice content. One of the two types of apple contains 10% real-juice content and the other contains 15% real juice content. how many bushels of each type of apple are needed?
Answers
Answer:
400 bushels of the 15%
600 bushels of the 10%
Step-by-step explanation:
x bushels of the 15% plus the balance of 1000 bushels at 10% yield 1000 bushels at 12%
15x + 10(1000 - x) = 12(1000)
distribute
15x + 10000 - 10x = 12000
Combine like terms
5x = 2000
Divide both sides by 5
x = 400 bushels of the 15%
1000 - x = 600 bushels of the 10%
The number of bushels of the 15% is 400, and the number of bushels of the 10% is 600.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A company blends 1000 bushels of two types of apples to make a beverage that contains 12% real-juice content.
Let x be the bushels.
One of the two types of an apple contains 10% real-juice content and the other contains 15% real juice content.
The linear equation can be framed:
15x + 10(1000 - x) = 12(1000)
By using the distributive property:
15x + 10000 - 10x = 12000
5x = 2000 (combine like terms)
x = 400 bushels of the 15%
= 1000 - x
= 1000 - 400
= 600 bushels of the 10%
Thus, the number of bushels of the 15% is 400, and the number of bushels of the 10% is 600.
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Ivan was the 31st person in line. His position in line was just behind 5/9 of the total number of people in line. How many people were in line? HELP PLEASE WILL MARK BRAINLIEST
Answers
31=1-(5/9)x
30=-(5/9)x
x=54
The answer is 54 people.
hope this helps :)
Solve for u.
–
7u–u+2u+11u=10
u=
Answers
Bc explain
Solve the problem using a system of equations: Donnette found a widescreen TV at a garage sale, but she isn't sure if it will fit in her entertainment center. The TV is 50". The size of a TV is measured on the diagonal of the screen, and a widescreen has a length that is larger than the width. The screen also has an area of 1,200 square inches. What are the length and width of the TV screen?
length=___inches, width=___ inches
Answers
Check the picture below.
[tex]\begin{cases} L^2+w^2=50^2\\ Lw = 1200\\[-0.5em] \hrulefill\\ L^2+w^2=2500\\ L=\sqrt{2500-w^2} \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{\sqrt{2500-w^2}~w=1200} \\\\\\ \stackrel{\textit{squaring both sides}}{w^2(2500-w^2) = 1200^2}\implies 2500w^2-w^4=1440000 \\\\\\ 0=w^4-2500w^2+1440000\implies 0=\stackrel{\textit{tis a quadratic}}{(w^2)^2-2500w^2+1440000}[/tex]
[tex]0=(w^2-900)(w^2-1600)\implies \begin{cases} 0=w^2-900\\ 900=w^2\\ \sqrt{900}=w\\ \boxed{30=w}\\[-0.5em] \hrulefill\\ 0=w^2-1600\\ 1600=w^2\\ \sqrt{1600}=w\\ \boxed{40=w} \end{cases} \\\\\\ \stackrel{\textit{we know that}}{L = \sqrt{2500 - w^2}}\implies \begin{cases} L=\sqrt{2500-30^2}\\ \boxed{L=40}\\[-0.5em] \hrulefill\\ L=\sqrt{2500-40^2}\\ \boxed{L = 30} \end{cases}[/tex]
The length of the given TV is 40 inches and width of the given TV is 30 inches.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
The area of rectangular shape TV is 1,200 square inches.
The TV is 50".
Now, L²+W²=50² ----------(I)
L×W=1200 ----------(II)
L²+W²=2500
⇒ L²=2500-W²
⇒ L=√(2500-W²)
Substitute L=1200/W in L=√(2500-W²), we get
1200/W=√(2500-W²)
Squaring on both the sides we get
1440000/W² =2500-W²
⇒ 1440000=2500W²-[tex]W^4[/tex]
⇒ [tex]W^4[/tex]-2500W²+1440000=0
⇒ (W²)²-2500W²+1440000=0
⇒ (W²)²-900W²-1600W²+1440000=0
⇒ W²(W²-900)-1600(W²-1600)=0
⇒ (W²-1600)(W²-900)=0
⇒ W²-1600=0 and W²-900=0
⇒ W²=1600 and W²=900
⇒ W=±40 and W=±30
So, W=40, -40, 30, -30
Length =1200/W =40 or 30
Therefore, the length of the TV is 40 inches and width is 30 inches.
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what is the probability of a 200 year flood this year
Answers
Answer:
0.5 chance
Step-by-step explanation:
Likewise, the term "100-year storm" is used to define a rainfall event that statistically has this same 1-percent chance of occurring.
Answer:
0.5
Step-by-step explanation:
The possibility are very very very low, but never a no
The total age of a cat, dog, and a monkey is 4 years 2 months. The dog is twice as old as the cat. The monkey is twice as old as the dog. How old is the monkey? (Correct answer will get BRAINLIEST)
Answers
Answer:
50/7
Step-by-step explanation:
Solve
Let's solve your equation step-by-step.
4x+2x+x=50
Step 1: Simplify both sides of the equation.
4x+2x+x=50
(4x+2x+x)=50(Combine Like Terms)
7x=50
7x=50
Answer:
50/7
Step-by-step explanation:
Solve
Let's solve your equation step-by-step.
4x+2x+x=50
Step 1: Simplify both sides of the equation.
4x+2x+x=50
(4x+2x+x)=50(Combine Like Terms)
7x=50
7x=50
help ASAP DUE in 10 minutes do not spam or you will get reported A farmer wants to increase the area of his rectangular pen but keep the pen a rectangular shape. He decides to add 5.7 yards of fencing to the width of the pen, but the length will remain 9.5 yards. The new area will be 77.9 square yards.
Answers
Answer:
The one you have selected is correct. 9.5(w+5.7)=77.9
Step-by-step explanation:
Area is length x width, but the length is the same. So, the 9.5 is not in the parentheses. The existing width (w) is having 5.7 yards added on before being multiplied for area calculations. Because of the order of operations, (w+5.7) must be in parentheses so it is done before multiplication.
Answer:
9.5(w+5.7)=77.9
Step-by-step explanation:
took the test
Review:
Match each decimal with its equivalent simplified fraction.
NOTE: Simplified fractions may be in the improper fraction format.
0.25
[Choose]
0.14
[Choose ]
1.4
[Choose ]
0.4
[Choose ]
0.375
[Choose ]
Answers
Answer:
0.25-1/4
0.14-7/50
1.4-7/5
0.4-2/5
0.375-3/8