two carts, a and b, are connected by a rope 39 ft long that passes over a pulley p. the point q is on the floor 12 ft directly beneath p and between the carts. cart a is being pulled away from q at a speed of 2 ft/s. how fast (in ft/s) is cart b moving toward q at the instant when cart a is 5 ft from q? (round your answer to two decimal places.)
Answers
The velocity of the cart b is found as 20/23 ft/s over the pulley.
What is defined as the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically define the percentage change in value over such a defined period of time.For the given data in the question.
q's velocity is 2 feet per second.
Rope length is 39 feet.
Assume x is the distance between A and Q. (refer the image).
Assume y is the distance between Q and B. (refer the image).
As a result of the image,
x² + 12² = L²
Now, with respect to time t, differentiate the above equation.
2x(dx/dt) + 0 = 2L.(dL/dt)
For x = 5 ft and L = 13 ft
dL/dt = (5×2)/13 = 10/13
In the case of B,
y² + 12² = (39 - L)² ; from diagram.
Differentiating now,
2y(dy/dt) + 0 = -2(39 - L).(dL/dt)
At x = 5 ft and y = 23 ft.
dy/dy = -20/23
(A negative sign indicates the opposite direction)
Thus, the velocity of cart b is found as 20/23 ft/s.
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Related Questions
Find the volume of a solid bounded by the paraboloids [tex]\displaystyle{z=4x^2+4y^2}[/tex] and [tex]\displaystyle{z=5-6x^2-y^2}[/tex]
Answers
The two surfaces meet in an ellipse in some plane with [tex]0\le z\le5[/tex], since
[tex]4x^2 + 4y^2 = 5 - 6x^2 - y^2 \implies 10x^2 + 5y^2 = 5 \implies 2x^2 + y^2 = 1[/tex]
so the solid is bounded by the elliptical cylinder with this equation. In cylindrical coordinates, with
[tex]\begin{cases}x = \frac1{\sqrt2} r \cos(\theta) \\ y = r \sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = \frac1{\sqrt2} r \, dr \, d\theta \, d\zeta\end{cases}[/tex]
the solid is the set
[tex]\begin{array}{c} R = \left\{(r,\theta,\zeta) ~:~ 0\le r\le1 \text{ and } 0 \le\theta\le2\pi \text{ and } \right. \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \left.3r^2 - r^2 \cos(2\theta) \le \zeta \le 5 - 2r^2 - r^2 \cos(2t)\right\} \end{array}[/tex]
and the volume is given by the integral
[tex]\displaystyle \iiint_R dV = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 \int_{3r^2 - r^2 \cos(2\theta)}^{5 - 2r^2 - r^2 \cos(2\theta)} r \, d\zeta \, dr \, d\theta \\\\ ~~~~ = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 r(5 - 5r^2) \, dr \, d\theta \\\\ ~~~~ = \frac{10\pi}{\sqrt2} \int_0^1 (r - r^3) \, dr \\\\ ~~~~ = 5\sqrt2\,\pi \left(\frac12 - \frac14\right) = \boxed{\frac{5\pi}{2\sqrt2}}[/tex]
which numbers are my Ys (-8-6) and (-1,0)
Answers
The numbers which correctly represents the y-coordinates of the given pairs; (-8-6) and (-1,0) as in the task content are; -6 and 0 respectively.
What is the xy- coordinate plane?It follows from simple definition that the x -y plane, is a two dimensional plane which contains the x and y axis. The x and y axis happen to be used in the description of plane shapes which are two- dimensional in nature.
Also, it is noteworthy that each point on the xy-coordinate is described by a pair of coordinates and takes the form; (x, y).
In which case, the x-coordinate is written first and y-coordinate is written second as indicated above.
On this note, the y's of the pair of coordinates, (-8-6) and (-1,0) as given in the task content by convention can be observed to be; -6 and 0 respectively.
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Find the x intercept and y intercept x + 18 = 9y
Answers
Answer:
x = 72 and y = 0 im just guessing so dont be completey
Information is given about a polynomial f(x) whose coefficients are real
numbers. Find the remaining zeros of f.
Degree 3; zeros: -4, -2- i
The remaining zero(s) of f is
(Use a comma to separate answers as needed.)
Answers
Answer: -2+i
Step-by-step explanation:
By the conjugate root theorem, since the coefficients are real, the complex conjugate of a root must also be a root.
3 5/11 as a decimal exspansion
Answers
Answer: 3 5/11 should be 3.4545454545 as a decimal
Hope this helps!
Answer:
3 + 0.4545454545454545 = 3.454545454545455
Step-by-step explanation:
3 5/11 as a decimal exspansion
3 + (5 : 11) =
3 + 0.4545454545454545 =
3.454545454545455
Flora is buying dog food for her dog. She wants to buy enough to last five weeks (35 days). If her dog eats 2 cups in a day, and there are 24 cups in each bag, how many bags of dog food does Flora need to buy to last 5 weeks? ⛔️ SOLVE USING A PROPORTIONAL RELATIONSHIP GRAPH! ⛔️
Answers
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.
Flora needs 3 bags of dog food.
How to find the food bags needed?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.
An equation in which two ratios are made equal is known as a percentage.
As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls.
Given,
Dog eats 2 cups in a day
There are 24 cups in each bag
Solution:
Dog eats one bag of food in 24 cups/2 cups = 12 days
One food bag is sufficient to feed the dog for 12 days
For 35 days, the number of food bags needed is
1/x = 12/35 where x be the number of food bags needed for the dog.
x = 2.92
That is 3 bags of dog food are needed for 35 days to feed the dog.
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Evaluate the expression when a = 2 and x = -4.
2a-x
Answers
The expression when a = 2 and x = -4, given 2a-x. The value will be 8.
What are mathematical operations?In mathematics, an operation is a function that transforms zero or more arguments or operands into a clearly defined output value. The number of operands in the operation determines how difficult it is.
Unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication, are the operations that are most frequently studied. The nullary operation, also referred to as a zero-arity operation, is a constant. The mixed product is an example of a ternary operation, also referred to as an operation of arity 3.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.
Since, a= 2 and x= -4, then,
2(2)-(-4)= 8
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The graph of a function f(x) passes through the following points:
(0,-2), (1,0), (-1,0)
Which of the following could be f(x)?
> f(x) = -2x - 2
> f(x) = 2x - 2
> f(x) = (2\sqrt[x])-2
> f(x) = 2x^2 - 2
Answers
*109
eight feral 103721
answer these 2 questions for a cookie
Answers
Answer:
1. C
2. D
5. C
Step-by-step explanation:
Answer:
C as j is a variable
D
C as 13+9+1.9= 23.9
pls mark as brainliest
Darcie wants to simplify 20 over 24 fully.
What number should she divide both the
numerator and the denominator by in order
to simplify the fraction fully in one step?
Answers
Answer: 4
Step-by-step explanation:
This simplifies to 5/6.
So 20 / 5 = 4
and 24 / 6 = 4
the daily useage time on the apple iphone is normally distributed with mean 5.4 hours and standard deviation 1.2 hours. suppose you survey 5 of your friends who have iphones. what is the probability that their mean useage time is between 4 and 7 hours? round your answer to three decimal places.
Answers
0.868 is the probability that their mean useage time is between 4 and 7 hours.
What are examples and probability?
It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.Given, population mean (μ) = 5.4
population standard deviation (σ) = 1.2
Sample size (n) = 5
Probability that the sum of their useage time is less than 30
= Probability that the sample mean is less than (30/5 = 6)
= p(x<6)3
Z score
= x - μ/σ/√n
= 6 - 5.4/1.2/√5
= 0.6/1.2/2.236068
= 0.6/0.536656
= 1.11803
Area to the left of (Z = 1.11803) = 0.86822 = 0.868
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6. Joshua took a bus from Orlando to Atlanta. The bus traveled 420 miles in 6 hours. What was the
average speed of the bus?
a) 60 miles per hour
b) 65 miles per hour
c) 70 miles per hour
d) 75 miles per hour
Answers
The subtraction of 8 from a number is 2. What is the number?
Answers
Answer:6
Step-by-step explanation:
8-6 = 2
Answer:
10
Step-by-step explanation:
Let the number be equal to y
y-8=2y=8+2y=10help fast i need to get this answer
Answers
Answer:
x = 3
Step-by-step explanation:
Plug in 1 for x:
- | 1 + 1 | + 5 = - |2| + 5 = -2 + 5 = 3
f(x) = 3 x + 1 and g (x) = 2x - 3. find f (g(x)) and g (f(x))
Answers
Step-by-step explanation:
f(x} = 3x + 1
g(x} = 2x -- 3
f(g(x)) = 3x + 1. (Calm down right?)
Let the x in the expression be (2x -- 3)
N.B x = g{x}
f(g(x)) = 3(2x --3} + 1
Open bracket
f(g(x)) = 6x -- 9 + 1
f(g(x)) = 6x -- 8...
2... Solve for g(f(x)), using the same strategy
g(f(x)) = 2x -- 3
x = f(x)
g(f(x)) = 2(3x + 1) -- 3
g(f(x)) = 6x + 2 -- 3
g(f(x)) = 6x -- 1
#AllonGod
Answer:
Step-by-step explanation:
f(g(x)) means substituting g(x) in f(x)
ie, 3(2x-3)+1 = 6x-9+1 = 6x - 8
g(f(x)) means substituting f(x) in g(x)
ie, 2(3x+1)-3 = 6x2-3 = 6x - 1
A saleswoman earns 9% commission on all the merchandise that she sells. Last month she sold $6000 worth of merchandise. How much commission (in dollars) did she earn last month?
Answers
Answer: she gets 540
Step-by-step explanation:
She earns 540 dollars since the saleswoman only gets 9% of it and she sold $6000 dollars worth of merchandise you divide by percentage
Example: 1. Find the percentage of the original or real number. In this case, it's 500.
2. Multiply the final number by 100. 500 x 100 = 50,000.
3. Divide the result of the multiplication by the percentage. 50,000 divided by 40% = 1,250. Thus, 500 is 40% of 1,250.
Please answer asap
Thank you
Answers
The y-intercept is the “starting point.” The line crosses the y-axis at 4, so 4 is the starting point.
The slope is the rate of increase or decrease. The slope increases 1 unit every 1 unit, so the rate of increase is 1.
Alfred is picking up chicken and steak to grill at a party
later that day. He has $60 to spend on the 30 pounds of
meat he needs for the party. The chicken is $1.50 per lb,
and the steak is $2.40 per lb.
Which graph models this situation, where cis pounds of
chicken, and s is pounds of steak?
Answers
Answer:
The graph should look like the one below.
Step-by-step explanation:
C is lbs of chicken
S is pounds of steak
Alfred spent 30 pounds of meat for the party:
c + s [tex]\leq[/tex] 30
Alfred spend $60 on the 30 lbs of meat.
The chicken is $1.50 per pound and the steak is $2.40 per lb then
1.5c + 2.50 [tex]\leq[/tex] 60
0.5c + 0.85 [tex]\leq[/tex] 20
The linear inequalities system that models situation is:
0.5c + 0.85 [tex]\leq[/tex] 20
c + s [tex]\leq[/tex] 30
c [tex]\geq[/tex] 0
s [tex]\geq[/tex] 0
The Graph:
A match-seller arranges his matchboxes in a
triangular pattern as shown in Fig. 18.4. He
continues until there are 11 matchboxes in
the bottom row of the triangle. How many
matchboxes are in the complete pattern?
MATO
MATCHES
MATCHES
Fig. 18.4
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
Answers
Using the properties of an arithmetic sequence we can conclude that the total number of match boxes is 66.
There is a consistent distinction between the words in a sequence of numbers known as a "arithmetic progression" or "arithmetic sequence" (AP).
In an arithmetic series, the space between subsequent terms is constant. The numbers 3, 5, 7, and 9 come to mind. because there is always a two-term difference between two succeeding terms, it is arithmetic.We know that the bottom row of the pyramid has 11 matchboxes .
As we can see in the figure that the each succeeding step has one matchbox less.
Therefore the number of matchboxes in each row is in an AP.
Therefore the AP has a common difference of -1 and the first term is 11
The last term of the AP is 1.
Therefore
aₙ = a + (n-1)d
or, 1 = 11 + (n-1)(-1)
or, n = 11
We know that the sum of all terms of an AP is given by
S=n/2{2a+(n-1)d}
or, S = 11/2 {2×11 + (10)(-1)}
or, S = 66
Therefore from the arithmetic progression we calculate that the total number of match boxes is 66.
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Disclaimer: The missing diagram is attached below.
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Can somebody help me with this please?
Answers
From the given figure < BAC = 180 - ( < ABC + < BCA ) because they are sum of angles in a triangle
How to find < BACgiven data
< ABC = 52 degrees
< BCA = 88 degrees
calculation for angle BAC
< ABC + < BCA + < BAC = 180 degrees ( sum of angles in a triangle )
< BAC = 180 - ( < ABC + < BCA )
< BAC = 180 - < ABC - < BCA
plugging in the values gives
< BAC = 180 - 52 - 88
< BAC = 180 - 140
< BAC = 40 degrees
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if a circle has a radius of 7 m then what is the circumference exactly
Answers
The circumference c=43.98 the formula is 2*pi*r
True or false? A corollary is a statement that can be easily proved using a
theorem.
O A. True
OB. False
SUBMIT
answer to this question for anyone who needs it
Answers
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
The given statement is True.
Is the meaning of corollary?The term "corollary" refers to an outcome that follows logically from another action. You could claim that your rediscovered passion of reading is a corollary to the recent opening of a bookstore in your area. The term corollary describes the result of an action, such as the need to study more as a corollary to receiving a poor grade.
Briefing:A theorem states that two angles that add up to 180° and form a straight line are regarded as "supplementary."
A corollary of this is known as the "Vertical Angle Theorem," which asserts that where two lines intersect, their angles across from each other are equal (in the diagram, a=c and b=d).
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
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let’s review some basics of probability. a bag of skittles has 9 reds, 10 oranges, 7 yellows, 8 purples, and 6 greens. what is the probability of a red skittle if one is selected at random?
Answers
Answer:
7/20
Step-by-step explanation:
is always right use without the s
a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 1ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?
Answers
After solving the question using Pythagoras' theorem we get, The ladder moving down the wall at 8 feet per second.
According to the question,
The bottom(base) of the ladder is 12 feet,
the height of the ladder is 13 feet.
Now, We have to find the top of the ladder moving down the wall
by using Pythagoras' theorem,
hypotenuse ^2 = base^2 + perpendicular ^2
13^2 = x^2 + y^2
169 = x^2 + y^2
After using Pythagoras' theorem
we have this equation and now we will differentiate both sides:
0 =2x*dx/dt + 2y*dy/dt
0 =24*1 + 3* dy/dt
dy/dt = - 8 feet per second
Positive whole number we have to take.
So, dy/dt = 8 feet per second
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What is the vertex of the graph of 3x^2 - 6x + 7?
Answers
Answer: (1,4)
Step-by-step explanation:
y = 3x^2 - 6x + 7
If the measure of angle 2 is 70 degrees, what is the measure of angle 7?
A. 70; Ls 2 and 7 corresponding angles
B. 70; Ls 2 and 7 are alternate exterior angles
C. 120; 2s 2 and 7 are supplementary angles
D. Unable to determine
Answers
Answer:
B
Step-by-step explanation:
∠ 2 and ∠ 7 are alternate exterior angles and are congruent, then
∠ 7 = ∠ 2 = 70°
If Aaron buys 5 watermelons for 9 how much would 4 cost at the same rate?
Answers
Answer: $ 7.20
Step-by-step explanation:
(9x4)/5
36/5
= 7.2
= $7.20
Find the exponential function in the form y=a*b^x that passes through the point (0,10) and (3,80).
Answers
[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y = 10 \end{cases}\implies 10=ab^0\implies 10=a(1)\implies 10=a~\hfill \underline{y = 10b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x = 3\\ y = 80 \end{cases}\implies 80=10b^3\implies \cfrac{80}{10}=b^3\implies 8=b^3 \\\\\\ \sqrt[3]{8}=b\implies 2=b~\hfill \underline{y = 10(2)^x}[/tex]
Given the equation 13.25y = 79.5, determine the value of y.
6.00
66.25
92.75
1053.38
Answers
Given the equation 13.25y = 79.5, the value of y is A. 6.00.
What is an equation?An equation is a mathematical statement that states that two mathematical expressions are equal in value.
Equivalent values are also expressed as algebraic equations sharing the same root.
We depict equations by using the equation symbol (=).
13.25y = 79.5
y = 6 (79.5/13.25)
Check:
13.25y = 79.5
13.25(6) = 79.5
79.5 = 79.5
Thus, given the equation 13.25y = 79.5, the value of y cannot be 66.25, 92.75, or 1,053.38 but Option A.
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g(x)=1/4x+1
what is g(-16)?
Answers
When we're solving with functions, it's no different than solving from a regular equation.
In most cases, we only need to substitute x with a given value.
Solving the Question
[tex]g(x)=\dfrac{1}{4}x+1[/tex]
⇒ To find g(-16), plug in -16 as x:
[tex]g(-16)=\dfrac{1}{4}(-16)+1\\\\g(-16)=-4+1\\\\g(-16)=-3[/tex]
Answer-3