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.)
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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10.962 rounded to the nearest tenth
Answer:
11.0Step-by-step explanation:
10.962 rounded to the nearest tenth:
10.962 ≈ 11.0 ⇒ round up 9 to 10 since the previous number is greater than 5, it adds 1 to 10 and makes it 11, and 9 is replaced with zero\(\\ \sf\longmapsto 10.962\)
2<5\(\\ \sf\longmapsto 10.96\)
6>5\(\\ \sf\longmapsto 10.0+1\)
\(\\ \sf\longmapsto 11.0\)
What is the equation of the following line written in general form?
Answer:
The first option
Step-by-step explanation:
\(4x + 5y - 34 = 0\)
you would use a pictogram to track progress toward completion of a six month construction project. T/F?
True. A pictogram is a visual representation of data or information that uses pictures or symbols to convey meaning.
In the context of a construction project, a pictogram can be used to track the progress of the project towards completion. The pictogram can show the percentage of completion, the milestones achieved, and the remaining tasks to be completed.
It can also be used to indicate any potential delays or issues that need to be addressed. By using a pictogram, the project team can easily communicate the progress of the construction project to stakeholders who may not be familiar with technical details or industry jargon.
Additionally, the use of a pictogram can make it easier for the team to identify areas that require attention and adjust their plans accordingly. Overall, the use of a pictogram can be a valuable tool in tracking the progress of a construction project and ensuring that it stays on track to meet its goals within the specified timeframe.
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The picture shows 3 steel rods. The rods are congruent, solid cylinders. The area of the top of the one rod is 7.07 square centimeters. The area of the body of one rod is 39.58 square centimeters. Find the total surface area of the 3 rods.
a) 53.72
b) 46.65
c) 139.95
d) 161.16
Answer: D, 161.16 square centimeters.
Step-by-step explanation:
The surface area of a cylinder (shape of each steel rod) is given by this formula:
\(A = 2\pi rh + 2\pi r^2\), where the first 2*pi*r*h measures the area of the curved surface while the second 2*pi*r^2 measures the area of the two circles on the top and bottom.
We are given the area of the top of one rod, which is 7.07 square centimeters.
We are also given the area of the body of one rod, which is 39.58 square centimeters.
The top of one rod is the shape of a circle, and we know there are two circles on both sides of a cylinder, so the surface area of both circular sides are 7.07.
The total surface area of a cylinder is the body plus both circular ends, so the surface area for this cylinder is:
39.58 + 7.07 + 7.07 = 53.72
There are three cylinders, so multiply this value by three to get the answer, 161.16 square centimeters.
what is equivalent to |14-20|
Answer:
7/10
Step-by-step explanation:
PLS HELP ASAP WILL GIVE BRAINLIEST. SHOW WORK
Answer:
80°
Step-by-step explanation:
I hope this helped!!! work is above
Consider the equation: 6x + 55 = x 2 power
1. Rewrite the equation by completing the square. Your equation should look like (x + c)² = dor (2-c)2 = d. 1. 2) What are the solutions to the equation? Choose 1 answer:
A. x=-3+_8
B. x=3+_8
C. x=-8+_3
D. x= 8+_3
Answer:
a
Step-by-step explanation:
Answer:
Im pretty sure its d its defenantly NOT A
Step-by-step explanation:
What is the value of x? Enter your answer in the box. x =
Check the picture below.
Arrange the following in descending order: 1/5,3/7,7/10
Answer:
7/10 - 3/7 - 1/5
Step-by-step explanation:
3/7-7/10-1/5
Step-by-step explanation:
Solve the differential equation: (y^2+xy)dx+x^2dy=0(y 2 +xy)dx+x 2 dy=0
To solve the given differential equation:
(y^2 + xy)dx + x^2dy = 0
Let's solve it step by step.
Step 1: Rearrange the equation
Rearrange the equation to isolate dy/dx:
(y^2 + xy)dx = -x^2dy
dy = -(y^2 + xy)dx / x^2
Step 2: Separate variables
Separate the variables by dividing both sides of the equation:
dy / (y^2 + xy) = -dx / x^2
Step 3: Integrate
Integrate both sides of the equation:
∫(1 / (y^2 + xy))dy = -∫(1 / x^2)dx
To integrate the left-hand side, we can use a substitution. Let u = y + x, then du = dy + dx.
Substituting these values, the left-hand side becomes:
∫(1 / (u^2))du
Integrating this gives:
-1/u + C1
For the right-hand side, we have:
-∫(1 / x^2)dx = 1/x + C2
Step 4: Apply initial conditions (if given)
If there are initial conditions given, substitute the values into the equation to solve for the constants of integration (C1 and C2). Otherwise, proceed to the next step.
Step 5: Combine the solutions
Combining the results from the integration:
-1/u + C1 = 1/x + C2
Substituting u = y + x back in:
-1/(y + x) + C1 = 1/x + C2
Multiply through by -1 to make the constants positive:
1/(y + x) - C1 = -1/x - C2
Rearrange the terms:
1/(y + x) + 1/x = C1 - C2
Let C = C1 - C2:
1/(y + x) + 1/x = C
This is the general solution to the given differential equation.
Note: The specific values of C1 and C2 would depend on the initial conditions if provided.
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PLEASE HELP MEEEEEEEEEEEEEEEEEEEE
Answer
bruh where's the explanation
Step-by-step explanation:
What is the expanded form of this expression?: 4(1/4a + b – 6)
Answer:
Step-by-step explanation:
4(1/4a) + 4b - 24
1/a+4b-24
Given that the probability of a company having a section in the newspaper is 0.43, and the probability of a company having a website given that the company has a section in the newspaper is 0.84, what is the probability of a company having a website and a section in the newspaper
To find the probability of a company having both a website and a section in the newspaper, we can use the formula for conditional probability.
Let's denote the events as follows:
A: A company has a section in the newspaper
B: A company has a website
We are given the following probabilities:
P(A) = 0.43 (Probability of a company having a section in the newspaper)
P(B|A) = 0.84 (Probability of a company having a website given that it has a section in the newspaper)
The probability of both events A and B occurring can be calculated as:
P(A and B) = P(A) * P(B|A)
Substituting in the values we have:
P(A and B) = 0.43 * 0.84
P(A and B) = 0.3612
Therefore, the probability of a company having both a website and a section in the newspaper is 0.3612 or 36.12%.
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PLS HELP ASAP❤
Find the median for the given set of data
⅝, ¾, 1⅛, 1¼
Answer:
15/16Step-by-step explanation:
Put the data in the ascending order, first bring to common denominator:
5/8, 3/4 = 6/8, 1 1/8 = 9/8, 1 1/4 = 5/4 = 10/85/8, 6/8, 9/8, 10/8Since the data is even the median is the average of 6/8 and 9/8:
(6 + 9)/8*1/2 = 15/16if 104=10,000, which is equal to 4? select the correct answer below: log100 log1,000 log10,000 log4 log40,000
The correct answer is log4. The given statement is 10^4 = 10,000. To find the value equal to 4, we need to look for the logarithm with a base of 10 that results in 4.
In this case, the correct answer is log10,000 because log10(10,000) = 4. This is because log is the inverse operation of exponentiation. In other words, log4 is asking the question "what power do I need to raise 10 to in order to get 4?"
We know that 104 is equal to 10,000, so we can rewrite the question as "what power do I need to raise 10 to in order to get 10,000?" The answer is 4, since 10 to the power of 4 is 10,000. Therefore, log10,000 is equal to 4.
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About 70% of Earth's surface is water.
About how much of Earth's surface is
water if Earth's diameter is about 7920
miles? Show your work.
Answer:
completamente respuesta
The surface area of a sphere is given by the formula:
4πr^2
where r is the radius of the sphere. The diameter of Earth is about 7920 miles, so the radius is approximately 3960 miles.
Substituting this value into the formula, we get:
4π(3960)^2 ≈ 197352720 sq miles
About 70% of this area is water, so we can find the amount of water on Earth by multiplying the total surface area by 0.7:
197352720 * 0.7 ≈ 138146904 sq miles
Therefore, about 138,146,904 square miles of Earth's surface is water.
PLEASE HELP MY FUTURE DEPENDS ON THIS QUESTION 6
Answer:
Five more than a number
Step-by-step explanation:
Are these 4 problems SSS SAS ASA AAS HL
1. The first figure posses the SSS property.
2. The second figure posses the ASA property.
3. The third figure posses the hypotenuse length property.
4. The fourth figure posses the SAS property.
Given:
1. The first figure shows the SSS property.
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
hence the two triangles are congruent.
2. The second figure posses the ASA property.
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
hence the two triangles are congruent.
3. The third figure posses the hypotenuse length properety.
RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.
hence the two triangles are congruent.
4. The fourth figure posses the SAS property.
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
hence the two triangles are congruent.
Hence we get the required answer.
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There were 15 bunnies at the pet store. Each of the 5 female bunnies had 5 babies! How many bunnies are there in the pet store now?
Answer:
45??!
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
If there were 15 bunnies 5 were females so there is 10 men and if each female had 5 babies each then that would be 25 babies plus the 10 men should be 35
The volume of the rectangular prism is ___ cubic units.
Answer:
144 cube units
Step-by-step explanation:
volume = width*height*length
V=12*3*4
V=144 cube units
Answer:
This is your answer. If I'm right so,
Please mark me as brainliest. thanks!!!
180º represent chocolate, 90º represent vanilla and 90º represents other flavor draw the pie chart.
will be marked as brainliest
Answer:
Look at attached.
Step-by-step explanation:
A full circle is 360 degrees. So 180 represents half of the circle and 90 represents a quarter.
Answer:
chocolate 180°
Step-by-step explanation:
chocolate=180°
vanilla=90°
othere flavor=90°
the total degrees of the pie chart 360 °
Use the distributive property to remove the parentheses.
-7 ( -2w - 4y + 1 )
Answer: \(14w+28y-7\)
Step-by-step explanation:
multiply everything by -7
Answer:
Step-by-step explanation:
14w+28y-7
tell whether this has one solution, infinitely many solutions, or no solution. Explain your reasoning. y=2x+7, y=3x-1
Answer:
One solution
Step-by-step explanation:
They have isolated y for you in both equations so you can plug either one into the other.
y = 3x - 1
2x + 7 = 3x - 1
isolate the x
7 = x - 1
x = 8
Go back to the original and plug 8 into x to get y.
y = 2 (8) + 7
y = 16 + 7
y = 23
This means at (8, 23) y = 2x+7 is equal to y = 3x-1. In other words they share a point at (8, 23). This is the only solution because for any other x and y they'd not be equal.
HELP!!! My math is due in 1 hour and I’m confused!
Answer:
welp guess its already due
Step-by-step explanation:
sorry
What of the angle is the vertex?
Answer:
Vertex: The common end point at which the two rays meet to form an angle is called the vertex. Here, the point O is the vertex of ∠AOB. We can find angles in various things around us, such as in a pair of scissors, a hockey stick, a chair.
A firm produces two goods in quantities x and y. Its cost function is C(x,y) = 10x + xy + 10y and the prices P, and P, it can charge are, respectively, Ps = 50 - x + y and Py = 50 - x + y. The firm is committed to delivering a total of 15 units. How much should the firm produce of each good to maximize profits?
To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.
To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.
The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.
By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.
Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.
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please Help quick due soon
The angle measures for this problem are given as follows:
a = 62º.b = 118º.c = 62º.d = 62º.How to obtain the angle measures?The sum of the measures of the internal angles of a triangle is of 180º.
The triangle in this problem is ABC, hence the measure of a is obtained as follows:
a + 68 + 50 = 180
a = 180 - (68 + 50)
a = 62º.
c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:
c = 62º.d = 62º.Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:
a + b = 180
62 + b = 180
b = 118º.
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Rewrite the expression in nonradical form without using absolute values for the indicated values of theta.
1 − cos2 (theta)
; 2.5 < theta < 3
To rewrite the expression 1 - cos^2(theta) without using absolute values for the given values of theta (2.5 < theta < 3), we can utilize the trigonometric identity for cosine squared:
cos^2(theta) = 1 - sin^2(theta)
Now, let's substitute this identity into the expression:
1 - cos^2(theta) = 1 - (1 - sin^2(theta))
= 1 - 1 + sin^2(theta)
= sin^2(theta)
Therefore, for the given range of theta (2.5 < theta < 3), the expression 1 - cos^2(theta) is equivalent to sin^2(theta).
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You are assigned some math exercises for homework.
You complete 87.5% of these before dinner.
How many do you have left to do after dinner if you completed 28 exercises before dinner?
Answer: 4 exercises
Step-by-step explanation:
If we completed 87.5% of the math exercises before dinner, then we have completed 0.875 × total number of exercises.
Let "\(x\)" be the total number of exercises.
\(0.875x = 28\)
Solving for \(x\), we get:
\(\boxed{\begin{minipage}{4 cm}\text{\LARGE 0.875x = 28 } \\\\\\ \large $\Rightarrow$ $\frac{0.875x}{0.875}$ = $\frac{28}{0.875}$\\\\$\Rightarrow$x = 32\end{minipage}}\)
Therefore, the total number of exercises is 32.
We completed 28 exercises before dinner, so we have: 32 - 28 = 4 exercises left to do after dinner.
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