The work W required to move a particle from a far distance to within radius r of another particle varies jointly as the product of the two particles' charges q1 and q2 and inversely as the radius r. Write a formula that models this proportion. (Use k as the constant of variation.)
Answers
Answer:
W = kq1q2 / r
Step-by-step explanation:
W varies jointly as the product of q1 and q2 and inversely as radius r
Product of q1 and q2 = q1q2
W = (k*q1"q2) / r
W = kq1q2 / r
Where,
W = work
q1 = particle 1
q2 = particle 2
r = radius
k = constant of proportionality
The answer is W = kq1q2 / r
Using proportions, it is found that the formula is:
\(W = k\frac{q_1q_2}{r}\)
Work varies jointly as the charges, thus, the charges are in the numerator.Inversely as the radius, thus, the radius is in the denominator.There is a constant of proportionality k, which multiplies the fraction;Then, the formula is:
\(W = k\frac{q_1q_2}{r}\)
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Related Questions
What is the lateral of this solid ?
Answers
The lateral surface area of the right prism is equal to 100 square inches.
How to find the lateral area of a solid
In this problem we find a right prism with a hexagonal base, whose lateral surface area must be found, that is, the areas of faces that are not bases of the solid. The area formula needed is shown below:
A = w · h
Where:
w - Widthh - HeightNow we proceed to determine the lateral surface area:
A = 5 · (4 in) · (5 in)
A = 100 in²
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i stuck on this answer help
Answers
Answer:
Step-by-step explanation:
althea normally saves $x each month; but in june she saved $4 more than twice her usual amount. in june she saved...
Answers
Answer:
The amount saved in June is;
$(2x + 4)
Step-by-step explanation:
Here, we want to get the amount saved in June
From the question, she saved $5 more than twice here usual amount
twice here usual amount is 2 * x = $2x
So, adding the extra $4; the amount saved will be;
2x + 4
Proportional or non proportional tables? URGENT
Answers
Answer:
Non proportional because The numbers don't go into each other.
Neil Dawson's Chalice is a truncated cone. A truncated
cone is the part that is left when a cone is cut by a plane
parallel to the base and the part containing the apex, or
vertex of the cone, is removed.
The height of the Chalice is 18 meters. The radius at the
top of the sculpture is 4.25 meters and the radius at the
bottom of the sculpture is 1 meter. The diagram shows
the Chalice as an untruncated cone.
Use the information in the diagram to calculate the lateral
area of the Chalice as a truncated cone. Please answer in a understanding short answer
Answers
The lateral area of the truncated cone is 246. 8 m²
How to determine the lateral areaThe formula that is used for calculating the lateral area of a cone is expressed as;
A = πrl
Such that the parameters of the formula are;
A is the arear is the radiusl is the lengthSubstitute the values, we have that;
L² = 18² + 4.25²
Find the squares, we get;
l² =342. 06
l = 18. 49m
Then, the lateral area is;
A = 3.14 × 4.25 × 18. 49
Multiply the values
A = 246. 8 m²
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Choose the correct sum of the polynomials (3x3 − 5x − 8) (5x3 7x 3). 8x3 2x 5 2x3 − 12x − 11 2x3 12x − 5 8x3 2x − 5.
Answers
Answer:
8x^3 + 2x - 5
Brainly Patrol keeps deleting my answer
Urgent! Ans pls
if p=-2, find the value of -2p³-3p²+4p+7
Answers
Answer:
3
Step-by-step explanation:
\(-2(-2)^3 - 3(-2)^2 + 4(-2) + 7\\= -2(-8) - 3(4) - 8 + 7\\= 16 - 12 - 8 + 7\\ = 3\)
With a 20% discount, Ella was able to save $40 on a dress. What was the original price of the dress?
Answers
Hope this helps :>
^>…~|-+First Answer Gets Brainliest+-|~…<^
Question Is in the picture!
Answers
Answer: ten times 3 x ^2
Step-by-step explanation:
Answer:
Substitute 10 for x in the equation. \(3(10)^2\). If that is not a choice for the answer then you would multiply 10 by the second power.
\(3(10)^2\\3(100)\)
Step-by-step explanation:
I hope this helps! May i please have brainliest? :)
help me find y intercept
Answers
Answer:
10
Step-by-step explanation:
The y intercept is when the slope crosses the y axis of the graph, we can find this by looking for the value at x=0. From the graph we can see that y=10 at x=0.
The y-intercept is the point in which the line passes through the y-axis :)
All the answers I want to know please this is important for me
Answers
2)4.08 times 10 to the 8th power
3)8 times 10 to the 7th power
4)1.502 times 10 to the 13th power
5)3.5 times 10 to the 2nd power
6)7.06 times 10 to the 3rd power
7)1.0504 times 10 to the 7th power
8) 42000000
9) 5.7100
10) 80030000000
11) 500000000
12) 7050
13) 1405000000
14) 5020300000
15) B
16) B
17) D
18) C
Does the graph shown below represent y as a linear function of x
Answers
Answer:
no
Step-by-step explanation:
a linear equation shows a straight line
how to find p value from t statistic on ti-84
Answers
Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.
To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.
Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.
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Write an equation in slope-intercept form for the line where x is the number of hours the kayak is rented and y is the total cost of renting the kayak.
Answers
Slope is:
S=rise/run
S=Y/X
pleassee HELPP me with 7,8 thank youuu
Answers
Answer:
y=8,y=0
that's the answer I got tho
what is a type ii error? rejecting a false null hypothesis accepting a false alternate hypothesis rejecting a false alternate hypothesis failing to reject a false null hypothesis
Answers
A type II error is a statistical term used to describe the failure to reject a false null hypothesis. It occurs when the null hypothesis is actually false but is not rejected because the statistical test failed to find significant evidence against it.
In other words, it happens when an alternative hypothesis is true, but we fail to reject the null hypothesis.
Types of errors in hypothesis testing
There are two types of errors in hypothesis testing:
Type I error: Rejecting a true null hypothesis
Type II error: Failing to reject a false null hypothesis.Type I error occurs when a true null hypothesis is rejected while Type II error occurs when a false null hypothesis is not rejected. These types of errors are inversely related, meaning that a decrease in one type of error causes an increase in the other.
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Is x = 5 a solution of the inequality x - 3<2 ? Explain
Answers
Answer:
No
Step-by-step explanation:
Plug in 5 for x
5 - 3<2
2<2
this is not true it should be equal to 2.
Answer:
Not a solution
Step-by-step explanation:
Plug in x = 5 in the equality,
x - 3 = 5 - 3 = 2 not < 2
So, x = 5 is not a solution
Mrs. Hugo and Mrs. Thompson left the conference at the same time and headed in opposite directions. After 4 hours, they were 452 miles apart. If Mrs. Hugo drove 3mph faster than Mrs. Thompson, how fast did Mrs. Thompson drive?
Answers
Mrs. Hugo and Mrs. Thompson left the conference at the same time and headed in opposite directions. After 4 hours, they were 452 miles apart. If Mrs. Hugo drove 3mph faster than Mrs. Thompson drove at a speed of 71.125 mph.
Thompson drove given that she and Mrs. Hugo left a conference at the same time and headed in opposite directions. After 4 hours, they were 452 miles apart, and Mrs.
Hugo drove 3 mph faster than Mrs. Thompson.
To solve this problem, we can use the formula
distance = rate x time.
Let's let x be the speed at which Mrs. Thompson drove.
Therefore, the speed at which Mrs.
Hugo drove would be x + 3.
Since they were driving in opposite directions, we can add their speeds to find the total distance they traveled, which would be 2x + 3.
Using the distance formula, we know that
452 = (2x + 3) x 4.
Simplifying this equation, we get:
452 = 8x + 123529 = 8x 71. 125 = x
Therefore, Mrs. Thompson drove at a speed of 71.125 mph.
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Answer:
55mph
Step-by-step explanation:
(Mrs. Hugo's distance) + (Mrs. Thompson's distance) = 452
Mrs. Hugo's distance (d = x * t) 4(x + 3)
Mrs. Thompson's distance 4x
4(x + 3) + 4x = 452
Distribute: 4x + 12 + 4x = 452
Add: 8x + 12 = 452
Change side: 8x = 452 - 12
Subtract: 8x = 440
Divide by 8: x = 55
x = 55mph
PLEASE HELP!! will mark brainliest! Complete the point-slope equation of the line through (1,3) and (5,1). y-3=
Answers
Answer:
Step-by-step explanation:
(1-3)/(5-1)= -2/4 = -1/2
y - 3 = -1/2(x - 1)
y - 3 = -1/2x + 1/2
y - 6/2 = -1/2x + 1/2
y = -1/2x + 7/2
Find the value of the variable in the equation.
8^{2}+b^{2}=17^{2}
Answers
The equation 8² + b² = 17² has two solutions, b = 15 and b = -15, which satisfy the equation and make it true.
To find the value of the variable 'b' in the equation 8² + b² = 17², we can solve it by simplifying and applying basic algebraic principles.
Start with the equation 8² + b² = 17².
Simplify the exponents:
64 + b² = 289.
Subtract 64 from both sides of the equation to isolate b²:
b² = 289 - 64.
Perform the subtraction:
b² = 225.
Take the square root of both sides to solve for b:
√(b²) = √225.
Evaluate the square root:
b = ±15.
Hence, the variable 'b' can have two possible values: b = 15 and b = -15.
When substituting these values back into the original equation, both cases hold true:
For b = 15:
8² + 15² = 17²
64 + 225 = 289
289 = 289.
For b = -15:
8² + (-15)² = 17²
64 + 225 = 289
289 = 289.
Therefore, the equation 8² + b² = 17² has two solutions, b = 15 and b = -15, which satisfy the equation and make it true.
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Formula of circumference
Answers
Answer:
cimcumference = 2 × π × radius of circle ( 2πr)
Answer:
circumference = 2πr
hope it helps
The depth of water at a dock can be modeled as y = 4 sin (62) + 9. At lowtide, the water is 5 feet deep. What is the depth of water at high tide (itsmaximum point)?A. 18 feetB. 14 feetC. 9 feetD. 13 feet
Answers
Step 1:
Re-state the given function.
\(y=4\sin (\frac{\pi}{6}x)+9\)Step 2:
We shall state the mathematical implication of the sine function at both minimum and maximum points.
At minimum point:
\(\begin{gathered} At\text{ minimum point: }\sin (\frac{\pi}{6}x)=-1 \\ \text{Similarly,} \\ At\text{ maxi}mum\text{ point: }\sin (\frac{\pi}{6}x)=1 \end{gathered}\)Step 3: We shall substitute the values in step 2 above in the given function.
We are only interested in the value at maximum point, so
\(\begin{gathered} y=4(1)+9 \\ y=4+9 \\ y=13\text{ fe}et \end{gathered}\)Thus, the correct answer is 13 feet ( option D)
How many four-digit odd numbers less than 6000 can be formed using the digits 2, 3, 4, 5, 6, and 8?
Answers
Answer:
288
Step-by-step explanation:
First position choice: 4 numbers
Second 6 numbers
Third 6
Fourth 6
TOTAL 4 digit numbers 4 * 6 * 6 * 6 = 864 combos
2 out of 6 of these will end in 3 or 5 (thus making an odd number)
864 * 2/6 = 288 such numbers
Joseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.
A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.
8 squared + 12 squared = d squared. 64 + 24 = d squared. 88 = d squared. StartRoot 88 EndRoot = d. 9.4 almost-equals d.
She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
She did not square the 12 in the problem. She should have used 12 squared = 144.
She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 44.
She should not have taken the square root of each side when solving. She should have just divided each side by 2.
She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
Answers
For this case the distance will be given by:
d ^ 2 = (12 * 1.5) ^ 2 + (8 * 1.5) ^ 2
Rewriting we have:
d ^ 2 = (18) ^ 2 + (12) ^ 2
d ^ 2 = 324 + 144
d ^ 2 = 468
d = root (468)
d = 21.63 Km
Answer:
1) She did not find the full distance each traveled in 1.5 hours.
2) She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance.
Answer:
a and b
Step-by-step explanation:
I REALLY NEED HELP!
Complete the equation to represent the relationship. Then solve the equation. Use the variable x to represent the unknown number.
Five less than 6 times a number is the same as the number plus 10.
The equation is .
x =
Answers
You are ready to spend your Christmas money! You go to your favorite store and buy some jewelry.
They are running a sale where everything is $10! You got $130 for Christmas and don't have any
more than that to spend. How many pieces of jewelry can you buy?
Solution: You can buy [ ]
pieces of jewelry or [ ]
-
Answers
Answer:
13
Step-by-step explanation:
130/10=13
You can buy 13 pieces of jewelry with $130.
If everything in the store is priced at $10, and you have a total of $130 to spend, you can calculate the number of pieces of jewelry you can buy by dividing the total amount of money you have by the price of each item:
Number of pieces of jewelry = Total money available / Price of each item
Number of pieces of jewelry = $130 / $10
Number of pieces of jewelry = 13
Therefore, you can buy 13 pieces of jewelry with $130.
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. Determine the standard equation of the ellipse using the stated information.
Foci at (8,−1) and (−2,−1); length of the major axis is twelve units
The equation of the ellipse in standard form is _____.
b. Determine the standard equation of the ellipse using the stated information.
Vertices at (−5,12) and (−5,2); length of the minor axis is 8 units.
The standard form of the equation of this ellipse is _____.
c. Determine the standard equation of the ellipse using the stated information.
Center at (−4,1); vertex at (−4,10); focus at (−4,9)
The equation of the ellipse in standard form is ____.
Answers
a. The standard equation of the ellipse with foci at (8, -1) and (-2, -1), and a length of the major axis of 12 units is: ((x - 5)² / 6²) + ((y + 1)² / b²) = 1.
b. The standard equation of the ellipse with vertices at (-5, 12) and (-5, 2), and a length of the minor axis of 8 units is: ((x + 5)² / a²) + ((y - 7)² / 4²) = 1.
c. The standard equation of the ellipse with a center at (-4, 1), a vertex at (-4, 10), and a focus at (-4, 9) is: ((x + 4)² / b²) + ((y - 1)² / 9²) = 1.
a. To determine the standard equation of the ellipse with foci at (8, -1) and (-2, -1), and a length of the major axis of 12 units, we can start by finding the distance between the foci, which is equal to the length of the major axis.
Distance between the foci = 12 units
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
√((x₂ - x₁)² + (y₂ - y₁)²)
Using this formula, we can calculate the distance between the foci:
√((8 - (-2))² + (-1 - (-1))²) = √(10²) = 10 units
Since the distance between the foci is equal to the length of the major axis, we can conclude that the major axis of the ellipse lies along the x-axis.
The center of the ellipse is the midpoint between the foci, which is (5, -1).
The equation of an ellipse with a center at (h, k), a major axis of length 2a along the x-axis, and a minor axis of length 2b along the y-axis is:
((x - h)² / a²) + ((y - k)² / b²) = 1
In this case, the center is (5, -1) and the major axis is 12 units, so a = 12/2 = 6.
Therefore, the equation of the ellipse in standard form is:
((x - 5)² / 6²) + ((y + 1)² / b²) = 1
b. To determine the standard equation of the ellipse with vertices at (-5, 12) and (-5, 2), and a length of the minor axis of 8 units, we can start by finding the distance between the vertices, which is equal to the length of the minor axis.
Distance between the vertices = 8 units
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
√((x₂ - x₁)² + (y₂ - y₁)²)
Using this formula, we can calculate the distance between the vertices:
√((-5 - (-5))² + (12 - 2)²) = √(0² + 10²) = 10 units
Since the distance between the vertices is equal to the length of the minor axis, we can conclude that the minor axis of the ellipse lies along the y-axis.
The center of the ellipse is the midpoint between the vertices, which is (-5, 7).
The equation of an ellipse with a center at (h, k), a major axis of length 2a along the x-axis, and a minor axis of length 2b along the y-axis is:
((x - h)² / a²) + ((y - k)² / b²) = 1
In this case, the center is (-5, 7) and the minor axis is 8 units, so b = 8/2 = 4.
Therefore, the equation of the ellipse in standard form is:
((x + 5)² / a²) + ((y - 7)² / 4²) = 1
c. To determine the standard equation of the ellipse with a center at (-4, 1), a vertex at (-4, 10), and a focus at (-4, 9), we can observe that the major axis of the ellipse is vertical, along the y-axis.
The distance between the center and the vertex gives us the value of a, which is the distance from the center to either focus.
a = 10 - 1 = 9 units
The distance between the center and the focus gives us the value of c, which is the distance from the center to either focus.
c = 9 - 1 = 8 units
The equation of an ellipse with a center at (h, k), a major axis of length 2a along the y-axis, and a distance c from the center to either focus is:
((x - h)² / b²) + ((y - k)² / a²) = 1
In this case, the center is (-4, 1), so h = -4 and k = 1.
Therefore, the equation of the ellipse in standard form is:
((x + 4)² / b²) + ((y - 1)² / 9²) = 1
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At a gardening store,seed packets cost 2$ each. Martin bought 6 packets of lettuce seeds and 7 packets of pea seeds. the expression 2×(6+7) represents the cost in dollars of martins seeds. identify the parts of the expression for 2×(6+7).
Answers
The expression 2*(6+7) represents the total cost of the seed packets.
The factor "2" represents the packet cost per unit ($/packet). Then, to find the total cost, we have to multiply that factor by another that represents all the packets he is buying.
This last factor is what is expressed as a sum "6+7".
This sum represents the packets he is buying separated in two terms:
- "6" represents the packets of lettuce seeds.
- "7" represents the packets of pea seeds.
If we look at the expression without the parenthesis, like 2*6+7, it will have a different result than 2*(6+7) because we are changing the order by which operations are solved.
For 2*6+7, we solve 2*6 first and then add 7 to the result.
In the case of 2*(6+7), because of the parenthesis, we first solve the sum whitin the parenthesis and then we multiply the result by 2.
2*6+7 may represent another situation.
We can represent with this equation the following situation: "Martin has 2 bags of 6 kg of sand and one bag that weights 7 kg of sand. The expression 2*6+7 represents the total amount of kg of sand he got".
Answer:
The part in parenthesis shows the sum of 6 and 7.
The sum represents the number of packets of lettuce seeds plus the number of packets of pea seeds.
One of the factors is 2. The other factor is the sum of 6 and 7
The product represents the price per packet times the number of packets Martin bought.
Answer:
Step-by-step explanation:
The part in parenthesis shows the sum of 6 and 7.
The sum represents the number of packets of lettuce seeds plus the number of packets of pea seeds.
One of the factors is 2. The other factor is the sum of 6 and 7
The product represents the price per packet times the number of packets Martin bought.
There are 1212 different colored pencils in a box. what is the probability that the orange pencil and then the green pencil will be chosen at random, without replacement?
Answers
The probability that the orange pencil and then the green pencil will be chosen at random, without replacement is 0.68.
What is probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true.The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.A probability formula can be used to calculate the probability of an event by simply dividing the favorable number of outcomes by the total number of possible outcomes.To find what is the probability that the orange pencil and then the green pencil will be chosen at random, without replacement:
Probability of orange pencil = 1/1212Probability of green pencil without replacement of orange pencil = 1/1211Total probability of both orange and green pencils:1/1212× 1/1211 = 1/1,467,732 = 0.68So, P = 0.68.Therefore, the probability that the orange pencil and then the green pencil will be chosen at random, without replacement is 0.68.
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What is the image of (x,y) after a translation of 3 units left and 5 units up?
Answers
the answer is number 3