Answers
Answer:
see attached
Step-by-step explanation:
You want a perpendicular to the line at point P.
ProcedureYou know how to construct a perpendicular bisector, so you do that—after you have created a segment with P as its midpoint.
To put P at the midpoint of a segment, set your compass to a length slightly less than the shortest part of the line segment from P. Use that radius to draw an arc (red) on the line on either side of P. Now P is the midpoint of those points of intersection (E and F in the attachment).
Perpendicular bisectorNow, increase the radius of your compass by some amount. It is convenient for it to be about half again what it was.
Using this setting and points E and F as centers, draw arcs (green) either side of the line so they intersect at points K and L.
The line KL is perpendicular to the given line at point P.
__
Additional comment
You don't need the whole circle or the continuous arc. You only need a short arc through the point of intersection.
We draw points K and L so there is a longer distance between the points defining the perpendicular line. This can help make it more accurately perpendicular.
It is important to keep the same radius for the arcs centered at E and F. That is what ensures K and L are equidistant from both E and F, which they must be if KL is to bisect EF. You can use this procedure to draw the perpendicular bisector of any segment EF. (It works well to make radius EK about 3/4 of the distance EF.)
You actually only need K or L for this problem, because you know point P is also on the perpendicular line.
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Related Questions
The histogram shows the birthweights of 1000 mice.
Answers
Answer:
60 mice.
Step-by-step explanation:
This equals the area of the rectangle to the left of 10 g.
= 2 * 3
= 6
The total area of all rectangles = 100 so for each small square this = 10 mice so the answer is 60 mice.
How many solutions does the nonlinear system of equations graphed below
have?
• A. One
• B. Two
• C. Four
O D. Zero
SUBMIT
Answers
Pleaseeee answer correctly !!!!!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
Answers
Answer:Answer is A
Step-by-step explanation:
Answer:
they are all squares, since all the sides are the same number and a quadrilaerals include the square in that category so A and B
Find the determinant of the elementary matrix. (Assume k # 0.) 1 0 0 4k 1 0 0 0 1 I Find 141. Begin by finding 4, and then evaluate its determinant. Verify your result by finding (A) and then applying the formula 14-11- A [21] 14-¹1- Need Help? Readi
Answers
The given matrix is an elementary matrix that represents an elementary row operation of multiplying the second row by 4k. The determinant of this matrix is determinant of the original matrix, which is 4k.
Therefore, the determinant of the given elementary matrix is 4k.
To verify this result, we can also compute the determinant using the formula for a 3x3 matrix. The matrix obtained by applying the elementary row operation to the identity matrix is:
\(\left[\begin{array}{ccc}1&0&0\\0&4k&0\\0&0&1\end{array}\right]\)
The determinant of this matrix is calculated as: det(A) = 1 * (4k) * 1 - 0 * 0 * 0 - 0 * (4k) * 0 = 4k. So, the determinant of the given elementary matrix is indeed 4k, which matches our previous result.
In summary, the determinant of the elementary matrix is 4k, and this can be verified by calculating the determinant using the formula for a 3x3 matrix.
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HELP ILL GIVE 10 POINTS
(LOOK AT SCREENSHOT BELOW)
Answers
process:
3/14^2
3/14 • 3/14
9/196
In ΔHIJ, the measure of ∠J=90°, the measure of ∠H=35°, and IJ = 72 feet. Find the length of HI to the nearest tenth of a foot.
Answers
Answer:
125.5 feet
Step-by-step explanation:
find the (real) eigenvalues and associated eigenvectors of the given matrix A. Find a basis for each eigenspace of dimension 2 or larger. 1. [ 4
1
−2
1
] 2. [ 5
3
−6
−4
] 3. [ 8
3
−6
−1
] 4. [ 4
2
−3
−1
] 5. [ 10
6
−9
−5
] 6. [ 6
3
−4
−1
]
Answers
1. The eigenvector associated with λ₂ is [1; 1].
2. The eigenvector associated with λ₂ is [3; 5].
3. The eigenvector associated with λ₂ is [3; 1].
4. The eigenvector associated with λ is [1; -1].
5. The eigenvector associated with λ is [2; -3].
6. The eigenvector associated with λ is [1; -2].
For the matrix A = [4 1; -2 1]:
The eigenvalues are λ₁ = 3 and λ₂ = 2.
For λ₁ = 3:
The eigenvector associated with λ₁ is [1; 2].
For λ₂ = 2:
The eigenvector associated with λ₂ is [1; 1].
For the matrix A = [5 3; -6 -4]:
The eigenvalues are λ₁ = -1 and λ₂ = 0.
For λ₁ = -1:
The eigenvector associated with λ₁ is [3; -2].
For λ₂ = 0:
The eigenvector associated with λ₂ is [3; 5].
For the matrix A = [8 3; -6 -1]:
The eigenvalues are λ₁ = 5 and λ₂ = 4.
For λ₁ = 5:
The eigenvector associated with λ₁ is [1; 2].
For λ₂ = 4:
The eigenvector associated with λ₂ is [3; 1].
For the matrix A = [4 2; -3 -1]:
The eigenvalue is λ = 2.
The eigenvector associated with λ is [1; -1].
For the matrix A = [10 6; -9 -5]:
The eigenvalue is λ = 1.
The eigenvector associated with λ is [2; -3].
For the matrix A = [6 3; -4 -1]:
The eigenvalue is λ = 2.
The eigenvector associated with λ is [1; -2].
Note: None of the given matrices have eigenspaces of dimension 2 or larger.
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help me find the following in the circle
Answers
The required diameter of the given circle is PR, radius of the given circle is PQ, chord of the given circle are ST and PR, the tangent of the given circle is FG, point of tangency of the given circle is F and secant of the given circle is AB.
Given the diagram of circle, which is marked with different line segments.
Diameter is the line passing through the centre of the circle, radius of the circle is the line segment between centre and other point on the circle, the chord is the line segment points on the circle and diameter is the biggest chord, tangent is the line segment which intersect the circle at only one point and that point is known as point of tangency and secant is the line segment which cuts the circles.
Hence, the required diameter of the given circle is PR, radius of the given circle is PQ, chord of the given circle are ST and PR, the tangent of the given circle is FG, point of tangency of the given circle is F and secant of the given circle is AB.
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All revenues, expenses, and the dividends account are closed through the Income Summary account. Group of answer choices True False
Answers
Revenues, expenses, and the dividends account are closed through the Income Summary account. The statement is false.
Revenues, expenses, and the dividends account are not closed through the Income Summary account. The Income Summary account is used during the closing process in accounting to transfer the balances of revenue and expense accounts to the retained earnings account. The purpose of the Income Summary account is to summarize the net income or net loss for the period.
After transferring the balances to the Income Summary account, the final step of the closing process involves closing the Income Summary account directly to the retained earnings account. The dividends account, on the other hand, is closed directly to the retained earnings account as well. Therefore, revenues, expenses, and the dividends account are closed directly to the retained earnings account, not through the Income Summary account.
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What is the value of x ?
Answers
Answer:
I think the value of x =50
I need help please I’m very confused
Answers
The values of d that make the inequality 9d > 9 true are given as follows:
2, 4, 11.
Hence the equivalent inequality is given as follows:
d > 1.
How to solve the inequality?The inequality in the context of this problem is defined as follows:
9d > 9.
To solve the inequality, we solve it similarly to an equality, isolating the desired variable d, hence the solution is given as follows:
d > 9/9
d > 1.
The > symbol means that the solution is composed by values that are greater than 1, hence the options are 2, 4, 6 and 11.
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Which term describes how to determine if a relation given in a table is a function
A. If none of the output values are repeated, the relation is a function
B. If none of the input values are repeated, the relation is a function
C. If any of the input values are equal to the output values, the relation is a function
D. If all the output values are paired with the same input value, the relation is a function
Answers
Answer:
A. If none of the output values are repeated, the relation is a function
Step-by-step explanation:
The reason why A is correct stems from the concept of the vertical line test. If each x-value has their own respective output (y-value), then the relation is a function.
Choice B just states that if none of the x-values are repeated. then the relation is a function. This is not correct because it doesnt follow the vertical line test, which analyzes if any y-values are being repeated
Choice C and D doesnt have any correlation with the vertical line test because an x-value doesnt have to equal a y-value to make the relation a function. Vice versa for any y value being equal to any x-value.
Based on a poll conducted by the Centers for Disease Control, 862 of 1013 randomly selected adults said that they always wear seat belts. Construct and interpret a 95% confidence interval for the proportion of adults who always wear seat belts.
Answers
The confidence interval is 0.028, 0.872
Given862 of 1013 randomly selected adults wear seat belts.
The 95% confidence interval for the proportion of adults who always wear seat belts.
What is confidence interval?A Confidence Interval is defined as a range of values we are sure our true value lies within it.
What is 95% confidence interval?A 95% confidence interval is defined as that if we take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value.
= 862/1013 = 0.85
At a 95% confidence interval ,the critical value is \(z_{0.025} = 1.96\)
The 95% confidence interval for proportion is
\(\widehat p +/- z0.025 * sqrt(\widehat p * (1 - \widehat p)/n)\)
\(= 0.85 +/- 1.96 * sqrt(0.85 * (1 - 0.85)/1013)\)
\(= 0.85 +/- 0.022\)
= 0.028, 0.872
The sample should use at least 10 successes and 10 failures.
\(n * \widehat p = 1013 * 0.85 = 861 > 10\)
\(n * (1 - \widehat p) = 1013 * 0.15 = 152 > 10\)
As the sample size is larger, we can use an approximate formula for the standard error.
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A bank features a savings account that has an annual percentage rate of r=4.5r=4.5% with interest compounded semi-annually. Monique deposits $2,000 into the account.
The account balance can be modeled by the exponential formula S(t)=P(1+rn)ntS(t)=P(1+rn)nt, where SS is the future value, PP is the present value, rr is the annual percentage rate, nn is the number of times each year that the interest is compounded, and tt is the time in years.
(A) What values should be used for PP, r, and nn?
P=, r=, n=
(B) How much money will Monique have in the account in 9 years?
Answer = $ .
Round answer to the nearest penny.
(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year).
APY= %.
Round answer to 3 decimal places.
Answers
The required answers ar(a)P = $2,000,r = 4.5%,n = 2 (b)$ 2985.17, (c) 4.45%
How to find the future value and interest?(A) Using the given information, we can identify the following values:
P = $2,000 (the present value or initial deposit)
r = 4.5% (the annual percentage rate)
n = 2 (the number of times per year that interest is compounded, since it is compounded semi-annually)
(B) To find the future value of the account balance after 9 years, we can use the formula:
\(S(t) = P(1 + r/n)^{nt}\)
where t is the time in years. Substituting the given values:
\(S(9) = $2,000(1 + 0.045/2)^{2*9}= $2,000(1.0225)^{18}\)
= $2,000(1.505016)
= $2985.17
Therefore, Monique will have $$2985.17 in the account in 9 years.
(C) The annual percentage yield (APY) takes into account the effect of compounding on the effective interest rate. It is calculated as:
\(APY = (1 + \frac{r}{n})^n - 1\)
Substituting the given values:
\(APY = (1 + 0.045/2)^2 - 1\)
= 0.0445 or 4.45%
Therefore, the annual percentage yield for the savings account is 4.45% rounded to 3 decimal places.
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What is the value of the following expression? 2w - 6, when w = 6
Answers
Answer:
The answer is 6.
Step-by-step explanation:
Since w = 6 you would input the 6 where the w value is. Your equation should look like this: 2(6)-6
First you multiple the 2 x 6 which equals 12. After you minus 12-6 which equals 6. Therefore your answer is 6.
The following table shows the number of candy bars bought at a local grocery store and the
total cost of the candy bars:
Candy Bars: 3, 5, 8, 12, 15, 20, 25
Total Cost: $6.65, $10.45, $16.15, $23.75, $29.45, $38.95, $48.45
If B represents the number of candy bars purchased and C represents the total cost of the candy bars, write the linear model that models the cost of any number of candy bars.
Answers
The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95
To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.
Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.
To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):
m = (C2 - C1) / (B2 - B1)
= ($48.45 - $6.65) / (25 - 3)
= $41.80 / 22
≈ $1.90
Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):
b = C - mB
= $6.65 - ($1.90 * 3)
= $6.65 - $5.70
≈ $0.95
Therefore, the linear model that represents the cost of any number of candy bars can be written as:
C = $1.90B + $0.95
This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.
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11. What is the equation of the line that has a slope of 0 and passes through the point (9,-4)?
Answers
Answer:
y = 9
Step-by-step explanation:
The line that has a slope of 0: y = 0*x + ?
pass through the point (9,-4): 9 =0*(-4) + ?, we can get 9.
So the answer is y = 9.
Answer: y=0x-4
Step-by-step explanation:
y=mx+b
-4 = (0)(9)+b
b = -4
y = -4
Which rate can you set StartFraction 30 miles Over 1 hour EndFraction equal to in order to find the time it takes to travel 900 miles at 30 miles per hour?
Answers
Answer:
\(\dfrac{30\,\text{mi}}{1\,\text{h}}=\dfrac{900\,\text{mi}}{t}\)
Step-by-step explanation:
Since you have miles in the numerator of your rate, you need miles in the numerator of the equivalent fraction:
\(\dfrac{30\,\text{mi}}{1\,\text{h}}=\dfrac{900\,\text{mi}}{t}\)
This can be rearranged to ...
\(\dfrac{t}{1\,\text{h}}=\dfrac{900\,\text{mi}}{30\,\text{mi}}=30\)
Then, multiplying by 1 h gives the solution ...
t = 30 h
It takes 30 hours to travel 900 miles at 30 miles per hour.
the answer is:
d. 900/? hours
how to solve a question about if one person can do in 5 hours, and another person does in 10 hours, how long will it take for them working togehter
Answers
It will take approximately 3.33 hours for both persons working together to complete the job.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.
To solve this problem, we can use the following formula:
1 / T = 1 / t1 + 1 / t2
Where T is the time it takes for both persons working together to complete the job, t1 is the time it takes for the first person to complete the job alone, and t2 is the time it takes for the second person to complete the job alone.
Plugging in the given values, we get:
1 / T = 1 / 5 + 1 / 10
Simplifying the right side, we get:
1 / T = 3 / 10
Multiplying both sides by 10T, we get:
10 = 3T
Dividing both sides by 3, we get:
T = 10 / 3 = 3.33 hours
Therefore, it will take approximately 3.33 hours for both persons working together to complete the job.
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Lavonne is single and earned $125,000 last year. Use the tax schedule
information below to determine how much tax Lavonne will owe.
Over-
$82,500
$18,150
$9,350
O $23,439
O $14,089
A
But not over-
$157,500
The tax is:
$14, 089.00 +22%
of the amount over-
$82,500
Answers
Lavonne's tax liability will be $23,439.00.
We have,
Lavonne's income falls between $82,500 and $157,500, according to the tax schedule information.
To determine her tax liability, we need to find the amount over $82,500, which is:
= $125,000 - $82,500
= $42,500
Lavonne's tax liability will be the sum of the fixed amount plus the percentage of the amount over $82,500, which is:
= $14,089.00 + 22%($42,500)
= $14,089.00 + $9,350.00
= $23,439.00
Therefore,
Lavonne's tax liability will be $23,439.00.
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if you wanted to examine whether the degree of parental involvement differs based on students’ grade in school (i.e., first, second, third, etc.), what is the dependent variable of interest?
Answers
The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.
In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.
The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.
By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.
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Can all problems be represented by graphs?
Answers
Answer:
depending on the size of graph
I'm a multiple of a between 50 and110,I'm also a multiple of 6,who could l be?
Answers
I'm a multiple of a between 50 and110,I'm also a multiple of 6, I am number 54.
To check this, we can divide 54 by 6 and see that it is an integer: 54 ÷ 6 = 9. Therefore, 54 is a multiple of 6.
We can also divide 54 by 54 and see that it is also an integer: 54 ÷ 54 = 1. Therefore, 54 is a multiple of 54 and it is between 50 and 110. Therefore, the number is indeed 54.
The number could be 54, which is a multiple of 6 and a multiple of 54 (since 54 is between 50 and 110).
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Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
Step-by-step explanation:
Choose two points on the graph: (-6,-7) and (6,-9)
The straight line equation is: y=mx+b
\(\displaystyle\\\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-6\ \ \ \ x_2=6\ \ \ \ \ y_1=-7\ \ \ \ y_2=-9\\\\m=\frac{-9-(-7)}{6-(-6)} \\\\m=\frac{-9+7}{6+6} \\\\m=\frac{-2}{12} \\\\m=-\frac{1}{6}\\\\Hence,\ y=-\frac{1}{6}x+b\ \ \ \ \ (1)\)
To determine the coefficient b, take any of the two points,
for example (-6,-7), that is, x=-6 y=-7
Substitute these values into formula (1):
\(\displaystyle\\-7=-\frac{1}{6}(-6) +b\\\\-7=1+b\\\\-7-1=1+b-1\\\\-8=b\\\\Thus,\ b=-8\\\\The\ result\ is\ y=-\frac{1}{6}x-8\)
Determine whether the statement "If A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3" is true or false. Choose the correct answer below. O The statement is true because if M is a 2 times 2 matrix, then the area of the parallelogram determined by the columns of B is |det B|. The given statement is the natural extension of this to 3 times 3 matrices.O The statement is false because |det A| equals the volume of the parallelepiped determined by a_1, a_2, a_3. It is possible that |det A| notequalto det A. The statement is false because it is possible to have det A = 0. When this happens, det A cannot be the volume of a parallelepiped since volume must be positive. O The statement is true because | det A| equals the volume of the parallelepiped determined by a_1, a_2, a_3. Because det A greaterthanorequalto 0 for all 3 times 3 matrices A, it follows that | det A| = det A. Determine whether the statement "det A^T = (- 1)det A" is true or false. Choose the correct answer below. O The statement is true because A^T = A for any n times n matrix A. The statement is true because a row interchange is needed to turn a matrix into its transpose. A row interchange changes the sign of the determinant. The statement is false because det A^T = (-1)^n det A for any n times n matrix A. The statement is false because det A^T = det A for any n times n matrix A.
Answers
The statement "If A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3" is true as the determinant of a 3x3 matrix equals the volume of the parallelepiped determined by its columns. The correct option is B). The second statement "det A^T = (- 1)det A" is false as det A^T = (-1)^(number of row interchanges) det A for any n x n matrix A. So, the correct option is B).
The first statement is true, and the correct answer is: "The statement is true because if A is 3 times 3, with columns a_1, a_2, a_3, then det A equals the volume of the parallelepiped determined by a_1, a_2, a_3. Because det A greater than or equal to 0 for all 3 times 3 matrices A, it follows that |det A| = det A." So, the correct answer is B).
The second statement is also false, and the correct answer is: "The statement is true because a row interchange is needed to turn a matrix into its transpose. A row interchange changes the sign of the determinant." So, the correct ansnwer is B).
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joel is planning to paint the outside of his house. he wants a green paint that requires 3 parts blue paint to 2 parts yellow paint. if he needs a total of 10 gallons to paint the whole house, how many gallons of blue paint does he need?
Answers
Joel needs 1.5 gallons of blue paint.
Joel needs a total of 10 gallons of paint to paint the outside of his house. Since the ratio is 3 parts blue paint to 2 parts yellow paint, we can use proportions to solve for the amount of blue paint needed.
We can set up the proportion like this:
3/2 = x/10
We can solve for x (the amount of blue paint) by cross-multiplying:
3*10 = 2*x
3*10 = 20x
20x = 30
x = 30/20
x = 1.5
Joel needs 1.5 gallons of blue paint.
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Lindsay has scored 15 goals in 10 lacrosse games this season. a) What is her unit rate of scoring? b) How many goals might Lindsay score in 35 games? What assumptions do you make?
Answers
b) 1.5x35= 52.5 so 53
Assuming she is consistent
(c) A non-uniform but spherically symmetric charge distribution has a charge density: rho(r)=rho 0
(1−r/R)
rho(r)=0
for r≤R
for r>R
where rho 0
=3Q/πR 3
is a positive constant. Show that the total charge contained in this charge distribution is Q. [4] Show that the electric field in the region r>R is identical to that created by a point charge Q at r=0 [2] Derive an expression for the electric field in the region r≤R. [5]
Answers
To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:
ρ(r) = ρ₀(1 - r/R) for r ≤ R,
ρ(r) = 0 for r > R,
where ρ₀ = 3Q/πR³.
To find the total charge, we integrate ρ(r) over the volume:
Q = ∫ρ(r) dV,
where dV represents the volume element.
Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.
The integral becomes:
Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.
Evaluating this integral gives:
Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.
Simplifying further, we get:
Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].
Simplifying the expression inside the parentheses:
Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].
Simplifying once more:
Q = ρ₀ * π * (R³ - R³/3),
Q = ρ₀ * π * (2R³/3),
Q = (3Q/πR³) * π * (2R³/3),
Q = 2Q.
Therefore, the total charge contained in the charge distribution is Q.
To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.
By Gauss's law, the electric field through a closed surface is given by:
∮E · dA = (1/ε₀) * Qenc,
where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.
Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.
For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q,
Simplifying:
E = Q / (4πε₀r²).
This is the same expression as the electric field created by a point charge Q at the origin (r = 0).
To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.
The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.
By Gauss's law, we have:
∮E · dA = (1/ε₀) * Qenc.
Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q.
Simplifying:
E = Q / (4πε₀r²).
This expression represents the electric field inside the charge distribution for r ≤ R.
Learn more about charge here:
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Answers
x:lessons
x=6
Mrs. Watson wants to buy some dresses for her trip to Houston. There are three boutiques, each offering a different deal.
Lara's Boutique 2 dresses for $32
The Dress Shop 6 dresses for $90
Marge's Dresses 8 dresses for $160
Which boutique has the best deal for dresses?
Answers
Answer
Dude my name is Lara and my fourth grade teacher was mrs. Watson..... but the dress shop is the answer.... guess my boutique just wasn’t it huh:
Step-by-step explanation: