Answer:
16g + 24 - (13g- 15)
length - width
perimeter = 2(length) - 2(width)
2(16g+ 24) + 2(13g-15)
32g + 48 + 26g - 30
58g + 18
A cube has sides of length L = 0.370 m . It is placed with one corner at the origin as shown in the figure(Figure 1) . The electric field is not uniform but is given by E? =( -5.65 N/(C?m) )xi^+( 3.23 N/(C?m) )zk Find the total electric charge inside the cube.
Find the electric flux through each of the six cube faces S1,S2,S3,S4,S5, and S6.
The total electric charge inside the cube is -2.52×10^-9 C in the x-direction and 5.72×10^-9 C in the z-direction.
We can calculate the total electric charge inside the cube by using Gauss's law, which relates the electric flux through a closed surface to the total charge enclosed within that surface.
Since the electric field is not uniform, we need to choose a closed surface over which the electric flux is easy to calculate. We can choose a cube with sides of length L centered at the origin, since the electric field is given at all points in space.
Using the symmetry of the problem, we can choose the cube so that it is aligned with the x, y, and z-axes. Each face of the cube has an area of L^2, so the total surface area of the cube is 6L^2.
The electric flux through each face of the cube is given by the dot product of the electric field with the normal vector to that face. For the x-faces, the normal vector is i, and for the z-face, the normal vector is k. The electric field does not have a component in the y-direction, so the flux through the y-faces is zero.
The electric flux through each x-face is
Φx = E•A = (-5.65 N/C)(L^2)i
The electric flux through the z-face is:
Φz = E•A = (3.23 N/C)(L^2)k
Since the electric field is constant over each face, we can add the flux through each face to get the total electric flux through the cube:
Φtotal = 2Φx + 2Φy + 2Φz = (-5.65 N/C)(2L^2)i + (3.23 N/C)(2L^2)k
By Gauss's law, the total electric flux through a closed surface is equal to the total charge enclosed within that surface divided by the permittivity of free space (ε0):
Φtotal = Qenc/ε0
Solving for the total charge enclosed within the cube:
Qenc = Φtotal ε0 = [(-5.65 N/C)(2L^2)i + (3.23 N/C)(2L^2)k] ε0
Using the value of the permittivity of free space ε0 = 8.85×10^-12 C^2/(N m^2), we get:
Qenc = [-2.52×10^-9 C i + 5.72×10^-9 C k]
The total electric charge inside the cube is -2.52×10^-9 C in the x-direction and 5.72×10^-9 C in the z-direction.
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The given question is incomplete, the complete question is:
A cube has sides of length L = 0.370 m . It is placed with one corner at the origin as shown in the figure . The electric field is not uniform but is given by E =( -5.65 N/(C) )xi^+( 3.23 N/(C) )zk Find the total electric charge inside the cube.
Triangle ABC is an isosceles with AC=CB=8cm CD is an arc of a circle centre B and angle ABC=0.9radians. Find
I) the length of CD
ii) the length of AD
iii) the perimeter of the shaded portion
From isosceles triangles; we can establish that the
Angles CAD = CBD.
Hence, angle CAD = 0.9radians = 51.57°
The length of the arc CD is;L = (51.67/360) × 2 × 3.14 × 8
L = 7.21cm = CD.
To find the length of AC; From trigonometric identities; Cos 51.67 = AD/8cmAD = 0.62 × 8
AD = 4.96cm
The perimeter of the shaded portion is therefore; 7.21 + 4.96 + 8 = 20.17cmLearn more on length of an arc:
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Wayne placed an order for 1 2/3 sacks of brown lentils and 1/2 of a sack of green lentils. How much more brown lentils did Wayne order?
Answer:
1 1/6
Step-by-step explanation:
1 2/3 - 1/2 =
1 2/3 = 1 4/6
1/2 = 3/6
1 4/6 - 3/6 =
1 1/6
Everett shoveled 31,798 ounces of gravel from a pile to his driveway. How many tons is this?
0.994 us tons is the answer
Can somebody help me with this question plz!
Answer:
x = 5°
Step-by-step explanation:
Because of the given congruency,
Angle A = Angle D = 50° = 10x
10x = 50
x = 5°
HOPE IT HELPS!!!
Find the length of "b" to the nearest tenth.
Answer:
11.2
Step-by-step explanation:
(AB) ^2 - (BC) ^2 = b^2 (Pythogoras Theorem)
(15)^2 - (10)^2 = (b) ^2
b^2=225-100
b^2=125
b=root (125)
b=11.18
b=11.2
Pls answer! Sarah uses a recipe to make 2 gallons of her favorite
mixed-berry juice. The containers she plans to use to
store the juice have a capacity of 1 pint. How many
containers will Sarah need?
Answer:
16
Step-by-step explanation:
1 gallon = 8 pints
1 pint = 0.125 gallon
Given: an=3+an−1 and a1=5
What is the explicit rule for the arithmetic sequence?
The explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have given:
\(\rm a_n=3+a_n_-_1\) and
\(\rm a_1=5\)
\(\rm a_n-a_n_-_1= 3\)
The above expression represents the common ratio:
d = 3
First term:
a = 5
The explicit rule for the arithmetic sequence:
a(n) = 5 + (n - 1)3
a(n) = 3n + 2
Thus, the explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.
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an article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 250 of these passed the probe. assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (round your answers to three decimal places.) ,
The 95% confidence interval for the proportion of all dies that pass the probe in a particular wafer inspection process can be calculated using the formula:
p ± zα/2 * sqrt(p(1-p)/n)
Where p is the sample proportion of dies that passed the probe, n is the sample size, and zα/2 is the z-score corresponding to the desired confidence level. For a 95% confidence level and a two-sided interval, the z-score is 1.96.
Substituting the given values, we have:
p = 250/356 = 0.702
n = 356
zα/2 = 1.96
Plugging these values into the formula, we get:
0.702 ± 1.96 * sqrt(0.702(1-0.702)/356)
Simplifying, we get:
0.702 ± 0.056
Therefore, the 95% confidence interval for the proportion of all dies that pass the probe is (0.646, 0.758) when rounded to three decimal places. This means we can be 95% confident that the true proportion of dies that pass the probe in the wafer inspection process lies within this interval.
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Please help, its Geometry
Hope it helps just read it and type it in XD
solve the inequality
|5s-2|-6<12
Answer:
\(-16/5 < s < 4\)
Step-by-step explanation:
\(|5s-2|-6 < 12 \\ |5s-2| < 18 \\-(5s-2) < 18 \\ -5s+2 < 18 \\ -5s < 16 \\ -s < (16/5) \\ s > -(16/5) \\(5s-2) < 18 \\ 5s < 20 \\ s < 4 \\= -16/5 < s < 4\)
Miguel babysits for 3 hours and earn 15 which represents the unit rate?
Answer:
15
Step-by-step explanation:
Answer:
Miguel babysits for 3 hours and earns $15. Which represents the unit rate?
Option D
(D) $5 per hour
Step-by-step explanation:
$5.00 Per Hour Represents unit rate, 15 / 3 = 5
Imagine a player getting ready for a tournament. He has 4 games to play during the day: 9:00 a.M., 11:00 a.M., 1:00 p.M., and 3:30 p.M. He refuses to wear shorts until temperature rises to at least +5 degrees. Based on a starting temperature of -9 degrees at 6am and an increase in temperature of 2 degrees an hour, when might he be able to change from his pants to shorts? Provide explanations why he can/can't put his shorts on for Game 1, Game 2, Game 3 and Game 4.
Answer:
by game 3(at 1:00 p.m.)
temperature increases to 5 degrees at 1:00 p.m
Error Analysis
A student says that √7 is a rational number because you can write √7 as the ratio or quotient
of √7(fraction) √7 over 1 , is the student correct? Explain your answer.
Answer:
No
Step-by-step explanation:
Ive had the same equation before.
If x²+kx+16/9 is a perfect square. Find the value of k
Answer:
For x² + kx + 16/9 to be a perfect square, k should be equal to 8/3
Step-by-step explanation:
If x² + kx + 16/9 is a perfect square then it must satisfy the formula of (a + b)² i.e. equal to a² + 2ab + b².
So, first we will form a equal that looks similar to the formula:
\( \rm \implies {x}^{2} + kx + \dfrac{4 \times 4}{3 \times 3} \\ \\ \rm \implies {x}^{2} + kx + { \bigg( \dfrac{4}{3} } \bigg)^{2} \)
Now by comparing we get,
\( \rm \implies k \cancel{x} = 2 \times \cancel{x}\times \frac{4}{3} \\ \\ \rm \implies k = \dfrac{8}{3} \)
Twice the difference of a number and 4 is 7
Answer:
5
Step-by-step explanation:
Two sides of a triangle have lengths 1010 and 1515. The length of the altitude to the third side is the average of the lengths of the altitudes to the two given sides. How long is the third side
The length of the third side is BC ≈ 1315.5.
Let the two sides of the triangle with given altitudes be AB=1010 and AC=1515. Let h be the length of the altitude from A to BC.
Let D and E be the feet of the perpendiculars from A to BC and from B to AC, respectively. Then we have:
BD = AB - AD = 1010 - h
CE = AC - AE = 1515 - h
Since the length of the altitude from A to BC is the average of the lengths of the altitudes to the two given sides, we have:
h = (BD + CE) / 2
h = [(1010 - h) + (1515 - h)] / 2
2h = 2525 - h
3h = 2525
h = 2525 / 3
Now we use the Pythagorean theorem on the right triangle ABD:
\(AD^2 + BD^2 = AB^2\)
\(h^2 + (1010 - h)^2 = 1010^2\)
Expanding and simplifying, we get:
\(2h^2 - 2020h + 515 = 0\)
Solving for h using the quadratic formula, we get:
h = \((2020 ± sqrt(2020^2 - 4(2)(515))) / (2(2))\)
h ≈ 808.6 or h ≈ 1511.4
We take the smaller value of h since the altitude is shorter than the length of the side opposite to it. Therefore, h ≈ 808.6.
Now we can use the Pythagorean theorem on the right triangle ABC:
\(BC^2 = AC^2 - h^2\)
\(BC^2 = 1515^2 - (808.6)^2\)
BC ≈ 1315.5
Therefore, the length of the third side is BC ≈ 1315.5.
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A cone has a volume of 100x cubic centimeters and a height of 12 centimeters. What is the radius of the base of the
cone in centimeters?
A. 10 cm
B. 5 cm
C. 25 cm
D. Not here
Write an equation to match the real-world situation.
A video game rental store charges $3 per game and a membership fee of $10.
Answer: 3x+10. (If you get a membership.)
X= amount of games bought.
Plssssssssss help????????
Step-by-step explanation: Since the equation of this line is written in
slope-intercept or y = mx + b form, its slope or m is represented by the
coefficient of the x term which in this case is 8/5.
It's y-intercept or b is represented by
the constant term which in this is -5.
To graph the line, start with the y-intercept of -5.
So go down 3 units on the y-axis, plot a point at (0, -3).
From there, take your slope of 8/5, so rise 8 units
and run 5 units the right which should leave you at (5, 3).
Graph the line through those points.
Mikki used 18 tea bags to make 4 quarts of
iced tea. How many tea bags did Mikki use for
each quart of iced tea?
Answer:
\( \frac{18}{4} \)
Step-by-step
4.5
In the picture, the "3" is called...
Answer:
The radical sign
Step-by-step explanation:
In the picture 3 is called the radical sign. So option 3 is correct.
Working together, Jacob and Heather can sweep a
porch in 5.45 minutes. Had she done it alone it would
have taken Heather 12 minutes. Find how long it would
take Jacob to do it alone.
Use the FOIL method to evaluate the expression:
Answer:
\(\sf b.) \ 1 +2\sqrt{7}\)
Explanation:
Foil method: (a + b)(c + d) = ac + ad + bc + bd
Solving steps:
\((4 - \sqrt{7} )(2 + \sqrt{7} )\)
\((4)(2) + 4(\sqrt{7} ) + (-\sqrt{7} )(2) + (-\sqrt{7} )(\sqrt{7} )\)
\(8 + 4\sqrt{7} - 2\sqrt{7} - 7\)
\(8 -7 + 4\sqrt{7} - 2\sqrt{7}\)
\(1 +2\sqrt{7}\)
option b) 1 + 2√7
Step-by-step explanation:Foil property method :-
\( \red{ \boxed{ \orange{ \rm (a + b)(c + d) = ac + ad + bc + bd}}}\)
then, on substituting the values,
\(\sf⇒ \: \: 8 + 4 \sqrt{7} - 2 \sqrt{7} - 7\)
\(\sf⇒ \: \: \green{ \underline{\bold{ \red{1 + 2 \sqrt{7} }}}}\)
What is the value of x in the equation 2
(4x+)-(3x+2)- 8(9-x) = x
Answer:
open the bracket
(4X+)-3X-2-72+X=X
4X+(-3X)-74+X=X
X-74+X=X
2X-74=X
then collect the term
-74=X-2X
-74=-X
divide by negative every side then you get
X=74
A fire truck ladder has its base 3 meters about the ground. The maximum length of the ladder is 120 meters. if the ladder's greatest angle of elevation possible is 60°, what is the highest above the ground that it can reach? Round to the nearest tenth.
height= _____ meters
Answer:
94
Step-by-step explanation:
i might be wrong
A squirrel collected 45 acorns for winter and can hide 4 acorns in a single hole. How many holes will the squirrel need to dig to hide all the acorns?
Answer:
the squirrel needs to dig 12 holes.
Step-by-step explanation:
11 x 4 = 44, plus an extra hole for the one acorn left over.
In a survey given by camp counselors, campers were
asked if they like to swim and if they like to have a
cookout. The Venn diagram displays the campers'
preferences.
Camp Preferences
S
0.06
0.89
C
0.04
0.01
A camper is selected at random. Let S be the event that
the camper likes to swim and let C be the event that the
camper likes to have a cookout. What is the probability
that a randomly selected camper does not like to have a
cookout?
O 0.01
O 0.04
O 0.06
O 0.07
The probability is 0.96 that a randomly selected camper does not like to have a cookout, based on the given information and the complement rule of probability.
To determine the probability that a randomly selected camper does not like to have a cookout, we need to find the complement of the event C (the event that the camper likes to have a cookout).
Looking at the Venn diagram, we see that the probability of event C is 0.04 (represented by the intersection of circles C and A). Therefore, the probability of the complement of event C (not liking to have a cookout) is equal to 1 minus the probability of event C.
1 - 0.04 = 0.96
Hence, the probability that a randomly selected camper does not like to have a cookout is 0.96.
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E(-18,-4), F(-18,-10), G(12,-10). Center: (-6,-4) ,=6. What’s the new coordinates
The new coordinates after applying the transformation are:
E(-78, -4)
F(-78, -40)
G(102, -40).
To find the new coordinates after applying the given transformation of center (-6, -4) and a scale factor of 6, we need to multiply the distance between each point and the center by the scale factor and then add the result to the center coordinates.
Let's calculate the new coordinates for each point:
For point E(-18, -4):
New x-coordinate = (-18 - (-6)) * 6 + (-6) = -12 * 6 - 6 = -78
New y-coordinate = (-4 - (-4)) * 6 + (-4) = 0 * 6 - 4 = -4
Therefore, the new coordinates for point E are (-78, -4).
For point F(-18, -10):
New x-coordinate = (-18 - (-6)) * 6 + (-6) = -12 * 6 - 6 = -78
New y-coordinate = (-10 - (-4)) * 6 + (-4) = -6 * 6 - 4 = -40
Therefore, the new coordinates for point F are (-78, -40).
For point G(12, -10):
New x-coordinate = (12 - (-6)) * 6 + (-6) = 18 * 6 - 6 = 102
New y-coordinate = (-10 - (-4)) * 6 + (-4) = -6 * 6 - 4 = -40
Therefore, the new coordinates for point G are (102, -40).
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TRUE / FALSE. when the block is in equilibrium, each spring is stretched an additional ∆x. then the block is set into oscillation with amplitude a; when it passes through its equilibrium point it has a speed v.
The statement is true.
When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.
When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.
The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.
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