Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate the flux of F across S. F(x, y, z) = x2yi + xy2j + 3xyzk, S is the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0, and x + 2y + z = 2.
Answer:
-14 / 3
Step-by-step explanation:
- Divergence theorem, expresses an explicit way to determine the flux of a force field ( F ) through a surface ( S ) with the help of "del" operator ( D ) which is the sum of spatial partial derivatives of the force field ( F ).
- The given force field as such:
[tex]F = (x^2y) i + (xy^2) j + (3xyz) k[/tex]
Where,
i, j, k are unit vectors along the x, y and z coordinate axes, respectively.
- The surface ( S ) is described as a tetrahedron bounded by the planes:
[tex]x = 0 \\y = 0\\x + 2y + z = 2[/tex]
[tex]z = 0\\[/tex]
- The divergence theorem gives us the following formulation:
[tex]_S\int\int {F} \,. dS = _V\int\int\int {D [F]} \,. dV[/tex]
- We will first apply the del operator on the force field as follows:
[tex]D [ F ] = 2xy + 2xy + 3xy = 7xy[/tex]
- Now, we will define the boundaries of the solid surface ( Tetrahedron ).
- The surface ( S ) is bounded in the z - direction by plane z = 0 and the plane [ z = 2 - x - 2y ]. The limits of integration for " dz " are as follows:
dz: [ z = 0 - > 2 - x - 2y ]
- Now we will project the surface ( S ) onto the ( x-y ) plane. The projection is a triangle bounded by the axes x = y = 0 and the line: x = 2 - 2y. We will set up our limits in the x- direction bounded by x = 0 and x = 2 - 2y. The limits of integration for " dx " are as follows:
dx: [ x = 0 - > 2 - 2y ]
- The limits of "dy" are constants defined by the axis y = 0 and y = -2 / -2 = 1. Hence,
dy: [ y = 0 - > 1 ]
- Next we will evaluate the triple integral as follows:
[tex]\int\int\int ({D [ F ] }) \, dz.dx.dy = \int\int\int (7xy) \, dz.dx.dy\\\\\int\int (7xyz) \, | \limits_0^2^-^x^-^2^ydx.dy\\\\\int\int (7xy[ 2 - x - 2y ] ) dx.dy = \int\int (14xy -7x^2y -14 xy^2 ) dx.dy\\\\\int (7x^2y -\frac{7}{3} x^3y -7 x^2y^2 )| \limits_0^2^-^2^y.dy \\\\\int (7(2-2y)^2y -\frac{7}{3} (2-2y)^3y -7 (2-2y)^2y^2 ).dy \\\\[/tex]
[tex]7 (-\frac{(2-2y)^3}{6} + (2-2y)^2 ) -\frac{7}{3} ( -\frac{(2-2y)^4}{8} + (2-2y)^3) -7 ( -\frac{(2-2y)^3}{6}y^2 + 2y.(2-2y)^2 )| \limits^1_0\\\\ 0 - [ 7 (-\frac{8}{6} + 4 ) -\frac{7}{3} ( -\frac{16}{8} + 8 ) -7 ( 0 ) ] \\\\- [ \frac{56}{3} - 14 ] \\\\\int\int {F} \, dS = -\frac{14}{3}[/tex]
A phone charger requires 0.5 A at 5V. It is connected to a transformer with 100 % of efficiency whose primary contains 2200 turns and is connected to 220-V household outlet.
(a) How many turns should there be in the secondary?
(b) What is the current in the primary?
(c) What would be the output current and output voltage values if number of secondary turns (N2) doubled of its initial value?
Answer:
a. 50 turns
b. 0.0114 A
c. 0.25 A, 10 V
Step-by-step explanation:
Given:-
- The required current ( Is ) = 0.5 A
- The required voltage ( Vs ) = 5 V
- Transformer is 100% efficient ( ideal )
- The number of turns in the primary coil, ( Np ) = 2200
- The Voltage generated by power station, ( Vp ) = 220 V
Find:-
a. The number of turns in the secondary coil of the transformer
b. The current supplied by the power station
c. The effect on output current and voltage when the number of turns of secondary coil are doubled.
Solution:-
- For ideal transformers that consists of a ferromagnetic core with two ends wounded by a conductive wire i.e primary and secondary.
- The power generated at the stations is sent to home via power lines and step-down before the enter our homes.
- A household receives a voltage of 220 V at one of it outlets. We are to charge a phone that requires 0.5 A and 5V for the process.
- The outlet and any electronic device is in junction with a smaller transformer.
- All transformers have two transformation ratios for current ( I ) and voltage ( V ) that is related to the ratio of number of turns in the primary and secondary.
Voltage Transformation = [tex]\frac{N_p}{N_s} = \frac{V_p}{V_s}[/tex]
Where,
Ns : The number of turns in secondary winding
- Plug in the values and evaluate ( Ns ):
[tex]N_s = N_p*\frac{V_s}{V_p} \\\\N_s = 2200*\frac{5}{220} \\\\N_s = 50[/tex]
Answer a: The number of turns in the secondary coil should be Ns = 50 turns.
- Similarly, the current transformation is related to the inverse relation to the number of turns in the respective coil.
Current Transformation = [tex]\frac{N_p}{N_s} = \frac{I_s}{I_p}[/tex]
Where,
Ip : The current in primary coil
- Plug in the values and evaluate ( Ip ):
[tex]I_p = \frac{N_s}{N_p}*I_s\\\\I_p = \frac{50}{2200}*0.5\\\\I_p = 0.0114[/tex]
Answer b: The current in the primary coil should be Ip = 0.0114 Amp.
- The number of turns in the secondary coil are doubled . From the transformation ratios we know that that voltage is proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output voltage is also doubled ( assuming all other design parameters remains the same ). Hence, the output voltage is = 2*5V = 10 V
- Similary, current transformation ratio suggests that the current is inversely proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output current is half of the required ( assuming all other design parameters remains the same ). Hence, the output current is = 0.5*0.5 A = 0.25 A
The longer leg of a 30-60-90° triangle is 18. What is the length of the other leg?
A) 1213
B) 93
C) 9
D) 63
Answer:
D
Step-by-step explanation:
In a 30-60-90 triangle, the longer leg is [tex]\sqrt{3}[/tex] times larger than the smaller leg. The length of the shorter leg is therefore:
[tex]\dfrac{18}{\sqrt{3}}= \\\\\\\dfrac{18\sqrt{3}}{3}= \\\\\\6\sqrt{3}[/tex]
Hope this helps!
Classify the triangle by its sides, and then by its angles.
6 in.
8 in.
10 in.
Classified by its sides, the triangle is a(n)
▼
isosceles
scalene
equilateral
triangle.
Classified by its angles, the triangle is a(n)
▼
acute
obtuse
right
triangle.
Answer: scalene and right
Step-by-step explanation:
A man is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet, all from different wineries. a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? (2 points) b) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (4 points) c) If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
Answer:
a. 336
b. 14.01%
c. 0.2%
Step-by-step explanation:
a. We have that the number of zinfandel bottles is 8 and that the number of zinfandel served is 3, therefore:
n = 8 and r = 3
we can calculate it by means of permutation:
nPr = n! / (n-r)!
replacing:
8P3 = 8! / (8-3)!
8P3 = 336
Which means there are 336 ways.
b. First we must calculate the ways to choose 2 bottles of each variety, through combinations:
nCr = n! / (r! * (n-r)!
We know that there are 8 bottles zinfandel, 10 of merlot, and 12 of cabernet, and we must choose 2 of each, therefore it would be:
8C2 * 10C2 * 12C2
8! / (2! * (8-2)! * 10! / (2! * (10-2)! * 12! / (2! * (12-2)!
28 * 45 * 66 = 83160
Now we must calculate the total number of ways, that is, choose 6 bottles of the 30 total (8 + 10 + 12)
30C6 = 30! / (6! * (30-6)! = 593775
Thus:
83160/593775 = 0.1401
In other words, the probability is 14.01%
c. In this case, we must calculate the number of ways of 8 bottles zinfandel, 10 of merlot, and 12 of cabernet choose 6, that is to say that they are all of the same variety, therefore:
8C6 + 10C6 + 12C6
8! / (6! * (8-6)! + 10! / (6! * (10-6)! + 12! / (6! * (12-6)!
28 + 210 + 924 = 1162
And that divide it by the total amount that we calculated the previous point, 30C6 = 593775
Thus:
1162/593775 = 0.002
In other words, the probability 0.2%
What value of x is in the solution set of 2x – 3 > 11 – 5x?
Given:
2x -3 > 11 -5x
Simplify both sides:
2x - 3 > -5x + 11
Add 5x to both sides:
2x - 3 +5x > -5x + 11 +5
7x - 3 > 11
Add 3 to both sides:
7x - 3 +3 > 11 + 3
7x > 14
Divided 7 to both sides:
[tex]\frac{7x}{7}[/tex] > [tex]\frac{14}{7}[/tex]
x > 2
Answer:
Any number greater than 2 would be the answer. In Edg, choose 4! Choosing 2 would be incorrect in their system.
Step-by-step explanation:
5.2 times a number is 46.8
Answer:
9
Step-by-step explanation:
"5.2 times a number is 46.8" as an equation is:
[tex]5.2*n=46.8[/tex]
Solve for 'n':
[tex]5.2*n=46.8\\5.2/5.2*n=46.8/5.2 \leftarrow \text {Division Property of Equality} \\\boxed {n=9}[/tex]
Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢ 580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of GH¢2,358.60, how much was his total investment?
Answer:
GH¢2082.12
Step-by-step explanation:
Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...
t = (a) +(a +580) = 2a+580
Solving for a, we get
a = (t -580)/2
__
The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.
1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60
0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens
1.13t + 5.8 = 2358.60 . . . . . . . . . simplify
1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8
t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t
Mr. Azu's total investment was GH¢2082.12.
The breaking strength of a rivet has a mean of 10,000 psi and a standard deviation of 714.2857 psi. What is the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200?
Answer:
[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]
[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]
And we can use the normal standard distribution table or excel and we can find the probability with this difference:
[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]
Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 10000[/tex] represent the mean
[tex] \sigma = 714.2857[/tex] represent the deviation
[tex] n = 49[/tex] represent the sample size selected
For this case since the sample size is large enough n>30 we have enough evidence to use the central llmit theorem and the distribution for the sample mena would be given by:
[tex] \bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}}) [/tex]
And we want to find the following probability:
[tex] P(9832 < \bar X< 10200)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we use the z score formula for the limits given we got:
[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]
[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]
And we can use the normal standard distribution table or excel and we can find the probability with this difference:
[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]
Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1521 and the standard deviation was 314. The test scores of four students selected at random are 1920, 1290, 2220, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual
Answer:
A score of 1920 has a z-score of 1.27.
A score of 1290 has a z-score of -0.74.
A score of 2220 has a z-score of 2.23.
A score of 1420 has a z-score of -0.32.
The score of 2220 is more than two standard deviations from the mean, so it is unusual.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is 2 or more standard deviations from the mean, it is considered unusual.
In this question, we have that:
[tex]\mu = 1521, \sigma = 314[/tex]
Score of 1920:
X = 1920. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1920 - 1521}{314}[/tex]
[tex]Z = 1.27[/tex]
A score of 1920 has a z-score of 1.27.
Score of 1290:
X = 1290. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1290 - 1521}{314}[/tex]
[tex]Z = -0.74[/tex]
A score of 1290 has a z-score of -0.74.
Score of 2220:
X = 1290. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2220 - 1521}{314}[/tex]
[tex]Z = 2.23[/tex]
A score of 2220 has a z-score of 2.23.
Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.
Score of 1420:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1420 - 1521}{314}[/tex]
[tex]Z = -0.32[/tex]
A score of 1420 has a z-score of -0.32.
What’s the correct answer for this?
Answer:
A:
Step-by-step explanation:
Using tangent-secant theorem
AE²=(EC)(ED)
12²=(8)(8+x+10)
144=8(x+18)
144=8x+144
8x = 144-144
8x = 0
So
x = 0
Now
ED = 8+x+10
ED = 8+0+10
ED = 18
This chart shows Dan’s budget:
A 3-column table has 5 rows. The first column is labeled Item with entries Internet, food, rent, discretionary spending, income. The second column is labeled Amount budgeted with entries 35, 100, 500, 100, 750. The third column is labeled Amount spent with entries 35, 95, 500, 140, blank.
Did Dan stay on budget? Why or why not?
Yes, Dan spent as much as he earned.
No, Dan should move to a new apartment.
Yes, Dan uses his savings to cover extra expenses.
No, Dan should reduce his discretionary spending
The correct answer is D No, Dan should reduce his discretionary spending
Explanation:
For Dan to stay on the budget he needs to spend the amount budgeted for each expense or less than the amount budgeted. This occurred in the case of the Internet, food, and rent; for example, the amount budgeted for the internet was $35 and Dan spent this money, also, the amount budgeted for food was $100 and Dan spent $95, which means he stood in the budget. However, this did not occur with discretionary spending, which refers to other non-necessary expenses, because in this case, Dan spent $140 even when the budget limit was $100. Also, this exceeds the total income considering 35 + 95 + 500+ 140 = $770, which is above the income ($750). Thus, Dan did not stay in the budget because he spent more money than expected in discretionary spending and should reduce this.
The correct answer is D. No, Dan should reduce his discretionary spending.
Hope this helps
:)
1) Ethan, Amir, Victoria, and Kayla share
3 apples equally. What fraction of an
apple does each friend get?
Answer:
3 apples / 4 people
3/4
to check divide fractions
Multiply reciprocal
3/1 x 4/1
3/1 / 1/4 = 3/4
3/4 x 4 = 12/4 = 3 apples
3/4 is the answer
Hope this helps
Step-by-step explanation:
Consider a value to be significantly low if its z score less than or equal to minus2 or consider a value to be significantly high if its z score is greater than or equal to 2. A data set lists weights (grams) of a type of coin. Those weights have a mean of 5.45961 g and a standard deviation of 0.05215 g. Identify the weights that are significantly low or significantly high. What weights are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice.
Answer:
lowest score is 5.35531
highest score is x=5.45961
Step by step Explanation:
· A Z-score reffered to as a numerical measurement that identifies a value's relationship to the mean of a group of values. Z-score is usually measured in terms of standard deviations from the mean.
We were to Consider a value to be significantly low if its z score less than or equal to minus2 or consider a value to be significantly high if its z score is greater than or equal to 2
the z-score is given by:
z-score=(x-μ)/σ
where:
x=score
μ=mean=5.45961
σ=std deviation=0.05215
To calculate the lowest cost when the the z-score is -2, we have
[tex]-2=(x-5.45961)/0.05215[/tex]
To get the value of x then we collect like terms
-0.1043 = =(x-5.45961)
x=-0.1043 + 5.45961
[tex]X=5.35531[/tex]
therefore, the lowest score is 5.35531
Let us calculate the highest score when the z-score is 2 ,
then highest score will be:
[tex]2=(x-5.45961)/0.05215[/tex]
To get the value of x then we collect like terms
0.1043 = =(x-5.45961)
x=0.1043 + 5.45961
[tex]X=5.45961[/tex]
therefore the highest score is x=5.45961
What term should be inserted in
p²-
___+36 to make it a perfect
Square
Answer:
12p
Step-by-step explanation:
the perfect square is form
(p - 6)² = p² - 12p + 36
Answer:
12p
Step-by-step explanation:
p² - ? + 36 = p² - ? + (-6)² = p² -2*6*p + (-6)² = p² - 12p + 36 = (p-6)²
A Realtor claims that no more than half of the homes he sells are sold for less than the asking price. When reviewing a random sample of 14 sales over the past year, he found that actually 10 were sold below the asking price.
Required:
a. The assumption of normality is justified.
b. Calculate a p-value for the observed sample outcome, using the normal distribution.
c. At the 0.05 level of significance in a right-tailed test, is the proportion of homes sold for less than the asking price greater than 50%?
According to market research, a business has a 75% chance of making money in the first 3 years. According to lab testing, of a certain kind of experimental light bulb will work after 3 years. According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7. 1. Write the scenarios in order of likelihood from least to greatest after three years: the business makes money, the light bulb still works, and the car needs major repairs.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Here are some scenarios:
According to market research, a business has a 75% chance of making money in the first 3 years.
According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.
According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.
1. Write the scenarios in order of likelihood from least to greatest after three years: the business makes money, the light bulb still works, and the car needs major repairs.
Answer:
The correct order in terms of likelihood from least to greatest would be
P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83
Car needs major repairs -> Business makes money -> Light bulb still works
Step-by-step explanation:
We are given probabilities of three different events.
According to market research, a business has a 75% chance of making money in the first 3 years.
P(Business) = 75% = 0.75
According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.
P(Light bulb) = 5/6 = 0.83
According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.
P(Car repair) = 0.70
We are asked to write these scenarios in order of likelihood from least to greatest after three years.
Which means that the events with least probability is less likely to occur.
The least probability is of car repair, then business and then light bulb.
So the correct order in terms of likelihood from least to greatest would be
P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83
Car needs major repairs -> Business makes money -> Light bulb still works
A particular extension cord can support up to 8 amps. Mo has an iron whose label states 1,200 watts and wonders if the iron can be plugged into the extension cord. If watts are converted to amps by dividing by 120, how many amps does the iron use?
Answer:
10 AStep-by-step explanation:
Given data
Current in cord is I = 8 a m p
Power of iron is P = 1200 W
Voltage converted is
V = 120 V
The power can be expressed as
[tex]P=IV=\\I=\frac{P}{V}[/tex]
Substitute the given value in above we get,
I = [tex]\frac{1200}{120}= 10amps[/tex]
Thus, the current use by iron is
10 A
Can someone please please help me
Answer:
The answer is None
Step-by-step explanation:
Multiply 6 2 and 1 and also multiply 12 4 and 2 separately now divide 96 with 12 and you get 8 which is none of the answer choices
One third of the sum of 15
and thrice a certain number is
equal to twice the number. Find
the number
Answer:
x=-1/39
Step-by-step explanation:
A science club has 16 members. How many ways can a president, a Vice President, and a treasurer be selected from the members?
Answer:
3,360
Step-by-step explanation:
We calculate the number of permutations for this problem where the order in which we accommodate people matters to us as follows:
[tex]P=\frac{n!}{(n-r)!}[/tex]
where n is the total number of options we have; the total number of members: [tex]n=16[/tex]
and r is the number of places or positions we are considering which in this case are the President position, the Vice president position and the treasurer position ⇒ 3 positions in total ⇒ [tex]r=3[/tex]
substituting n and r in the formula:
[tex]P=\frac{16!}{(16-3)!} \\\\P=\frac{16!}{13!} \\\\P=3,360[/tex]
A president, a Vice President, and a treasurer can be selected from the members in 3,360 ways
A company determines that monthly sales S(t), in thousands of dollars, after t months of marketing a product is given by S(t)equals2 t cubed minus 45 t squared plus 180 t plus 130. a) Find Upper S prime(1), Upper S prime(2), and Upper S prime(4). b) Find Upper S double prime(1), Upper S double prime(2), and Upper S double prime(4). c) Interpret the meaning of your answers to parts (a) and (b).
Answer: a) S'(1) = 136; S'(2) = 104; S'(4) = 76;
b) S''(1) = -38; S''(2) = -26; S''(4) = -2
Step-by-step explanation:
a) S' means first derivative;
[tex]\frac{d}{dt}[/tex](6t³ - 45t² +180t +130) = 6t² - 50t + 180
S'(1) = 6.1² - 50.1 + 180
S'(1) = 136
S'(2) = 6.2² - 50.2 + 180
S'(2) = 104
S'(4) = 6.4² - 50.4 + 180
S'(4) = 76
b) S'' is the second derivative of S:
[tex]\frac{d^2}{dt^2}[/tex](6t² - 50t + 180) = 12t - 50
S''(1) = 12.1 - 50
S''(1) = -38
S''(2) = 12.2 - 50
S"(2) = -26
S"(4) = 12.6 - 50
S"(4) = -2
c) Derivative is the rate of change of a function. The first derivative is the slope of the tangent line to the graph if the function in a determined point, while the second derivative measures how the rate of change is changing.
Analysing the values, we can conclude that the sales of the product after t months is decreasing at a rate of 12.
If someone have all the proofs of this I’ve been trying since yesterday PLEASE
Answer:
Please see steps below
Step-by-step explanation:
Notice the following:
(a) Angles 5 and 1 are alternate angles between parallel lines, and then they must be congruent (equal in measure) [tex]\angle 1 \,=\,\angle 5[/tex]
(b) Angles 6 and 3 are also alternate angles between parallel lines, so they must be congruent (equal measure) [tex]\angle 3 \,=\,\angle 6[/tex]
Therefore, instead of expressing the addition:
[tex]\angle 5\,\,+\,\,\angle 2\,\,+\,\,\angle 6[/tex]
we can write:
[tex]\angle 1\,\,+\,\,\angle 2\,\,+\,\,\angle 3[/tex]
which in fact clearly add to [tex]180^o[/tex]
Solve the equation then write how many solutions there is in this problem: 8x-3+14=24x+5
Answer:
x = 0.375
Step-by-step explanation:
Step 1: Simplify both sides of the equation
8x − 3 + 14 = 24x + 5
(8x) + (−3 + 14) = 24x + 5
8x + 11 = 24x + 5
- 24
-16x + 11 = 5
-11
-16x = -6
-16x/-16 = -6/-16
x = 3/8
x = 0.375
Harasti was inspired to build his hotels after he saw seahorses living in old fishing traps. What is the volume of a fishing trap that is 2 feet wide, 5 feet long, and 3 feet tall?
HELP ME DO THIS !!!!
Answer:
volume of rectangular prism = 30 ft³
Step-by-step explanation:
The fishing trap he wants to build to house sea houses are mostly rectangular prism. The traps are mostly glass like. The volume of the fishing trap will be the volume of the rectangular prism.
volume of rectangular prism = LWH
where
L = length
W = width
H = height
volume of rectangular prism = LWH
Length = 5 ft
width = 2 ft
Height = 3 ft
volume of rectangular prism = 5 × 2 × 3
volume of rectangular prism = 10 × 3
volume of rectangular prism = 30 ft³
g Using a calculator, find the actual error in measuring volume if the radius was really 6.5 cm instead of 6 cm, and find the actual error if the radius was actually 5.5 cm instead of 6 cm. Compare these errors to the answer you got using differentials
Answer:
The answer is "[tex]58.625 cm^3[/tex]"
Step-by-step explanation:
Consider the cube volume of x =6 cm.
Substitute x = 6 cm in the volume
[tex]V= x^3\\\\ V = (6)^3\\\\ V = 216[/tex]
Therefore, whenever the cube volume
[tex]x=6 \ cm \ is \ V= 216 \ cm^3[/tex]
Then consider the cube's volume
x = 6.5 cm.
Substitute x = 6.5 cm in the volume
[tex]V_1 = x^3\\V_1 = (6.5)^3\\V_1 = 274.625 \\[/tex] by using the calculator.
Therefore, when another cube volume
[tex]x = 6.5 cm \\\\ V_1 = 274.625 cm^3.[/tex]
The real volume error x = 6.5 cm instead of x = 6 cm is calculated as,
[tex]dV= V_1-V\\[/tex]
[tex]=274.625-216\\=58.625\\[/tex]
Hence, the actual error in the volume when x = 6.5 cm instead of x = 6 cm is [tex]58.625 \ cm^3.[/tex]
In a class of 20 students 11 people have a brother 9 people have a sister 6 people have neither fill in the Venn diagram
Answer:
Draw a Venn diagram with the left circle labeled brother, and the right labeled sister. Label the middle both and fhe outisde neither. Put 5 in brother, 3 in sister, 6 in both and 6 in neithrr.
Step-by-step explanation:
11+9 = 20
20-6 = 14
20-14=6
There are 6 that have both
Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
Answer:
-3 =n
Step-by-step explanation:
11(n – 1) + 35 = 3n
Distribute
11n -11 +35 = 3n
Combine like terms
11n +24 = 3n
Subtract 11n from each side
11n +24 -11n = 3n -11n
24 = -8n
Divide each side by -8
24/-8 = -8n/-8
-3 =n
Answer: n=-3
Step-by-step explanation:
11n-11+35=3n
24=-8n
n=-3
You are choosing between two different window washing companies. The first charges $5 per window. The second charges a base fee of $40 plus $3 per window
Answer:
you forgot the rest of the question homie but once there is 20 companies both companies will be equal
Step-by-step explanation:
Answer:
20 windows
Step-by-step explanation:
How many solutions does the system have? y = -2x-4 \\\\ y = 3x+3
Answer:
The system has one solution.
Step-by-step explanation:
We have two equations:
y = -2x - 4
y = 3x + 3
Equalling them:
y = y
-2x - 4 = 3x + 3
5x = -7
[tex]x = -\frac{7}{5}[/tex]
And
[tex]y = 3x + 3 = 3(-\frac{7}{5}) + 3 = \frac{-21}{5} + 3 = \frac{-21}{5} + \frac{15}{5} = -\frac{6}{5}[/tex]
Replacing in the other equation we should get the same result.
[tex]y = -2x - 4 = -2(-\frac{7}{5}) - 4 = \frac{14}[5} - 4 = \frac{14}{4} - \frac{20}{5} = -\frac{6}{5}[/tex]
So the system has one solution.