Answer:
D :)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Braily please
Given the following diagram, are and opposite rays? yes no
Answer:
Where is the diagram?
Step-by-step explanation:
Answer:
OC and OE are apposite rays so the Answer is yes
At the beginning of the season,jamie pays full price for a ticket to see the panthers,her favorite baseball team.
Corrected Question
At the beginning of the season, Jamie pays full price($49.64) for a ticket to see the panthers, her favorite baseball team. Ticket prices decrease $0.41 for every game the panthers lose this season. the panthers currently have 33 wins and 31 losses.
(a)Represent the total change in the cost of a ticket given their losses.
(b) What is the cost of a ticket for the next game they play?
Answer:
(a)$(49.64-0.41x)
(b)$36.93
Step-by-step explanation:
(a)Cost of a Full Ticket =$49.64
Let x be the number of losses
The ticket price reduces by $0.41 for every loss
Therefore:
Ticket Price after x losses =$(49.64-0.41x)
Therefore, total change in the cost of a ticket given their losses=$(49.64-0.41x)
(b)For this season the Panthers has suffered 31 losses.
Number of Losses, x=31
Therefore, cost of a ticket for the next game they play
= $(49.64-0.41*31)
=49.64-12.71
=$36.93
If 5=3+2,then 3+2=5. What is the truth value
Answer:
true
Step-by-step explanation:
Solve for x
A) 36
B) 54
C) 72
D) 84
Ayo help a girl out
Answer:
72°
Step-by-step explanation:
This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°
Answer:
A
Step-by-step explanation:
Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)
The total angle of triange is 180°
So 180-72-72=36°
A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute. Plan A: $ 40 fee plus $0.45 per minute Plan B: $70 fee plus $0.35 per minute a) Write an equation to represent the cost of Plan A b) Write an equation to represent the cost of Plan B c) Which plan would be least expensive for a total of 100 minutes?
*Please Show Work*
Answer:
Plan A would be the least expensive
Step-by-step explanation:
Plan A= $0.45x100= 45, 45+40=$85
Plan B= $0.35x100= 35, 35+70= %105
(Each plan is for 100 minutes)
(please answer as soon as possible)If two lines intersect at a point, then vertically opposite angles are always: a)Complememtary b)Supplementary c)Unequal d)Equal
Answer:
D
Step-by-step explanation:
This is the veritcal angles theorem
Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as the probability of an arrival in any other one-minute period. Answer the following questions, assuming a mean arrival rate of three customers per minute.
Required:
a. What is the probability of exactly three arrivals in one-minute period?
b. What is the probability of at least three arrivals in a one-minute period?
Answer:
a)0.2240
b)0.5768
Step-by-step explanation:
Given:
µ=3
Poison probability is given by :
[tex]f_k=\frac{\mu^ke^-^\mu}{k!}[/tex]
a) Evaluating at k=3
[tex]f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240[/tex]
b)Evaluating at k=0,1,2:
[tex]f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498[/tex]
[tex]f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494[/tex]
[tex]f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240[/tex]
Use complement rule:
P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket , to the nearest 100th of a foot. y=-16x^2+230x+112
Answer:
The maximum height reached by the rocket is of 938.56 feet.
Step-by-step explanation:
The height y, after x seconds, is given by a equation in the following format:
[tex]y(x) = ax^{2} + bx + c[/tex]
If a is negative, the maximum height is:
[tex]y(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
In this question:
[tex]y(x) = -16x^{2} + 230x + 112[/tex]
So
[tex]a = -16, b = 230, c = 112[/tex]
Then
[tex]x_{v} = -\frac{230}{2*(-16)} = 7.1875[/tex]
[tex]y(7.1835) = -16*(7.1835)^{2} + 230*7.1835 + 112 = 938.56[/tex]
The maximum height reached by the rocket is of 938.56 feet.
Use the quadratic formula to find both solutions to the quadratic equation given below. 2x^2+3x-5=0
Answer:
[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where a = 2 , b= 3, c= -5, replacing we have this:
[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]
And simplifying we got:
[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]
And the two solutions are:
[tex] x_1 = \frac{-3+7}{4}= 1[/tex]
[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]
And the correct options are:
B and C
Step-by-step explanation:
We have the following equation given:
[tex] 2x^2 +3x -5=0[/tex]
And if we use the quadratic formula given by:
[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where a = 2 , b= 3, c= -5, replacing we have this:
[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]
And simplifying we got:
[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]
And the two solutions are:
[tex] x_1 = \frac{-3+7}{4}= 1[/tex]
[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]
And the correct options are:
B and C
Answer:
B and C
Step-by-step explanation:
Any help would be great
Answer:
30%
Step-by-step explanation:
fat ÷ total
15 ÷ 50
.3
30%
Answer:
30%
Step-by-step explanation:
To find the percent from fat, take the calories from fat and divide by the total
15/50
.3
Multiply by 100%
30%
I WILL GIVE BRAINLIEST ANSWER ASAP
Answer: B
Step-by-step explanation:
For this problem, to solve for x, you want to move all like terms to one side.
[tex]\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8} +\frac{1}{8}[/tex]
Now that you have moved like terms to one side, you can directly add and subtract to combine like terms.
[tex]-\frac{1}{4} x=1[/tex]
x=-4
Answer:
[tex]x = - 4[/tex]
Second answer is correct
Step-by-step explanation:
[tex] \frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x \\ \frac{1}{4} x - \frac{1}{2} x = \frac{1}{8} + \frac{7}{8} \\ \frac{1x - 2x}{4} = \frac{8}{8} \\ - \frac{1}{4} x = 1 \\ - 1x = 1 \times 4 \\ - 1x = 4 \\ x = - 4[/tex]
hope this helps you
The graph of Ax), shown below, resembles the graph of G(X) = x, but it has
been stretched and shifted. Which of the following could be the equation of
Fx)?
Answer:
sorry'but I don't know the answer
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [Start 2 By 3 Matrix 1st Row 1st Column 1 2nd Column 4 3rd Column negative 2 2nd Row 1st Column 3 2nd Column h 3rd Column negative 6 EndMatrix ]
Answer:
Step-by-step explanation:
Consider the augments matrix (the right most column is the extra vector).
[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]
By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix
[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]
Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.
If a function f(x) is defined as 3x2 + x + 2, what is the value of Lim h-0 f(x+h)-f(x)/h? A. 3x + 1 B. 3x + 2 C. 6x + 1 D. 6x + 2
Answer:
[tex] f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2[/tex]
[tex]f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2[/tex]
And replacing we got:
[tex] lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}[/tex]
And if we simplfy we got:
[tex] lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h [/tex]
And replacing we got:
[tex]lim_{h \to 0} 6x + 1 +3h = 6x+1[/tex]
And the bet option would be:
C. 6x + 1
Step-by-step explanation:
We have the following function given:
[tex] f(x) = 3x^2 +x+2[/tex]
And we want to find this limit:
[tex] lim_{h \to 0} \frac{f(x+h) -f(x)}{h}[/tex]
We can begin finding:
[tex] f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2[/tex]
[tex]f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2[/tex]
And replacing we got:
[tex] lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}[/tex]
And if we simplfy we got:
[tex] lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h [/tex]
And replacing we got:
[tex]lim_{h \to 0} 6x + 1 +3h = 6x+1[/tex]
And the bet option would be:
C. 6x + 1
Answer:
6x+1
Step-by-step explanation:
Plato :)
Scientists think that robots will play a crucial role in factories in the next several decades. Suppose that in an experiment to determine whether the use of robots to weave computer cables is feasible, a robot was used to assemble 507 cables. The cables were examined and there were 9 defectives. If human assemblers have a defect rate of 0.035 (3.5%), does this data support the hypothesis that the proportion of defectives is lower for robots than humans
Answer:
The data support the hypothesis that the proportion of defectives is lower for robots than humans.
Step-by-step explanation:
To know if the proportion of defectives is lower for robots than humans so as to prove if the hypothesis is true.
From the data given:
Total number of cables a robot assembled = 507
Defectives = 9
To get the defect rate = the number of defects divided by the total number of cables, multiplied by 100.
Defect rate = (9 / 507) x 100 = 0.01775 x 100
Defect rate for the robot = 1.775%
From the question, a robot was used and the defect rate after the calculation is 1.775%. While for humans, the defect rate is 3.5%. This implies, if humans were used to assembling the same 507 cables, there will be 17.745 defectives.
x / 507 = 3.5%
x (defectives) = 17.745
Therefore, the data support the hypothesis that the proportion of defectives is lower for robots than humans.
5 inches is blank times big as 1 inch
Answer:
5 inches is 5 times as big as 1 inch
At the beginning of year 1, Paolo invests $500 at an annual compound
interest rate of 4%. He makes no deposits to or withdrawals from the
account.
Which explicit formula can be used to find the account's balance at the
beginning of year 5? What is the balance?
Answer:
see below
Step-by-step explanation:
The way the problem is worded, we expect "n" to represent the year number we're at the beginning of. That is the initial balance is that when n=1, and the balance at the beginning of year 5 (after interest accrues for 4 years) is the value of obtained when n=5.
After compounding interest for 4 years, the balance will be ...
500·1.04^4 = 584.93
The matching answer choice is shown below.
Answer:
b
Step-by-step explanation:
Alguien me puede ayudar con esto por favor!!!!
Answer:
8 + 15i
Step-by-step explanation:
(-2 + 3i) + 2(5 + 6i) =
= -2 + 3i + 10 + 12i
= 8 + 15i
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor
Answer:
= 0.0041
Step-by-step explanation:
Given that:
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away
mean number of flights to be 57
a standard deviation of 12
fewer flights on average in the next 40 rows
[tex]\mu = 57\\\\\sigma=12\\\\n=40[/tex]
so,
[tex]P(x<52)[/tex]
[tex]=P(\frac{x-\mu}{\sigma/\sqrt{n} } <\frac{52-57}{12/\sqrt{40} } )\\\\=P(z<\frac{-5\times6.325}{12} )\\\\=P(z<\frac{-31.625}{12})\\\\=P(z<-2.64)[/tex]
using z table
= 0.0041
The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor is 0.0041 and this can be determined by using the properties of probability.
Given :
The distribution of grasshoppers may not be normally distributed in his field due to growing conditions.The mean number of flights to be 57 with a standard deviation of 12.The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor, can be determined by using the following calculations:
[tex]\rm P(x<52)=P\left (\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}<\dfrac{52-57}{\dfrac{12}{\sqrt{40} }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-5\times 6.325}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-31.625}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<-2.64\right)[/tex]
Now, using z-table:
P(x < 52) = 0.0041
For more information, refer to the link given below:
https://brainly.com/question/21586810
Here It Is !!
More Otw
Answer:
3
Step-by-step explanation:
0 pairs mean when two "boxes" add together to make 0. For the x's we only have one because x + (-x) = x - x = 0. For the other ones we have two (the + means 1 and the - means -1) because 1 + (-1) = 1 - 1 = 0. Therefore the answer is 1 + 2 = 3.
Donte simplified the expression below. 4(1+3i) - (8-5i)
4 + 3i - 8 + 5i
-4 + 8i
What mistake did donte make?
Answer:
Donde didn't multiply 4(1+3i)
Answer: it’s A he did not apply distributive property yo
Step-by-step explanation:
What is the equation of the line that passes through (4, 2) ) and is parallel to 3x - 2y = - 6 ?
Answer:
[tex]y=\frac{3}{2} x-4[/tex]
Step-by-step explanation:
The graph I provided shows it passes thru (4,2) and that it is parallel
Answer:
y = 3/2x -4
Step-by-step explanation:
3x - 2y = - 6
First find the slope by putting it in slope intercept form
Subtract 3x from each side
-2y = -3x-6
Divide by -2
y = -3x/-2 -6/-2
y = 3/2x +3
The slope is 3/2
Parallel lines have the same slope
We have the slope 3/2 and a point (4,2)
y = mx+b where m is the slope and b is the y intercept
y =3/2x+b
Substitute the point into the equation
2 = 3/2(4) +b
2 = 6 +b
Subtract 6
2-6 = 6-6+b
-4 =b
y = 3/2x -4
List the four possible results of the combinations of decisions and true states of nature for a test of hypothesis. Which of the following lists the four possible results of the combinations of decisions and true states of nature for a test of hypothesis? A. Reject Upper H 0H0 when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true; reject Upper H 0H0 when Upper H Subscript aHa is true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true B. Reject Upper H 0H0 when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true; reject Upper H Subscript aHa when Upper H Subscript aHa is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true C. Reject Upper H 0H0 when Upper H Subscript aHa is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true; reject Upper H Subscript aHa when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true D. Reject Upper H 0H0 when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true; reject Upper H 0H0 when Upper H Subscript aHa is true; accept Upper H Subscript aHa when Upper H 0H0 is true
Answer:
A
Step-by-step explanation:
The combinations of decisions and true states of nature for a test of hypothesis is given below:
When [tex]H_o[/tex] is True, Accept [tex]H_o[/tex]When [tex]H_o[/tex] is True, Reject [tex]H_o[/tex] (Type I Error)When [tex]H_o[/tex] is False, Accept [tex]H_o[/tex] (Type II Error)When [tex]H_o[/tex] is False, Reject [tex]H_o[/tex]Note that when [tex]H_o[/tex] is False, then the Alternate Hypothesis, [tex]H_a[/tex] is True.
Therefore Option A gives the possible combinations.
The possible choices in Option A are ordered below to correspond to the results above.
Insufficient evidence to reject [tex]H_o[/tex] when [tex]H_o[/tex] is true; Reject [tex]H_o[/tex] when [tex]H_o[/tex] is true; Type 1 Error Insufficient evidence to reject [tex]H_o[/tex] when [tex]H_a[/tex] is true -Type II Error Reject [tex]H_o[/tex] when [tex]H_a[/tex] is true;Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Answer:
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Step-by-step explanation:
Complete Question
According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
Solution
The Central limit theorem allows us to say
The mean of sampling distribution is approximately equal to the population mean.
μₓ = μ = 1.20 kg
And the standard deviation of the sampling distribution is given as
σₓ = (σ/√N)
σ = population standard deviation = 0.14 kg
N = sample size = 3
σₓ = (0.14/√3) = 0.08083
Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.
P(1.10 ≤ x ≤ 1.30)
We first normalize or standardize 1.10 and 1.30
The standardized score for any value is the value minus the mean then divided by the standard deviation.
For 1.10 kg
z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24
For 1.30 kg
z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24
To determine the required probability
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
We'll use data from the normal distribution table for these probabilities
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)
= P(z ≤ 1.24) - P(z ≤ -1.24)
= 0.89251 - 0.10749
= 0.78502 = 78.502%
The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.
Hope this Helps!!!
which quadrilateral will always have four reflection symmetry
Step-by-step explanation:
a rectangle has reflectional symmetry when reflected over the line through the midpoints of its opposite sides
Answer: A square always has a four reflection symmetry no matter the size.
Please help will mark brainliest.
Answer:
parallel lines both have slope 1/3; non-parallel lines both have length 5
Step-by-step explanation:
It generally works well to follow instructions.
A graph of the points shows you that the parallel sides are RA and PT. The difference between the end points of these segments are ...
A - R = (6, 8) -(-3, 5) = (9, 3) = (Δx, Δy)
So, the slope of RA is Δy/Δx = 3/9 = 1/3
And the other difference and slope are ...
P -T = (9, 4) -(-3, 0) = (12, 4) ⇒ Δy/Δx = 4/12 = 1/3
The slope of RA is the same as the slope of PT, so those segments are parallel.
__
The length of segment TR can be found from the differences of the end point coordinates:
R - T = (-3, 5) -(-3, 0) = (0, 5)
Since these points are on the same vertical line, this tells us the segment length is 5.
The other difference of coordinates is ...
A - P = (6, 8) -(9, 4) = (-3, 4)
The distance formula tells us the length of AP is then ...
AP = √((-3)² +4²) = √25 = 5
Non-parallel sides TR and AP have the same lengths, so the trapezoid is isosceles.
The sum of three numbers is 10. Two times the second number minus the first number is equal to 12. The first number minus the second number plus twice the third number equals 7. Find the numbers. Listed in order from smallest to largest, the numbers are , , and .
Answer:
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
Step-by-step explanation:
Step(i):-
Given sum of the three numbers is 10
Let x , y , z be the three numbers is 10
x +y + z = 10 ...(i)
Given two times the second number minus the first number is equal to 12
2 × y - x = 12 ...(ii)
Given the first number minus the second number plus twice the third number equals 7
x + y + 2 z = 7 ...(iii)
Step(ii):-
Solving (i) and (iii) equations
x + y + z = 10 ...(i)
x + y + 2 z = 7 .. (iii)
- - - -
0 0 -z = 3
Now we know that z = -3 ...(a)
from (ii) equation
2 × y - x = 12 ...(ii)
x = 2 y -12 ...(b)
Step(iii):-
substitute equations (a) and (b) in equation (i)
x+y+z =10
2 y - 12 + y -3 =10
3 y -15 =10
3 y = 10 +15
3 y =25
[tex]y = \frac{25}{3}[/tex]
Substitute [tex]y = \frac{25}{3}[/tex] and z = -3 in equation(i) we will get
x+y+z =10
[tex]x + \frac{25}{3} -3 = 10[/tex]
[tex]x +\frac{25-9}{3} = 10[/tex]
[tex]x +\frac{16}{3} = 10[/tex]
[tex]x = 10 - \frac{16}{3}[/tex]
[tex]x = \frac{30 -16}{3} = \frac{14}{3}[/tex]
Final answer :-
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
Answer:
-2, 5, 7 on Edge.
Step-by-step explanation:
I got the Answer right.
When converting measurements in the metric system, you can move the decimal point to the left or to the right. Why? Select all that apply. A. When converting from smaller to larger units, you are dividing by a power of 10. B. Moving a decimal point is the same as adding or subtracting. C. The metric system is based on powers of 10. D. When converting from larger to smaller units, you are multiplying by a power of 10.
Answer:
This has multiple answers, A, C, And D
Step-by-step explanation:
Answer:
It is definitely A, C, and D.
Step-by-step explanation:
I just answered this question and got it right. I hope this helps and please mark brainliest!
please help you will get 10 points and brainliest. and explain your answer.
Answer:
Top prism = 262 in.² Bottom prism = 478 in.²
Step-by-step explanation:
top prism:
front + back: 5 x 3 = 15
sides: 19 x 4 x 2 = 152
bottom: 19 x 5 = 95
15 + 152 + 95 = 262
bottom prism:
front + back: 5 x 6 x 2 = 60
sides: 19 x 6 x 2 = 228
top + bottom: 19 x 5 x 2 = 190
60 + 228 + 190 = 478
Write an integral for the area of the surface generated by revolving the curve y equals cosine (2 x )about the x-axis on negative StartFraction pi Over 5 EndFraction less than or equals x less than or equals StartFraction pi Over 5 EndFraction .
Answer:
The integral is
∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
x₁ = (-π/5)
x₂ = (π/5)
And the area of the surface generated by revolving = 9.71 square units
Step-by-step explanation:
When a function y = f(x) is revolved about the x-axis, the formula for the area of the surface generated is given by
A = 2π ∫ˣ²ₓ₁ f(x) √[1 + (f'(x))²] dx
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
For this question,
y = cos 2x
x₁ = (-π/5)
x₂ = (π/5)
y' = -2 sin 2x
1 + y'² = 1 + (-2 sin 2x)² = (1 + 4 sin² 2x)
So, the Area of the surface of revolution is
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
= ∫ˣ²ₓ₁ 2πy √[1 + y'²] dx
Substituting these variables
A = ∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
Let 2 sin 2x = t
4 cos 2x dx = dt
2 Cos 2x dx = (dt/2)
dx = (1/2cos 2x)(dt/2)
Since t = 2 sin 2x
when x = (-π/5), t = 2 sin (-2π/5) = -1.90
when x = (π/5), t = 2 sin (2π/5) = 1.90
A
= ∫¹•⁹⁰₋₁.₉₀ π (2 Cos 2x) √(1 + t²) (1/2cos 2x)(dt/2)
= ∫¹•⁹⁰₋₁.₉₀ (π/2) √(1 + t²) (dt)
= (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
But note that
∫ √(a² + x²) dx
= (x/2) √(a² + x²) + (a²/2) In |x + √(a² + x²)| + c
where c is the constant of integration
So,
∫ √(1 + t²) dt
= (t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)| + c
∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= [(t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)|]¹•⁹⁰₋₁.₉₀
= [(1.90/2) √(1 + 1.90²)+ 0.5In |1.90+√(1 + 1.90²)|] - [(-1.9/2) √(1 + -1.9²) + (1/2) In |-1.9 + √(1 + -1.9²)|]
= [(0.95×2.147) + 0.5 In |1.90 + 2.147|] - [(-0.95×2.147) + 0.5 In |-1.90 + 2.147|]
= [2.04 + 0.5 In 4.047] - [-2.04 + 0.5 In 0.247]
= [2.04 + 0.70] - [-2.04 - 1.4]
= 2.74 - [-3.44]
= 2.74 + 3.44
= 6.18
Area = (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= (π/2) × 6.18
= 9.71 square units.
Hope this Helps!!!
