Answer:
A. 2•5(7.5+7.5+7.0)
b. -55
Can you write an Orginal Oratory speech on benefits of solar energy
Throughout the solar system, solar energy is continuously emitted by the sun. The Earth is warmed by solar energy, which also affects the weather, the wind, and the survival of plant and animal life. Electromagnetic radiation, which is a kind of energy, heat, and light, is released from the sun (EMR).
What is solar system?Anything produced by the sun is considered to be solar energy.Nuclear fusion that occurs in the sun is the source of solar energy. Hydrogen atom protons clash ferociously in the sun's core, where they fuse to form helium atoms, which is the process of fusion.An large quantity of energy is released during this process, which is sometimes referred to as a PP (proton-proton) chain reaction. Around 620 million metric tons of hydrogen are fused by the sun every second in its core. Other stars, similar in size to our sun, also experience the PP chain reaction, which supplies them with ongoing heat and energy. These stars have an average Kelvin temperature of 4 million degrees (about 4 million degrees Celsius, 7 million degrees Fahrenheit).The CNO cycle is responsible for energy production in stars that are around 1.3 times larger than the sun. Carbon, nitrogen, and oxygen (C, N, and O) are required for the CNO cycle to convert hydrogen to helium. As of right now, the CNO cycle produces less than 2% of solar energy.To Learn more About solar system, refer To:
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pls help quick!!! ill give brainliest:)
Answer:
The first one is $0.12
The second one is $0.14
Step-by-step explanation:
Have a blessed day and remember to keep smiling! :)
Hope this helps! :)
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
Answer:
The first box is $0.12 Second box is $0.14
Step-by-step explanation:
1.20 ÷ 10 = .12
1.12 ÷ 8 = .14
Please solve this using Microsoft Excel and show its formula in
each cells
Let m = 2
2. Solve the integration below m TT (2 + m cos x) dx using Trapezoidal Method with a. n=10 b. n=15 c. n=40 Also, calculate the %error for each value of n. 5pts 5pts 5pts
The Trapezoidal Method was used to approximate the integral, and the calculated values for n=10, n=15, and n=40 were obtained along with their respective percentage errors.
To solve the given integration using the Trapezoidal Method in Microsoft Excel, we can set up a table with the necessary formulas to perform the calculations. Here's how you can set it up:
Create a new Excel spreadsheet.
In cell A1, enter the heading "x" to represent the values of x.
In cell B1, enter the heading "f(x)" to represent the function values at each x.
In cell C1, enter the heading "h" to represent the step size.
In cell D1, enter the heading "Trapezoidal Rule" to represent the calculated values using the Trapezoidal Method.
In cell E1, enter the heading "%Error" to represent the percentage error.
In cells A2 to A12 (for n = 10), enter the equally spaced values of x from 0 to π. If you're calculating for n = 15 or n = 40, adjust the range accordingly.
In cell B2, enter the formula "=2+$M$1*COS(A2)" to calculate the function values (replace $M$1 with the value of m).
In cell C2, enter the formula "=(PI()/($M$2-1))" to calculate the step size (replace $M$2 with the value of n).
In cell D2, enter the formula "=0.5*(B2+B3)*C2" to calculate the Trapezoidal Rule for the first interval (replace B3 with the cell reference for the next function value).
Copy the formula from cell D2 and paste it down to cells D3 to D11 (or the corresponding range for n = 15 or n = 40) to calculate the Trapezoidal Rule for the remaining intervals.
In cell D12, enter the formula "=SUM(D2:D11)" to calculate the final result of the integration using the Trapezoidal Method.
In cell E2, enter the formula "=ABS((D12 - $M$3)/$M$3*100)" to calculate the percentage error (replace $M$3 with the actual value of the integral you're comparing against).
Copy the formula from cell E2 and paste it down to cells E3 to E12 (or the corresponding range for n = 15 or n = 40) to calculate the percentage error for each value of n.
You can now input the values of m, n, and the actual integral into cells M1, M2, and M3, respectively. Excel will automatically update the calculations based on these values.
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which expression is equivalent to the given expression after using the distributive property? 9 + 5 + 7x² + 3x²y + 2x²
Answer:
9 and 5 I guess enjoy.
.
Step-by-step explanation:
and yeah no explanation
81x^6-(y+1)^2 what are the U and V
The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.
In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.
To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:
\(81x^6 - (y + 1)^2\)
Replacing U and V:
\(81(3x^3)^2 - (V)^2\)
Simplifying:
\(81 \times 9x^6 - V^2\)
\(729x^6 - V^2\)
Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)
In this way, we can represent the original expression in a simplified form using the assigned values for U and V.
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Consider the expression: \(81x^6 - (y + 1)^2\)
If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?
In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.
Graphical For the following exercises, graph the inequality. 20.x2 + 2y > 7 21.y2 – 2x2 > -3and x2 + y2 <9 Extensions For the following exercises, graph the inequality. 22.y 2 ()* 23. y < 302.X + 1 Real-World Applications For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions. 24. Two numbers add up to 144. One number is half the square of the other number. What are the numbers? 25. The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number. What are the numbers?
The graph of the inequality y^2 > 0 represents all real numbers except y = 0.
The graph of the inequality y < 30 represents all real numbers less than 30.
The inequality y^2 > 0 represents all values of y where y squared is greater than 0. Since the square of any nonzero number is always positive, the solution is all real numbers except y = 0, which can be graphed as a number line with an open circle at y = 0.
The inequality y < 30 represents all values of y that are less than 30. This can be graphed as a horizontal line on the y-axis with an open circle at y = 30, indicating that 30 is not included in the solution set.
For the real-world applications, let's solve them step-by-step:
Two numbers add up to 144. One number is half the square of the other number.
Let's assume the two numbers are x and y. We have the following system of equations:
x + y = 144 (Equation 1)
x = (1/2)y^2 (Equation 2)
From Equation 1, we can solve for x in terms of y: x = 144 - y.
Substituting this into Equation 2, we get 144 - y = (1/2)y^2.
Rearranging the equation, we have: (1/2)y^2 + y - 144 = 0.
Now we can solve this quadratic equation for y. Once we find the value(s) of y, we can substitute them back into Equation 1 to find the corresponding values of x.
The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number.
Let's assume the two numbers are x and y. We have the following system of equations:
x^2 + y^2 = 1156 (Equation 1)
y = √(3x^2) (Equation 2)
Substituting Equation 2 into Equation 1, we get: x^2 + (√(3x^2))^2 = 1156.
Simplifying, we have x^2 + 3x^2 = 1156.
Combining like terms, we get 4x^2 = 1156.
Now we can solve this quadratic equation for x. Once we find the value(s) of x, we can substitute them back into Equation 2 to find the corresponding values of y.
Remember to leave a 1 line space between paragraphs in your answer.
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Updated/Repost.
Given: 3x + 2y + 7 = 5x +3y +10
Prove: m = -2
(Hint: slope)
Answer:
3x + 2y = -2
Reason: This is because 3x + 2y = 10 for the variable y. 3x-10= 2y.
Since
_____________________________________________________
3x + 7 = -2
Reason: This is because 3x+10= 2y
_____________________________________________________
how do we know a given number in the radical is whether rational or irrational
number is described as rational if it can be written as a fraction (one integer divided by another integer). A number is irrational if it cannot be written as a fraction. The decimal form of an irrational number does not terminate or recur.
Harriet is cultivating a strain of bacteria in a petri dish, she has 10^3 bacteria in the dish. The bacteria divided every two hours such that the number of bacteria has doubled by the end of every second hour. How many bacteria will Harriet have in the dish at the end of 6 hours?
Answer:
4000
Step-by-step explanation:
A=P(2)^(t/d)
A=future amount
P=starting amount
t=time elapsed
h=doubling time
given
P=10^3
t=6
d=2
A=10^3(2)^(6/2)
A=10^3(2)^2
A=10^3(4)
A=4*10^3
A=4000
4000 bacteria
#2) Salim bought 32 feet of window trim at a hardware store. The trim cost $1.75 per foot. Salim used a 20\% coupon to purchase the window trim. A sales tax of 9.5% was applied to the total purchase. How much does Salim end up paying for the window trim?
Answer: $49.056
Step-by-step explanation:
Salim bought 32 feet of window trim at a hardware store and the trim cost $1.75 per foot. The total cost will then be:
= 32 × $1.75
= $56
She used a 20% coupon to purchase the window trim. The amount she will pay will be:
= $56 - (20% × $56)
= $56 - (0.2 × $56)
= $56 - $11.2
= $44.8
A sales tax of 9.5% was then applied to the total purchase. The amount Salim will end up paying will be:
= $44.8 + (9.5% × $44.8)
= $44.8 + (0.095 × $44.8)
= $44.8 + $4.256
= $49.056
PLEEEEEEASE HELP A square rug covers 80 square feet of floor. What is the approximate length of one side of the rug? (Approximate to the nearest hundredth foot.)
O 8.91 feet
O 8.92 feet
O 8.93 feet
O 8.94 feet
Answer:
c
Step-by-step explanation:
i had the same q and got it right
a number y is 15 larger than a positive number x. if their sum is not more than 85, what are the possible values of y?
Answer:
y = x + 15 –(1)
x + y = 85
Putting (1)'s value,
x + x + 15 = 85
2x + 15 = 85
2x = 85 - 15 = 70
x = 70/2 = 35
\(\)
The value of y is 50.
Two simultaneous equations can be formed from the given question:
y - x = 15 equation 1
y + x = 85 equation 2
In order to determine the value of x, subtract equation 1 from 2
2x = 70
Dvidie both sides of the equation by 2
x = 70 / 2
x = 35
Substitute for x in equation 1
y - 35 = 15
y = 35 + 15
y = 50
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Complete the following problems. It is over everything we've done the last few days. Take your time.
Make sure you insert your equation when having to write equations.
Question 3
5 pts
In 2015, 2200 students attended Polaris High School. The enrollment has been
declining 2% annually. If this trend continues, estimate how many students will be
enrolled in 2030.(Remember it is people that you have.)
Answer:
Welcome to Gboard clipboard, any text you copy will be saved here.
SOMEONE PLS HELP ME ASAPPP: The odometer of a vehicle tells you how far it has traveled in its lifetime. The "trip odometer" can be reset at any time to tell you the length of a particular trip. Suppose the main odometer of a new car is at 467 miles and the trip odometer is at 22 miles. How many more miles do you have to travle before the main odometer is precisely two times the trip odometer?
Answer:
423 milesStep-by-step explanation:
x - the miles to travel
467+x - the main odometer after x miles travel
22+x - the trip odometer after x miles travel
2(22+x) - two times the trip odometer after x miles travel
2(22+x) = 467 + x
44 + 2x = 467 + x
- 44 -44
2x = 423 + x
-x -x
x = 423
Answer:
how far you've driven
Step-by-step explanation:
Simplify the Expression
2(x +14) - (2x - 5)
your answer would be 33.
step 1
2(+14)−1(2−5)
2+28−1(2−5)
step 2 distribute
2+28−1(2−5)
2+28−2+5
step 3 then add the numbers
2+28−2+5
2+33−2
combine
2+33−2
ANSWER IS
33
the point where the ppf intersects the vertical axis is?
The point where the PPF intersects the vertical axis is unattainable and efficient.
Using fixed resources, a distinct combination of two items can be created, as shown by the production possibility curve or frontier. The bundles of goods that are productively efficient and attainable are displayed at each point on the production potential curve.
The bundles that are feasible but productively efficient are represented by the points below the curve. The bundles that are unachievable because they demand additional resources are represented by the points above the production possibility curve. The PPF's intersection with the vertical axis is a productive, efficient, and reachable position.
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The school that Kathryn goes to is selling tickets to a
play. On the first day of ticket sales the school sold 4
adult tickets and 1 student ticket for a total of $58
dollars. The school took in $82 on the second day by
selling 6 adult tickets and 1 student ticket. Find the
price of an adult ticket and the price of a student
ticket.
Answer:
Both 6
Step-by-step explanation:
Hi there, Adult tickets = 'x' Child's ticket = 'y' 8x + 2y = 60......(1) 2x + 3y = 30......(2) Multiply (1) by 3 and (2) by 2 24x + 6y = 180....(1) 4x + 6y = 60......(2) Subtract (2) from (1) 20x = 120 x = 6 Substitute x = 6 into (2) 2x + 3y = 30 2(6) + 3y = 30 12 + 3y = 30 3y = 30 - 12 3y = 18 y = 6 Adult's ticket = $6 Child's ticket = $6 Hope this helps :-)
Does anybody know the answer to this I just need to finish the homework assignment to work on other stuff lol
Answer: C
Step-by-step explanation:
Construct concrete non-empty relations R, S and T on X = {1, 2}, as well as a non-empty relation U on Y-1, 2, 31, such that the following properties are satisfied. (1) A relation R on X such that R is symmetric and is antisymmetric (2) A relation S on X such that S is symmetric and is not antisymmetric. (3) A relation T on X such that T is not symmetric and is antisymmetric (4) A relation U on Y such that U is not symmetric and is not antisymmetric.
This relation is not Symmetric because (3,1) is not in U, and it is not antisymmetric because both (1,2) and (2,1) are in U.
(1) Relation R on X that is symmetric and antisymmetric:
R = {(1,1), (2,2)}
This relation is symmetric because (1,1) and (2,2) are both in R, and antisymmetric because there are no distinct pairs (a,b) and (b,a) in R.
(2) Relation S on X that is symmetric but not antisymmetric:
S = {(1,2), (2,1), (1,1), (2,2)}
This relation is symmetric because for any pair (a,b) in S, (b,a) is also in S. However, it is not antisymmetric because both (1,2) and (2,1) are in S.
(3) Relation T on X that is not symmetric but antisymmetric:
T = {(1,2)}
This relation is not symmetric because (2,1) is not in T, but it is antisymmetric because there are no distinct pairs (a,b) and (b,a) in T.
(4) Relation U on Y that is neither symmetric nor antisymmetric:
U = {(1,2), (2,1), (1,3)}
This relation is not symmetric because (3,1) is not in U, and it is not antisymmetric because both (1,2) and (2,1) are in U.
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The measure of one angle of a triangle is 105°. What do you know about the measures of the other two angles? Check all
that apply.
O Both angles are acute.
O The sum of the measures of the two angles is 75°.
O The sum of the measures of the two angles is 155°.
OOne of the angles is a right angle.
O The measure of neither angle is more than 75°.
O The measures of the other angles must be 105° too.
D The measure of one of the other angles equals 75°.
O The measure of one of the other angles must be 45°.
Save and Exit
Submnit
Answer:
both angles are acute
Step-by-step explanation:
State the domain and the range.
1. f(x) = x² -1
2. f(x) = 1/ (3x+5)
3. f(x) = x4
4. f(x) = 1/2x
5. f(x) = (9x-7)/3
Step-by-step explanation:
remember, the domain is the interval or set of all valid x values, the range is the interval or set of all valid y values (functional result values).
1.
domain : -infinity < x < +infinity
range : -1 <= y < +infinity
due to the x² term that part can never be negative. the minimum is 0, and then -1 gives us a overall minimum -1. and then up ... the sky is the limit ...
2.
domain : every value of x that does not turn (3x + 5) to 0 and therefore does not cause a 1/0 situation.
the only forbidden value of x is therefore
3x + 5 = 0
3x = -5
x = -5/3
so, (-infinity < x < -5/3) OR (-5/3 < x < +infinity)
range : -infinity < y < +infinity
3.
domain : -infinity < x < +infinity
range : 0 <= y < +infinity
due to the x⁴ term (even exponent) all results will be positive starting with 0. similar to 1.
4.
this is 1/(2x) as I understand it.
similar to 2. we must avoid at 1/0 situation.
so, x must not be 0. everything else is possible
domain : (-infinity < x < 0) OR (0 < x < +infinity)
range : -infinity < y < +infinity
5.
everything is allowed and possible.
domain : -infinity < x < +infinity
range : -infinity < y < +infinity
Consider two digital fuel pumps A and B that could be used in a single gas station. Pump A has a mean effective process time of 4 minutes with squared-coefficient of variation of 0.5. Pump B has a mean effective time of 3 minute with squared-coefficient of variation of 5. Assume that the arrival rate of cars is 0.2 car per minute with squared-coefficient of variation of 1. Which pump will have a longer average cycle time? (Hint: the number of machines, m, is 1.)
Therefore, Pump B will have a longer average cycle time compared to Pump A.
To determine which pump will have a longer average cycle time, we need to calculate the cycle time for each pump based on the given information and compare the results. The cycle time for a single-server system can be calculated using Little's Law: Cycle Time = (1 / Arrival Rate) * (1 / (1 - Utilization))
Given:
Arrival Rate = 0.2 car per minute
Squared-Coefficient of Variation (CV^2) for Arrival Rate = 1
Utilization can be calculated as the product of the mean effective process time and the arrival rate:
Utilization = Mean Effective Process Time * Arrival Rate
For Pump A:
Mean Effective Process Time (A) = 4 minutes
Squared-Coefficient of Variation for Pump A = 0.5
Utilization (A) = 4 * 0.2 = 0.8
For Pump B:
Mean Effective Process Time (B) = 3 minutes
Squared-Coefficient of Variation for Pump B = 5
Utilization (B) = 3 * 0.2 = 0.6
Now, let's calculate the cycle time for each pump:
Cycle Time (A) = (1 / 0.2) * (1 / (1 - 0.8))
= 5 minutes
Cycle Time (B) = (1 / 0.2) * (1 / (1 - 0.6))
= 2.5 minutes
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For a standard normal random variable, what z-score has(a) probability 0.225 to the right?(b) probability 0.900 to the left?
The z-score with probability 0.225 to the right is 0.15 and the z-score with probability 0.900 to the left is -1.28. This can be calculated using the Z-score table for a standard normal distribution.
(a) Probability 0.225 to the right is equal to z-score 0.15.
This can be calculated using the Z-score table for a standard normal distribution.
The probability to the right of z-score is equal to the cumulative probability of the z-score.
The cumulative probability of 0.15 is 0.225, which is the probability to the right.
(b) Probability 0.900 to the left is equal to z-score -1.28.
This can be calculated using the Z-score table for a standard normal distribution.
The probability to the left of z-score is equal to the cumulative probability of the z-score.
The cumulative probability of -1.28 is 0.900, which is the probability to the left.
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If f ( x ) = 3x⁴ + x² + 5 - 3 cos x + 2 sin² x , Then Prove that f ( x ) + f ( -x ) = 2f ( x ).
Thanx!!!!
\( \: \: \)
\( \qquad \qquad\huge \sf༆ Answer ༄\)
Here's the solution ~
\(\qquad \sf \dashrightarrow \: f(x) = 3 {x}^{4} + x {}^{2} + 5 - 3 \: cos(x) + 2 \: \sin {}^{2} (x) \)
now, let's solve for f ( -x) :
\(\qquad \sf \dashrightarrow \: f( - x) = 3 {( - x)}^{4} +( - x {}^{2}) + 5 - 3 \: cos( - x) + 2 \: ( \sin {}^{} ( - x) ) {}^{2} \)
\(\qquad \sf \dashrightarrow \: f( - x) = 3 { x}^{4} + x {}^{2} + 5 - 3 \: cos( x) + 2 \: ( - \sin {}^{} ( x) ) {}^{2} \)
\(\qquad \sf \dashrightarrow \: f( - x) = 3 { x}^{4} + x {}^{2} + 5 - 3 \: cos( x) + 2 \: \sin {}^{} ( x) {}^{2} \)
Now, let's add both equations ~
\(\qquad \sf \dashrightarrow \: f(x) + f( - x) = 3 {x}^{4} + {x}^{2} + 5 - 3 \: cos(x) + 2 \: {}^{} sin {}^{2} (x) + 3 {x}^{4} +{x}^{2} + 5 - 3 \: \cos(x) + 2 \: \sin {}^{2} (x) \)
\(\qquad \sf \dashrightarrow \: f(x) + f( - x) = 2(3 {x}^{4} + x² + 5 - 3 \: \cos(x) + 2 \sin {}^{2} (x) )\)
\(\qquad \sf \dashrightarrow \: f(x) + f( - x) = 2(f(x) ) \)
The sum of the function and its reflection is twice the function
Functions and trigonometryGiven the function expressed as:
f(x) = 3x⁴ + x² + 5 - 3 cos x + 2 sin² x
Its reflection f(-x) is expressed as:
f(-x) = 3(-x)⁴ + (-x)² + 5 - 3 cos (-x) + 2 sin² (-x)
f(-x) = 3x⁴ + x² + 5 - 3 cos x + 2 (-sinx)²
f(-x) = 3x⁴ + x² + 5 - 3 cos x + 2 sin²x
Take the sum of f(x) and f(-x) to have:
f (x) + f (-x) = 3x⁴ + x² + 5 - 3 cos x + 2 sin² x + ( 3x⁴ + x² + 5 - 3 cos x + 2 sin²x )
f (x) + f (-x) = f(x ) + f(x)
f (x) + f (-x) = 2f(x) proved
Hence the sum of the function and its reflection is twice the function
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Find the solutions to the equation 102x 11 = (x 6)2 – 2. Which values are approximate solutions to the equation? Check all that apply.
The approximate solutions to the equation 102x 11 = (x 6)2 – 2 need to be checked.
To find the solutions to the equation, we need to solve for x. Rearranging the equation, we have 102x + 11 = (x - 6)^2 - 2. Expanding the right side, we get 102x + 11 = x^2 - 12x + 36 - 2. Simplifying further, we have 102x + 11 = x^2 - 12x + 34.
To determine the approximate solutions, we can graph the equation or use numerical methods such as the Newton-Raphson method or the bisection method. Unfortunately, without further information or access to a graphing tool or numerical method, it is not possible to provide the specific approximate solutions. Therefore, the values of the approximate solutions to the equation cannot be determined without additional calculations or tools
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Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = e4t cos 4t i + 3 j + e4t sin 4t k
The Reparametrized curve with respect to arc length is:
r(s) = (1/2) * sqrt(2) * e^(4t) cos(4t) i + 3 j + (1/2) * sqrt(2) * e^(4t) sin(4t) k
To reparametrize the curve with respect to arc length, we need to find the expression for the curve in terms of the arc length parameter s.
The arc length parameter s is given by the integral of the speed function |r'(t)| with respect to t:
s = ∫|r'(t)| dt
Let's calculate the speed function |r'(t)| first:
r(t) = e^(4t) cos(4t) i + 3 j + e^(4t) sin(4t) k
r'(t) = (4e^(4t) cos(4t) - 4e^(4t) sin(4t)) i + 0 j + (4e^(4t) sin(4t) + 4e^(4t) cos(4t)) k
|r'(t)| = sqrt((4e^(4t) cos(4t) - 4e^(4t) sin(4t))^2 + (4e^(4t) sin(4t) + 4e^(4t) cos(4t))^2)
= sqrt(16e^(8t) cos^2(4t) - 32e^(8t) cos(4t) sin(4t) + 16e^(8t) sin^2(4t) + 16e^(8t) sin^2(4t) + 32e^(8t) cos(4t) sin(4t) + 16e^(8t) cos^2(4t))
= sqrt(32e^(8t))
Now, we can express s in terms of t by integrating |r'(t)|:
s = ∫sqrt(32e^(8t)) dt
To find the integral, we can make a substitution u = 8t, du = 8 dt:
s = (1/8) ∫sqrt(32e^u) du
= (1/8) ∫2sqrt(2e^u) du
= (1/8) * 2 * sqrt(2) ∫e^(u/2) du
= (1/4) * sqrt(2) * ∫e^(u/2) du
= (1/4) * sqrt(2) * 2e^(u/2) + C
= (1/2) * sqrt(2) * e^(4t) + C
Therefore, the reparametrized curve with respect to arc length is:
r(s) = (1/2) * sqrt(2) * e^(4t) cos(4t) i + 3 j + (1/2) * sqrt(2) * e^(4t) sin(4t) k
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The curve reparametrized with respect to arc length is:
r(u) = e^(2u/√2) cos(2u/√2) i + 3j + e^(2u/√2) sin(2u/√2) k
We have the curve given by:
r(t) = e^(4t) cos(4t) i + 3j + e^(4t) sin(4t) k
The speed of the curve is:
|v(t)| = √( (dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 )
= √( 16e^(8t) + 16e^(8t) )
= 4e^(4t) √2
Thus, the arc length from t = 0 to t = s is:
s = ∫0s |v(t)| dt
= ∫0s 4e^(4t) √2 dt
= √2 e^(4t) |_0^s
= √2 ( e^(4s) - 1 )
Solving for s, we get:
s = (1/4) ln( (s/√2) + 1 )
Let u be the parameter with respect to arc length, then we have:
u = ∫0t |v(t)| dt
= ∫0t 4e^(4t) √2 dt
= √2 e^(4t) |_0^t
= √2 ( e^(4t) - 1 )
Solving for t, we get:
t = (1/4) ln( (u/√2) + 1 )
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How can we classify the following shapes ? Please choose correct answers that apply !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!
Answer:
A C and D
Step-by-step explanation:
Please give me thx
I am thinking of 3 consecutive numbers less than 100.The first number has 5 as one of its factors, the second number has 1 as its factors and the last number has 2 a one of its factors
Answer:
10, 11 and 12.
Step-by-step explanation:
A number has 5 as one of its factors, when last digit is 5 or 0. Only prime numbers have 1 as the only factor and a number has 2 as one of its factors when last digit is 2, 4, 6, 8 or 0.
Three possible consecutive numbers are 10, 11 and 12. 10 is the product of 2 and 5, 11 is a prime number and 12 is the product of 3 and 2². Therefore, possible choice is 10, 11 and 12.
Write as a fraction the probability of rolling a 3 on a six-sided die.
Answer:
1/6 is the probability of rolling a 3
line I is parallel to line m.if the maesure of angle 6 is 75 what is the measure of angle 3
Answer:
105
Step-by-step explanation:
l is parallel m so angle 3+angle 6=180