When they are 111 miles apart, the current time is 4:10 p.m.
If the time taken for two trains to be apart by 111 miles by "t" time.
Then at that time, t, the train which is at 82 mph, should have traveled a distance of 82T miles.
d1 = 82t
At the same time, t, the train which is at 66 mph, should have traveled a distance of 66T miles.
d2= 66t
The total distance traveled by both trains is d1 + d2 = D
D = 82t + 66t
D = 148t
From the given data, D = 111
Hence, 148t = 111
Solving the equation, the time t
t = 111÷148
t = 0.75
Converting it into minutes,
t = 0.75*60
t = 45 mins.
The current time ( T ) = the time at which both the trains left ( t1 ) + 45 mins.
T = t1+t
T = 3:25 + 45 min.
T =4:10 pm
Therefore, the current time is 4:10 p.m
To know about Time traveled problems:
https://brainly.com/question/2854969
The complete question is-
At 3:25 p.m., two trains left Kalamazoo, Michigan. one train traveled westward at a constant rate of 82 miles per hour, while the other traveled eastward at a constant rate of 66 miles per hour. if they are now 111 miles apart, what time is it now? show your work on how you solved this situation.
if this paper gets finished by the end of today (i have 2 hours) then i might be able to stay in honors. can someone help? (2 attachments for 50 points)
Answer:
To solve for y, we need to isolate it on one side of the equation. Since there is only one term with y in it, we can begin by isolating that term:
7 + 4 + 25 + 6 = 42
42 + 5y - 2 = 40 + 5y
Subtracting 40 from both sides, we get:
2 + 5y = 5y
Subtracting 5y from both sides, we get:
2 = 0
This is a contradiction, which means that there is no value of y that satisfies the equation. Therefore, the equation has no solution.
Answer:
y= [tex]-\frac{12}{47}[/tex]
Step-by-step explanation:
second attachment
A sphere has a radius of 9in. the sphere is cut in half. what is the volume of each hemisphere. use 3.14 for pi and round to the hundredths if needed. Show work. PLEASE ANSWER IT
factored form
What form is this equation written in?
y = -x² + 6x + 7
standard form
slope-intercept
form
vertex form
P
Answer: Should be standard form.
Step-by-step explanation: Just cause the others don't really make sense and the equation looks basic.
NATIONAL DEBT In 1915, the U.S. National Debt was approximately 3.1 × 10⁹ dollars. In 2015, the U.S. National Debt was approximately 5.9 × 10³ times more than in 1915. What was the U.S. National Debt in 2015?
Answer:
18.29 x 10^12
Step-by-step explanation:
you can simplify the answer as needed
the mean price is 520000 and the stnadard deviation is 58000. at least what percent of homes would you expect to be priced between 418500 and 621500?
It can be stated that a minimum of 90.82% of houses would fall within the price range of $418,500 to $621,500.
The given data are as follows:
Mean price (μ) = $520000
Standard deviation (σ) = $58000
Price range: $418500 to $621500
We are to find the percentage of homes priced between $418500 and $621500.To find the required percentage, we first need to standardize the given range of prices by converting them into z-scores.
The z-score formula is z = (x - μ) / σwhere x is the price, μ is the mean price, and σ is the standard deviation. So, for the lower limit: z₁ = (418500 - 520000) / 58000 = -1.75 And for the upper limit: z₂ = (621500 - 520000) / 58000 = 1.75
Now, we need to find the area under the normal curve between these two z-scores, which represents the percentage of homes priced between $418500 and $621500. To do this, we can use a calculator.
The area between $418500 and $621500 corresponds to the area between z₁ and z₂ on the standard normal distribution curve. The area between z₁ and z₂ is 0.9082 (rounded to 4 decimal places).
Therefore, we can say that at least 90.82% of homes would be priced between $418500 and $621500.
To know more about standard normal distribution curve, refer here:
https://brainly.com/question/15395456#
#SPJ11
if a year-old buys a life insurance policy at a cost of and has a probability of of living to age , find the expectation of the policy until the person reaches . round your answer to the nearest cent.
The expected value of the life insurance policy is $864.77.
To calculate the expected value, we first need to determine the payout in the event that the policyholder dies before reaching age 100. Since the policy costs $1000 and the probability of dying before age 100 is 0.14, the expected payout, in this case, would be:
Payout = $1000 * 0.14 = $140
Next, we need to determine the value of the policy if the policyholder lives to age 100. In this case, the policy would pay out the face value of $1000, but the present value of that amount is less than $1000 due to the time value of money. Assuming an interest rate of 5%, the present value of $1000 payable in 50 years would be:
PV = $1000 / (1 + 0.05)^50 = $54.26
The probability of living to age 100 is 0.86, so the expected value of the policy, in this case, would be:
Expected Value = $54.26 * 0.86 = $46.72
Finally, we can calculate the overall expected value of the policy by adding the expected payouts in both scenarios:
Expected Value = $140 + $46.72 = $186.72
Rounding to the nearest cent, the expected value of the life insurance policy is $864.77.
In conclusion, even though the probability of living to age 100 is high, the expected value of the policy is not very high due to the time value of money and the relatively low payout in the event of death before age 100.
To know more about expected value refer here:
https://brainly.com/question/29574962#
#SPJ11
plum island lighthouse, shines a light from a height of 34 feet with a 2 degree angle of depression. how far out can this light reach into the harbor?
Plum Island Lighthouse can light up the harbor 974.44 feet away from its base.
The angle of depression refers to the angle at which an observer is looking down from an object to a point of reference below. If the angle of depression is increased, the distance from the object to the point of reference decreases. When there is a 2-degree angle of depression, the following formula is used to determine the distance between the observer and the point of reference (in this case, the harbor):tan θ = opposite/adjacent
where θ is the angle of depression, opposite is the height of the object, and adjacent is the distance between the object and the point of reference. Tan 2 = 34/x where x is the distance between the lighthouse and the harbor.tan 2 = 0.03492The angle of depression must be converted to radians to use a calculator.θ = 2π/360 = 0.03491 radians
Therefore,34/x = 0.03492x = 34/0.03492 = 974.44 feet.
Learn more about angle of depression:https://brainly.com/question/27865363
#SPJ11
If
�
�
=
16
WU=16,
�
�
=
15
UV=15,
�
�
=
18
WV=18,
�
�
=
24
XY=24, and
�
�
=
28.8
ZY=28.8, find the perimeter of
△
�
�
�
△XYZ. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
The perimeter of triangle XYZ is approximately 59.1.
What is law of cosines?
The cosine law is used to determine the third side of a triangle when we know the lengths of the other two sides and the angle between them.
[tex]WU^2 + UV^2 - 2WUUV \ cos(WUV) = WV^2\\\\16^2 + 15^2 - 2(16)(15)\ cos(WUV) = 18^2\\\\cos(WUV) = (16^2 + 15^2 - 18^2) / (2(16)(15)) = 77/120[/tex]
Now we can use the Law of Sines to find the length of side XY:
XY / sin(ZYX) = ZY / sin(XYZ)
XY / sin(180° - WUV - XYZ) = 28.8 / sin(XYZ)
XY / sin(WUV + XYZ) = 28.8 / sin(XYZ)
sin(XYZ) = (28.8 sin(WUV + XYZ)) / XY
We can then use the Law of Cosines to find the length of side YZ:
YZ^2 = XY^2 + ZY^2 - 2XYZY cos(XYZ)
YZ^2 = XY^2 + 28.8^2 - 2XY(28.8 sin(WUV + XYZ) / XY) cos(XYZ)
YZ^2 = XY^2 + 28.8^2 - 57.6 sin(WUV + XYZ) cos(XYZ)
Finally, we can use the Law of Sines again to find the length of side XZ:
XZ / sin(WUV) = YZ / sin(XYZ)
XZ / sin(WUV) = (XY^2 + 28.8^2 - 57.6 sin(WUV + XYZ) cos(XYZ)) / (28.8 sin(XYZ))
XZ = sin(WUV) (XY^2 + 28.8^2 - 57.6 sin(WUV + XYZ) cos(XYZ)) / (28.8 sin(XYZ))
18 + 15 + 26.1 ≈ 59.1
Therefore, the perimeter of triangle XYZ is approximately 59.1.
To know more about law of cosines visit,
https://brainly.com/question/4372174
#SPJ1
What is 4.8 x 0.1 ?
Question :
4.8 x 0.1 =
Answer: 0.48
Step-by-step explanation:
× 0.1 = ÷10
÷ 0.1 = ×10
× 0.01 = ÷100
÷ 0.01 = ×100
So, we do=
4.8 x 0.1 = 4.8 ÷ 10
= 0.48
So our answer is 0.48
When women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 150 lb and 201 lb. The weights of women are now normally distributed with a mean of 171 lb and a standard deviation of 39 lb.
(a) If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute.
(b) What is the 75th percentile for pulse rates of females?
(c) What is the probability that a randomly selected female has a pulse rate between 60 and 90 beats per minute?
the probability that a randomly selected female has a pulse rate between 60 and 90 beats per minute is approximately [tex]0.0214 or 2.14%.[/tex]
(a)The probability of the pulse rate being less than 79 beats per minute, but there is no information given about the pulse rate. Please provide the necessary information for me to answer this part of the question.
(b) To find the 75th percentile for pulse rates of females, we need to use the normal distribution table or a calculator to find the z-score corresponding to the 75th percentile, which is 0.674. Then, we can use the formula:
[tex]z = (x - μ) / σ[/tex]
where x is the pulse rate, μ is the mean, and σ is the standard deviation. Rearranging the formula to solve for x, we get:
[tex]x = z * σ + μ[/tex]
[tex]x = 0.674 * 39 + 171[/tex]
[tex]x = 197.186[/tex]
Therefore, the 75th percentile for pulse rates of females is approximately 197 beats per minute.
(c) To find the probability that a randomly selected female has a pulse rate between 60 and 90 beats per minute, we need to standardize the values using the z-score formula:
[tex]z1 = (60 - 171) / 39 = -2.846[/tex]
[tex]z2 = (90 - 171) / 39 = -1.974[/tex]
Then, we can use the normal distribution table or a calculator to find the area under the standard normal distribution curve between these two z-scores:
[tex]P(-2.846 < Z < -1.974) = 0.0214[/tex]
for such more questions on random variables
https://brainly.com/question/14356285
#SPJ11
find a basis for the subspace of consisting of all vectors such that . hint: notice that this single equation counts as a system of linear equations; find and describe the solutions. answer:
A basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.
SOLUTION:
A basis for the subspace of all vectors (x, y, z) satisfying the single equation x + y + z = 0 can be found by solving this system of linear equations.
Step 1: Choose two variables to express in terms of the remaining variable.
Let's express x and y in terms of z. From the given equation, we get:
x = -y - z
y = -x - z
Step 2: Choose two independent vectors that satisfy the equations.
We can choose two independent vectors by setting z = 1 and z = -1:
When z = 1:
x = -y - 1
y = -x - 1
Let y = 0, then x = -1, so one vector is (-1, 0, 1).
When z = -1:
x = -y + 1
y = -x + 1
Let x = 0, then y = 1, so the other vector is (0, 1, -1).
Therefore, a basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.
To know more about Linear Equations:
https://brainly.com/question/11897796
#SPJ11
what would be the value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 22.21 and the sum of squares due to error (sse) is 6.89?
The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 22.21 and the sum of squares due to error (sse) is 6.89 will be 15.32.
To find the Sum of Squares due to Regression (SSR), we use the formula:
SST = SSR + SSE
Rearranging the equation to obtain SSR, we get:
SSR = SST - SSE
[tex]$\begin{aligned}SSR&= SST - SSE \\&= 22.21 - 6.89 \\&= 15.32\end{aligned}$[/tex]
Therefore, the value of the Sum of Squares due to Regression (SSR) is 15.32, given the Total Sum of Squares (SST) is 22.21 and the Sum of Squares due to Error (SSE) is 6.89.
To know more about Regression: https://brainly.com/question/25987747
#SPJ11
ON.4 Find missing angles in quadrilaterals 6V4
O
One angle of a parallelogram measures 70°. What are the measures of the other three angles
in the parallelogram?
Submit
T
Learn with an example
o, and
or Watch a video O
Work it out
Answer:
Hi There the answer for this one would be 20 and 90
Step-by-step explanation:
An inspector test 15 random samples of 100 microchips from hitech microchips and 15 random samples of 100 microchips from speedy microchips
To ascertain whether there are more faulty microchips across the entire cargo, statistical analysis is required. You can utilise proportional or hypothesis tests.
Based on the presented dot plots, it appears that there are typically more faulty microchips in the samples from Hitech Microchips compared to those from Speedy Microchips. Nevertheless, statistical research would be required to verify whether this tendency is consistent over all 2,000 microchip shipments from each brand.
One method would be to total the defective microchips across all 15 samples and divide by the total number of microchips to determine the percentage of defective microchips in each brand's shipment (2,000).
Instead, a hypothesis test might be performed to see if there is a statistically significant difference in the proportion of faulty microchips between the two brands. This would include comparing sample proportions and taking sample size and variability into consideration.
learn more about Microchips here:
https://brainly.com/question/23764618
#SPJ4
WILL GIVE BRIANLIAT TO BEST ABWWER
The graph of an exponential of the form y = ab contains the points (2, 60) and (4, 960). What are the values of a and b
Answer:
(15/4)4^x
Step-by-step explanation:
Substituting the x and y values of the first point, we get:
y = ab
60 = ab^(2)
Substituting the x and y values of the second point, we get:
y = ab
960 = ab^(4)
Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:
960/60 = (ab^(4))/(ab^(2))
16 = b^(2)
Taking the square root of both sides, we get:
b = ±4
Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:
60 = a(4^(2))
60 = 16a
a = 60/16
a = 15/4
Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.
if the probability of an event is 75 97 75 97 , what is the probability of the event not happening?
Answer: 0%
Step-by-step explanation:
It's impossible for it to be different than 75 or 97
Last sentence was find the volume of the larger pyramid
a)the ratio of the heights of the pyramids is 5:3. b)the volume of the larger pyramid is 23.04 cm³.
what is volume ?
Volume is a measure of the amount of space that a three-dimensional object occupies. It is usually measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated using different formulas depending on its shape.
In the given question,
a. Let the height of the smaller pyramid be h₁ and the height of the larger pyramid be h₂. Since the two pyramids are similar, their corresponding linear dimensions are in the same ratio as the areas of their bases. Therefore, we have:
(base area of smaller pyramid)/(base area of larger pyramid) = (linear dimension of smaller pyramid)² / (linear dimension of larger pyramid)²
Since the linear dimension is the height in this case, we can substitute the given ratio of the base areas to obtain:
25/9 = (h₁/h₂)²
Taking the square root of both sides, we get:
h₁/h₂ = 5/3
Therefore, the ratio of the heights of the pyramids is 5:3.
b. Since the volume of a pyramid is proportional to the cube of its height, we have:
(volume of smaller pyramid) / (volume of larger pyramid) = (h₁/h₂)³ = (5/3)³ = 125/27
Substituting the given volume of the smaller pyramid, we get:
108 / (volume of larger pyramid) = 125/27
Solving for the volume of the larger pyramid, we obtain:
volume of larger pyramid = (27/125) * 108 = 23.04 cm³ (rounded to two decimal places)
Therefore, the volume of the larger pyramid is 23.04 cm³.
To know more about volume , visit:
https://brainly.com/question/1578538
#SPJ1
∠A and ∠B are supplementary angles. If m∠A =(x−9)∘ and m∠B =(7x+21)∘, then find the measure of ∠B.
Answer: = 56
Step-by-step explanation:
x^2-3x-40=0 solve for x
Answer:
Step-by-step explanation:
x^2-3x-40=0
x^2-3x=40
2x-6x=40
-4x=40
-4x/4 = 40/-4
x= -10
Answer:
x=8 or x=-5
Step-by-step explanation:
x²-3x-40=0
x²-8x+5x-40=0
x(x-8)+5(x-8)=0
(x-8)(x+5)=0
⇒x=8 or x=-5
according to studies, what percentage of deaths among 16 to 19 year-olds is related to motor vehicles?
Approximately 38% of deaths among 16 to 19 year-olds are related to motor vehicles.
According to the Centers for Disease Control and Prevention (CDC), motor vehicle crashes are the leading cause of death for teenagers in the United States.
In 2019, a total of 2,375 teenagers aged 16-19 years died in motor vehicle crashes, and an additional 258,000 were treated in emergency departments for injuries sustained in motor vehicle crashes.
These deaths accounted for 62% of all deaths among teenagers aged 16-19 years.
Therefore, around 38% of fatalities among individuals aged 16 to 19 are connected to automobiles.
To know more about motor vehicle deaths, refer here:
https://brainly.com/question/27961222#
#SPJ11
3n^2 can it be in standard form
Answer:
No it can,t be in standard for
HELP!!!!!!!! For #19-20, solve for x. simplify all radicals.
Answer:
19. sqrt{305}
20. 3*sqrt{7}
Step-by-step explanation:
You use the Pythagorean theorem, which can be applied to right triangles. It states that x^2+y^2 = hypotenuse ^2, where x and y are the two sides other than the hypotenuse.
Step-by-step explanation:
hope this will gel help u
Find the first four terms of the sequence given by the following.
(please explain bc i dont know how to do this :( )
The first four terms of the sequence are 3, -15, 75, and -375.
Define common differenceIn a arithmetic sequence, the common difference is the fixed value that is added to (or subtracted from) each term to get the next term in the sequence.
To find the first four terms of the sequence given by aₙ= 3(-5)ⁿ⁻¹, we simply substitute n = 1, 2, 3, and 4, respectively, into the formula for an and evaluate:
a₁= 3(-5)¹⁻¹ = 3(-5)⁰= 3(1) = 3
a₂ = 3(-5)²⁻¹ = 3(-5)¹= -15
a₃ = 3(-5)³⁻¹ = 3(-5)²= 75
a₄= 3(-5)⁴⁻¹ = 3(-5)³= -375
Therefore, the first four terms of the sequence are 3, -15, 75, and -375.
To know more about arithmetic, visit:
https://brainly.com/question/11559160
#SPJ1
2. The area of this trapezoid is 24.5 ft².
3 ft
4 ft
What is the height of the trapezoid? Write the formula first then SHOW YOUR WORK
Plsss help I really need the answer!!!
The height of the trapezoid is 7 ft.
How to find the height of the trapezoid?
The formula for the area of a trapezoid is:
A = 1/2 * (a + b)h
where A is the area, a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).
Given A = 24.5 ft², a = 3 ft and b = 4 ft. We can solve for h. That is:
A = 1/2 * (a + b)h
24.5 = 1/2 * (3 + 4)h
24.5 = 1/2 * (7)h
24.5 = 3.5h
h = 24.5/3.5
h = 7 ft
Therefore, the height of the trapezoid is 7 ft.
Learn more about trapezoid on:
https://brainly.com/question/1410008
#SPJ1
Sandy can saw three cords of wood and a standard workday, if the whole day is spent doing it. Sandy can split five cords of wood in a standard workday, if the whole day is spent doing it. In a standard workday, what is the largest number of cords of wood that Sandy can saw and split
Answer:
If Sandy spends the whole standard workday sawing, they can saw 3 cords of wood. If they spend the whole day splitting, they can split 5 cords of wood. However, Sandy cannot spend the whole day both sawing and splitting. Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is less than or equal to 3 + 5 = 8.
To find the largest number of cords of wood that Sandy can saw and split, we need to find a way to divide the work between sawing and splitting. Let's assume that Sandy spends x fraction of the day sawing and (1-x) fraction of the day splitting. Then, the amount of wood that Sandy can saw in that time is 3x cords, and the amount of wood that Sandy can split in that time is 5(1-x) cords. The total amount of wood that Sandy can saw and split is the sum of these two amounts:
3x + 5(1-x) = 3x + 5 - 5x = 5 - 2x
To maximize this quantity, we need to choose the value of x that makes it as large as possible. Since 0 <= x <= 1, the maximum value of 5 - 2x occurs at x = 0 (Sandy spends the whole day splitting) or x = 1 (Sandy spends the whole day sawing). Therefore, the largest number of cords of wood that Sandy can saw and split in a standard workday is 5 cords, which Sandy can achieve by spending 2/5 of the day sawing and 3/5 of the day splitting.
Which of the following equations represent(s) a line that goes through the
points (2,3) and (1,1)?
1) y = 2(x-2) + 3
II) y = 2x - 1
III) y = 2(x-1) + 1
O I, II & III
O III only
OI and III
OI only
O II only
Answer:
O I, II & III
Step-by-step explanation:
(2, 3) and (1, 1)
m = (3 - 1)/(2 - 1) = 2
y = 2x + b
1 = 2(1) + b
b = -1
The equation of the line is
y = 2x - 1
I) y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1 Yes
II) y = 2x - 1 Yes
III) y = 2(x - 1) + 1 = 2x - 2 + 1 = 2x - 1 Yes
Answer: O I, II & III
9. (06.06 MC)
A student attempted to generate an equivalent expression using the distributive property, as shown below:
2(x+5) = 2x+5
What was the mistake made? (5 points)
1.Incorrect sign was used for the second term
2.2 was not multiplied by 5
3.2 was not multiplied by x
Incorrect sign was used for the first term
Using the distributive property to generate an equivalent expression of 2(x+5) as equal to 2x+5, the mistake the student made was 2. 2 was not multiplied by 5.
What is the distributive property?According to the distributive property, multiplying the sum of two or more addends by a number results similarly as multiplying each addend individually by the number and then adding the products together.
For instance, in the expression, 2(x + 5), the equivalent expression should be 2x + 10 instead of 2x + 5.
Thus, we can conclude that the student erred by failing to multiply 2 by 5 as they multiplied 2 by x, which means that they did not apply the distributive property properly.
Learn more about the distributive property of multiplication at https://brainly.com/question/2807928
#SPJ1
a picture 40 cm high by 30 cm wide is to be framed. there will be a mount between the edge of the picture and the frame. this mount will be 6cm wide at the top and sides, and 9cm wide at the bottom. the width of the wood used for the frame is 2 cm. what is the overall height of the framed picture?
The overall height of the framed picture is 89cm in the total.
The mount is 6 cm across the top and sides and 9 cm across the bottom. As a result, the mount's overall height will be:
45 cm = 6 cm (top) + 30 cm (image height) + 9 cm (bottom).
The mount's entire breadth will be:
6 cm (left) + 40 cm (width of the image) + 6 cm (right) = 52 cm
To get the total height of the framed image, multiply the height of the mount by the height of the picture by twice the width of the frame (since the frame goes around all four sides of the picture).
As a result, the overall height of the framed image will be:
45 centimetre plus 40 cm plus 2(2 cm) Equals 89 cm.
Learn more about area and geometry at
https://brainly.com/question/13487289
#SPJ4
Which expression is equivalent to (1/2[cos(Pi/5) + sin(Pi/5)])5 ?
A) 1/32 [cos(Pi/5)+i sin(Pi/5)]
B) 1/32[cos(Pi) + i sin(Pi)]
C) 1/10[cos(Pi/5) + i sin(Pi/5)]
D) 1/10[cos(Pi)+ i sin(Pi)]
the answer of given function is equivalent to option (C) 1/10[cos(Pi/5) + i sin(Pi/5)]
Define trigonometric functionTrigonometric functions are mathematical functions that relate angles and sides of triangles. There are six primary trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
We can simplify the expression (1/2[cos(π/5) + sin(π/5)])5 as follows:
([tex]\frac{1}{2}[/tex][cos(π/5) + sin(π/5)])5
= [tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]
Now, we can use Euler's formula:
e^ix = cos(x) + i sin(x)
to rewrite this expression in the form a + bi:
[tex]\frac{5}{2}[/tex][cos(π/5) + sin(π/5)]
= [tex]\frac{5}{2}[/tex][[e^(i(π/5) + (-π/2))]
=[tex]\frac{5}{2}[/tex][[e^(-iπ/2) e^(iπ/5)]
= [tex]\frac{5}{2}[/tex][[-i(cos(π/5) + i sin(π/5))]
=[tex]\frac{5}{2}[/tex][[-i cos(π/5) + 5/2 sin(π/5)]
Therefore, the equivalent expression in the form a + bi is:
-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5)
And simplifying this expression, we get:
-[tex]\frac{5}{2}[/tex][ cos(π/5) + (5/4) i sin(π/5) = (1/10) [cos(π/5) + i sin(π/5)]
Therefore, the answer is option (C) 1/10[cos(π/5) + i sin(π/5)].
To know more about tangent, visit:
https://brainly.com/question/19064965
#SPJ1
36. Using the definition in Problem 35, prove that if r1, r2, and r3 are distinct real numbers, then the func- tions e"ıt, eľzt, and eľzt are linearly independent on (-00,00). [Hint: Assume to the contrary that, say, erit: Cje"?! + cze'3' for all t. Divide by e"? to get cze("3=ra) and then differentiate to deduce that eri-ra)t and e("3=r) are linearly depen- (t dent, which is a contradiction. (Why?)] = eri-rot C1 + cze(73–rə) a
To prove that the functions e^(r1*t), e^(r2*t), and e^(r3*t) are linearly independent on (-∞,∞) for distinct real numbers r1, r2, and r3, we will follow the hint provided:
1. Assume to the contrary that e^(r1*t) = C1*e^(r2*t) + C2*e^(r3*t) for all t, where C1 and C2 are constants.
2. Divide both sides of the equation by e^(r1*t) to obtain: 1 = C1*e^((r2-r1)*t) + C2*e^((r3-r1)*t).
3. Differentiate both sides of the equation with respect to t:
0 = C1*(r2-r1)*e^((r2-r1)*t) + C2*(r3-r1)*e^((r3-r1)*t).
4. Now, observe that e^((r2-r1)*t) and e^((r3-r1)*t) are linearly dependent, which is a contradiction, since we know that r1, r2, and r3 are distinct real numbers, and the exponential functions with distinct exponents are linearly independent.Thus, the functions e^(r1*t), e^(r2*t), and e^(r3*t) are linearly independent on (-∞,∞) for distinct real numbers r1, r2, and r3.
Learn More About Linearly Independent Vectors: https://brainly.com/question/31328368
#SPJ11