The minimum amount of glass used for the exterior 615340.84 m ²
How to find the minimum amount?We must calculate the lateral area which is given by:
A = (1/2) * pb * Ap
Where,
pb: perimeter of the base
Ap: Apotema
Calculating the apothem we have:
Ap = root ((646/2) ^ 2 + (350) ^ 2)
Ap = 476.27 feet
Calculating the perimeter of the base we have:
pb = 4 * (646)
pb = 2584 feet
Substituting values:
A = (1/2) * pb * Ap
A = (1/2) * (2584) * (476.27)
A = 615340.84 m ^ 2
The minimum amount of glass used for the exterior is:
A = 615340.84 m ²
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Correct question:
The luxor hotel in las vegas is a square base pyramid that is 646 feet wide at the base and 350 feet tall. if the outer walls of the hotel are covered in glass, what was the minimum amount of glass used for the exterior?
Simon, Sarah and Matthew are given a total of £300. They share it in the ratio 10:11:9. How much does each receive?
Based on given ratio of 10:11:9, the share for each person is as follows:
Simon = £100Sarah = £110Matthew = £90.What is ratio?Ratio is the relative size of one value or variable compared to another.
Ratios show how much each quantity is contained in another.
Ratios are fractional values obtained as the quotient of one value divided by another, and are depicted in fractions, decimals, or percentages.
The total shareable amount = £300
The sharing ratio = 10:11:9
The sum of ratios = 30
Simon's share = £100 (10/30 x £300)
Sarah's share = £110 (11/30 x £300)
Matthew's share = £90 99/30 x £300)
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Ethan and enoch hare a reward of $133 in a ratio of 2:5. How much doe each boy get?
So, Ethan gets $38 and Enoch gets $95.
We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.
Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.
So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.
Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.
And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.
So, to summarize:
Ethan gets $38
Enoch gets $95
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So, Ethan gets $38 and Enoch gets $95.
We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.
Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.
So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.
Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.
And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.
So, to summarize:
Ethan gets $38
Enoch gets $95
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You can solve the equation 3x + 2 = 8 by graphing y = 3x + 2 and y = 8 and finding their point of intersection.
Use the drop-down menus to complete the statements below.
The solution of 3x + 2 = 8 is
A. 2
B. 8
C. (2,8)
D. (8,2)
(2, 8) is a solution of
1. only y = 3x + 2
2. only y = 8
3. both y = 3x + 2 and y = 8
4. neither y = 3x + 2 nor y = 8
Answer:
A. and 3
Step-by-step explanation:
3x+2=8
3x=6
x=2
a. squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. the resulting piece of cardboard is then folded into a box without a lid. find the volume of the largest box that can be formed in this way.
The largest box that can be formed has a volume of 20 cubic feet.
Let's call the side length of the square cutout x. The original piece of cardboard measures 3 feet by 4 feet, so the dimensions of the piece of cardboard after the cutouts are made are (3 - 2x) by (4 - 2x).
When this piece is folded into a box, the length and width of the box will be (3 - 2x) and (4 - 2x) respectively. The height of the box will be x, as that is the height of the cutout squares.
The volume of the box can be found by multiplying the length, width, and height: V = (3 - 2x)(4 - 2x)x
We want to find the maximum volume, so we need to differentiate the expression for the volume and set it equal to zero, and then solve for x.
dV/dx = 2x(4 - 2x) - (3 - 2x)(2x) = 0
2x(4 - 2x) = (3 - 2x)(2x)
2x(4 - 2x) = 2x^2 - 6x^2
-4x^2 + 4x = 0
x(4 - x) = 0
x = 0 or x = 4
Since the side length of the cutout square cannot be negative, we reject x = 0 and keep x = 4. So, the maximum volume will occur when the side length of the cutout squares is 4 feet.
Substituting x = 4 into the expression for the volume, we find:
V = (3 - 2x)(4 - 2x)x = (3 - 2x)(4 - 2x) = (3 - 2x)(4 - 2x) = (3 - 8)(4 - 8) = -5 * -4 = 20 cubic feet
So, the largest box that can be formed has a volume of 20 cubic feet.
Therefore, The largest box that can be formed has a volume of 20 cubic feet.
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The largest box that can be formed has a volume of 20 cubic feet.
Let's call the side length of the square cutout x. The original piece of cardboard measures 3 feet by 4 feet, so the dimensions of the piece of cardboard after the cutouts are made are (3 - 2x) by (4 - 2x).
When this piece is folded into a box, the length and width of the box will be (3 - 2x) and (4 - 2x) respectively. The height of the box will be x, as that is the height of the cutout squares.
The volume of the box can be found by multiplying the length, width, and height: V = (3 - 2x)(4 - 2x)x
We want to find the maximum volume, so we need to differentiate the expression for the volume and set it equal to zero, and then solve for x.
dV/dx = 2x(4 - 2x) - (3 - 2x)(2x) = 0
2x(4 - 2x) = (3 - 2x)(2x)
2x(4 - 2x) = 2x² - 6x²
-4x² + 4x = 0
x(4 - x) = 0
x = 0 or x = 4
Since the side length of the cutout square cannot be negative, we reject x = 0 and keep x = 4. So, the maximum volume will occur when the side length of the cutout squares is 4 feet.
Substituting x = 4 into the expression for the volume, we find:
V = (3 - 2x)(4 - 2x)x = (3 - 2x)(4 - 2x) = (3 - 2x)(4 - 2x) = (3 - 8)(4 - 8) = -5 * -4 = 20 cubic feet
So, the largest box that can be formed has a volume of 20 cubic feet.
Therefore, The largest box that can be formed has a volume of 20 cubic feet.
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006 (part 1 of 2) 10. 0 points consider two conductors 1 and 2 made of the same ohmic material; i. E. , rho1 = rho2. Denote the length by ℓ, the cross sectional area by
a. The same voltage v is applied across the ends of both conductors and the field e is inside of the conductor. V1 ~e1 i1 ℓ1 r1 b v2 ~e2 i2 ℓ2 r2 b if a2 = 2 a1 , ℓ2 = 2 ℓ1 and v2 = v1 , find the ratio e2 e1 of the electric fields. 1. E2 e1 = 1 8 2. E2 e1 = 8 3. E2 e1 = 1 12 bancroft (acb3943) – hw03 – lai – (55310) 2 4. E2 e1 = 4 5. E2 e1 = 1 2 6. E2 e1 = 1 7. E2 e1 = 1 3 8. E2 e1 = 1 16 9. E2 e1 = 1 4 10. E2 e1 = 2
Ohm's Law states that the current passing through a conductor is proportional to the voltage across the conductor, and inversely proportional to the resistance of the conductor.
Mathematically, this can be expressed as:
V = IR,
where V is the voltage, I is the current, and R is the resistance of the conductor. The resistance of a conductor is given by:
R = ρℓ/a,
where ρ is the resistivity of the material, ℓ is the length of the conductor, and a is the cross-sectional area.
From Ohm's Law, we can also derive an expression for the electric field inside the conductor:
E = V/ℓ = IR/ℓ = ρI/a
In the case of conductors 1 and 2, the voltage across both conductors is the same (v2 = v1), so the electric field in conductor 2 can be expressed as:
E2 = V2/ℓ2 = v1/(2ℓ1) = ρI2/a2 = (ρ/2a1)I2
Similarly, the electric field in conductor 1 can be expressed as:
E1 = V1/ℓ1 = v1/ℓ1 = ρI1/a1 = (ρ/a1)I1
Finally, the ratio of the electric fields in conductors 1 and 2 can be calculated as:
E2/E1 = (ρ/2a1)I2 / (ρ/a1)I1 = a1/2a1 = 1/2
So, the ratio of the electric fields, E2/E1, is equal to 1/2. This means that the electric field in conductor 2 is half the electric field in conductor 1, despite the fact that the voltage across both conductors is the same. This happens because the cross-sectional area of conductor 2 is twice that of conductor 1, which compensates for the fact that the length of conductor 2 is also twice that of conductor 1.
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15 pt = _______ qt
240
15/16
7 1/2
30
Answer:
7.5qt is the correct answer
find the phase shift of the sin function
y = -2 sin (2x - π/pi)
The phase shift of the sin function , y = -2 sin (2x - π)-3 is =π/-3.
What is phase shift ?Amplitude: The amplitude of a wave is a maximum displacement of a particle from its rest position
Period: The ratio of wavelength to the velocity.
Phase shift: The phase shift represents the amount a wave has shifted horizontally from the the usual position.
here, we have,
The equation of a wave is
f(x) = a sin(bx - c)+d
Where
amplitude = |a|
phase shift = c/d
now,
Given equation of wave is
f(x) =-2 sin (2x - π)-3
Here a=-4, b=2, c = π, d = -3
i.e.
phase shift = c/d
=π/-3
Therefore, phase shift =π/-3.
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precalculus and i dont understand it much
The equation of the graph is (a) [tex]\frac{2x^2-8}{x^2+x-6}[/tex]
How to determine the equation of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph and the list of options
Next, we test the graph with the options
On the graph, we have:
f(0) = 1.3
f(-1) = -1
From the list of options, the equation that has the above properties is option (a)
Hence, the equation is (a)
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eric walks around a man-made circular lake (pictured above) four times. how far (in miles) has he walked?
The amount of total distance walked has walked by Eric in a man-made circular lake is 75.36 miles.
A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.
Circumference = D* π
Total distance walked four times = 4.C
= 4 * D * π
= 4 * 6 * 3.14
= 75.36 miles
So, the total distance is 75.36 miles.
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use the properties of logarithms to expand the following expression. logy7xz3
The expanded logarithmic expression is 7log y + log x + 3log z.
The use of a logarithm can be utilised to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Log interpretation is not that tough. It suffices to know that an exponential equation can also be written as a logarithmic equation in order to comprehend logarithms.
Exponent and logarithm are inverses of one another. This is explained in the section below. John Napier, a mathematician, first developed logarithms as a technique to perform computations simply, and other scientists, engineers, etc. immediately embraced this idea.
The given logarithmic equation is:
log ([tex]y^{7}xz^{3}[/tex])
Now, we can use the properties of logarithms to expand this fully.
log (abc) = log a + log b+ log cTherefore,
log ([tex]y^{7}xz^{3}[/tex]) = log ([tex]y^{7}[/tex]) + log (x) + log ([tex]z^{3}[/tex])
log (a²) = 2log aTherefore,
log (y⁷) = 7 log y
log (z³) = 3 log z
Therefore, the expanded logarithmic expression is 7log y + log x + 3log z.
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A primary credit cardholder has a current APR of 19.99%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent?
1.67%
0.17%
16.67%
19.99%
Anyone who needs the answer its 1.67%
19.99/12
The monthly Period interest rate is 1.67( nearest hundredth)
What is APR?Annual percentage rate (APR) refers to the yearly interest rate you'll pay if you carry a balance on your credit card. Some credit cards have variable APRs, meaning your rate can go up or down over time.
To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.
The APR of the card holder is 19.99%
Therefore the monthly Period interest will be calculated as ;
19.99/12
= 1.67% ( nearest hundredth)
therefore the monthly periodic interest is 1.67%
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The equation of Line D is y = 3/8x +3. The equation of the line E is y = 3/8x + 8/3, Are line D and Line E perpendicular,parallel or neither.
The given lines are parallel.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: The two equations given are y = 3/8x +3 & y = 3/8x + 8/3
We can observe that both the equations are in slope-intercept form we get
the slope of both the lines m=3/8
Two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.
Clearly the two given lines have the same slope and different y intercept
Hence, The two lines are parallel
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17) Suzanne arrange flower in vae at her retaurant. Each vae ha 12 flower, and 2/3 of the flower are yellow. What other fraction can repreent the part of the flower that are yellow?
4 over 6 because when you multiply 2 over 3 by 2 over two the answer is 4 over 6.
a group of eight kids lines up in random order. each ordering of the kids is equally likely. there are five girls and three boys in the group. what is the probability that all the boys are ahead of all the girls?
Using the arrangements formula, it is found that there is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.
The number of possible arrangements of the n elements is the factorial of n, that is:
[tex]A_{n} = n![/tex]
The total number of outcomes is the arrangement of 8 elements, hence:
T = 8! = 40320
The desired number of outcomes is all-girls(5!), then all-boys(3!), hence:
D = 5! × 3! =120× 6=720
Hence, the probability is:
p = D/T =720/40320 = 0.0178
There is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.
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The square shape wall whose length is 10m has a door of length 2m and breadth 1m. It also has a window of length 1m and breadth 0.5m. What will be the cost of painting the wall at Rs.5 per meter.
The cost of painting the wall is Rs.48.75 .
How to find the cost to paint the wall?The square shape wall whose length is 10m has a door of length 2m and breadth 1m. It also has a window of length 1m and breadth 0.5m.
Therefore, the cost of painting the wall can be calculated as follows:
cost of painting per meters = Rs0.5 per metre square
Therefore, the area of the wall to be painted will exclude the window and the door.
Hence,
area of wall of the wall to be painted = area of the wall - area of the window - area of the door
Therefore,
area of wall of the wall to be painted = 10² - (1 × 0.5) - (2 × 1)
area of wall of the wall to be painted = 100 - 0.5 - 2
area of wall of the wall to be painted = 97.5 metres²
Therefore,
1 metres square = Rs0.5
97.5 metres squared = ?
cross multiply
cost to paint the wall = 0.5 × 97.5
cost to paint the wall = Rs.48.75
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use the method of corners to find the point(s) that maximize the objective function p = 3x y
For the function P = 3x + y, there is no solution present to maximize it.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given objective function -
P = 3x + y
Subjected to the constraints -
5x + 7y ≥ 35
3x + 4y ≤ 12
x ≥ 0, y ≤ 0
First consider the inequality 5x + 7y ≥ 35.
The equation of the above inequality is as follows -
5x + 7y = 35
Find two points that satisfies the above equation.
Take x = 0, then -
5(0) + 7y = 35
7y = 35
y = 5
The first point is (0,5).
Take y = 0, then -
5x + 7(0) = 35
5x = 35
x = 7
The second point is (7,0).
Substitute (x,y) = (0,0) and see the direction of the region for 5x + 7y ≥ 35.
5(0) + 7(0) ≥ 35
0 ≥ 35
This is not true.
Therefore, the region is non-origin side.
Now consider the inequality 3x + 4y ≤ 12.
The equation of the above inequality is as follows -
3x + 4y = 12
Find two points that satisfies the above equation.
Take x = 0, then -
3(0) + 4y = 12
4y = 12
y = 3
The first point is (0,3).
Take y = 0, then -
3x + 4(0) = 12
3x = 12
x = 4
The second point is (4,0).
Substitute (x,y) = (0,0) and see the direction of the region for 3x + 4y ≤ 12.
3(0) + 4(0) ≤ 12
0 ≥ 12
This is true.
Therefore, the region is origin side.
Plot the graph.
From the graph it can be seen that there are no corner points and no feasible region.
Therefore, there is no solution for the function.
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If using the method of completing the square to solve the quadratic equation
x² - 19x39 = 0, which number would have to be added to "complete the
square"?
Answer:
below
Step-by-step explanation:
x^2 - 19x ± 39 take 1/2 of the 'x' coefficient square it and add and subtract it
x^2 - 19x + 90.25 - 90.25 ±39
(x-9.5)^2 - 90.25 ±39 so I guess the answer is 90.25
Lunch for the band cost $209.96 the band has 58 members. How much does each members lunch cost? Enter the correct answers to complete the statement Each luck cost:
Answer:
each member's lunch costs $3.62
Step-by-step explanation:
$209.96 is the total cost of all the members' lunches. To find the price of 1 lunch, divide 209.96 by 58. You will get 3.62.
g(x)= (x+10)^2 find the inverse function
The inverse of the function is given by x=√y-10
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here; g(x)= (x+10)²
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
Thus y=(x+10)²
√y=x+10
x=√y-10
Hence, The inverse of the function is given by x=√y-10
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Describe the relationship you would expect between the data. Explain.
1. age of the automobile and the odometer reading
The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.
What is the age of Automobiles:The age of automobiles indicates the lifetime of the Automobiles from their manufacturing day to the present workday. For example, if the car was made in 2010 and working till 2020 then the age of the car will be 10 years.
Odometer reading:Odometer is a machine or instrument which is used to calculate the distance traveled by a vehicle in its lifetime. The reading of the Odometer shows the distance covered by the car in the number of milages.
Here the more age of the automobile increases the more the distance covered by the automobile will increased hence the reading of the Odometer will increase.
As we know in mathematics, if two quantities are in relation such as one quantity is increased then the other quantity will also increase then two quantities are said to be in Direct proportion.
So here we can conclude that the age of the automobile and the odometer reading will be in direct proportion Since both are increases both variables will have a strong positive correlation.
Therefore,
The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.
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Help please, I was not in class when the lesson was happening and now I’m very confused.
Thank you :)
11. The measure of ∠EBF = 20°
12. The measure of ∠DBE = 32°.
13. The measure of ∠GBC = 56°.
What is the angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that m∠EBF = 60°, m∠EBG = 2m∠EBF
The m∠EBF is the sum of the angles and the angles are m∠EBG and m∠EBF.
Therefore,
m∠EBF = m∠EBG + m∠EBF
Putting m∠EBF = 60° and m∠EBG = 2m∠EBF in aboue equation:
60° = 2m∠EBF + m∠EBF
3m∠EBF = 60°
Divide both sides by 3:
∠EBF = 20°.
12.
Given that, m∠ABE = 64°.
From the diagram, m∠ABD = m∠DBE.
The m∠ABE is the sum of the angles and the angles are m∠ABD and m∠DBE.
m∠ABE = m∠ABD + m∠DBE
64° = 2m∠DBE
Divide both sides by 2:
m∠DBE = 32°
13.
Given that, m∠GBH = 28°.
From the diagram, m∠GBH = m∠HBC.
m∠HBC = 28°.
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what is the ordered pair for -5x + y = -10
Answer:
x = (2, 0), y = (0, -10)
casey and darnell went to the movies a total of 11 times last month. darnell went one less than twice as many times as casey did. how many times did each boy go to the movies last month?
Casey went too movie for 4 times and Darnell went to movie for 7 times.
Casey and Darnell went to the movies a total of 11 times last month, Darnell went one less than twice as many times as Casey did.
Let us say that Casey went to movie for X times,
So, the amount of times that Darnel went for movie is 2X-1
It is given that they went for a total of 11 times.
We can make a simple algebraic equation by using the above data.
X + 2X - 1 = 11
3X = 12
X = 4
So, Casey went to movie for 4 times and Darnell went to movie for 7 times.
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Jorimiah scored 85 points in a basketball game. That was 1/8 of the points that he scored for the season. How many points did jorimiah score in the season.
Jorimiah score 680 points in the season.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Jorimiah scored 85 points in a basketball game.
That was 1/8 of the points that he scored for the season.
let Jorimiah score x points
So, 1/8 of x= 85
x= 85(8)
x= 680 points.
Hence, he score 680 points.
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vgrehesssdddddddd dgthw
Answer: 7
Step-by-step explanation:
a = 11, b = 7 a = 11, b = 10 a = 28, b = 7 a = 28, b = 10
✓ a = 11, b = 7You just needed to multiply the terms together
Solve the inital value problem dy/dt= ey-t sec(y)(1+t2) y(0)=0. Solve the inital value problem.
The solution of the initial value problem is [tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex].
What is initial value problem?Initial value issues are a specific kind of calculus issue. Calculus initial value issues include differential equations with a known beginning condition that identifies the function's value at a certain point. Finding the function that best describes the system is the goal of these puzzles, and this can be accomplished by integrating the differential equation.
There is always an unknown constant present when doing an integration with an indeterminate integral or without initial conditions. The constant of integration is what is commonly indicated by the letter C.
Given that the initial value problem is:
dy/dt= e^(y-t) sec(y)(1+t2)
This can be re written as follows:
dy/ dt = e^(y-t) (1 + t^2) / sec (y)
Separate the derivative in terms of y and t and take integration:
[tex]\int{e^{-y}cos(y)} \, dy = \int {e^{-t}(1 + t^2)} \, dt[/tex]
Integrate the following:
[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + c\\[/tex]
The initial conditions given are y(0) = 0, substitute the value of the variables as 0:
[tex]\frac{e^{0}}{2} [sin0 - cos0] = -e^{0} [0^2 + 2(0) + 3] + c\\\\\\\frac{1}{2} [-1] = 3 + c[/tex]
c = 5/2
Hence, the solution of the initial value problem is:
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#SPJ4[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex]
the price of an item has been reduced by 15%. the original price was $91 find the price of the item now.
Answer:
77.35
Step-by-step explanation:
I'm sorry because I don't know how to explain it...
Shawn's Pizzeria made 5 pizzas with pepperoni and 18 pizzas without pepperoni. What is the ratio of the number of pizzas with pepperoni to the number of pizzas without pepperoni?
Answer: 5 : 18 = 10 : 36
Step-by-step explanation:
The ratio is already in lowest terms so we found an equivalent ratio by multiplying both terms by 2.
Answer:
5 to 18
Step-by-step explanation:
Ted says that the triangle below cannot be classified because all sides are different lengths. Is Ted correct? Explain why or why not.
Answer:
he is not because triangles can be different sides but they always have to equal 180 if it's a right triangle but if it does not it's a ln acute or obtuse triangle
solve the equation z2 z 1 = 0 for z = (x,y) by writing (x,y)(x,y) (x,y) (1,0) = (0,0)
The solutions of x = 0 or x = y and y = 0 or y = 1 can then be found. Therefore, the solutions of the equation are (0,0), (0,1), (1,0), and (1,1).
x2 - xy + y2 - x = 0
x(x - y) + y(y - 1) = 0
x(x - y) = 0 and y(y - 1) = 0
x = 0 or x = y and y = 0 or y = 1
Therefore, the solutions are (0,0), (0,1), (1,0), and (1,1).
The equation z2 z 1 = 0, when written as (x,y)(x,y) (x,y) (1,0) = (0,0), can be manipulated to x2 - xy + y2 - x = 0. By factoring out the x and y terms, the equation can be rearranged to x(x - y) + y(y - 1) = 0. This then can be further simplified to x(x - y) = 0 and y(y - 1) = 0. The solutions of x = 0 or x = y and y = 0 or y = 1 can then be found. Therefore, the solutions of the equation are (0,0), (0,1), (1,0), and (1,1).
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