Answer:
y=3(x-2)^2-12
please let me know if its right.
A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters). It travels at 625 km/hour at a constant height of 7500 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60∘ north of east from Denver. Find parametric equations describing the plane's motion. Assume the origin is at sea level beneath Denver, that the x-axis points east and the y-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours.
The final parametric equations describing the plane's motion are:
x(t) = 0 + (425 km - 0) * t = 425t
y(t) = 0 + (736.6 km - 0) * t = 736.6t
z(t) = 1650 meters
where t varies from 0 to 1.36 hours.
Let's set up a coordinate system with the origin at sea level beneath Denver.
We'll use the x-axis to point east, the y-axis to point north, and the z-axis to point upward.
The plane starts directly above Denver at an altitude of 1650 meters.
We can represent this as the initial point P₀(0, 0, 1650).
The plane then flies to Bismark, which is about 850 km in the direction 60° north of east from Denver.
Let's represent the position of Bismark as the point P₁(x, y, z), where x and y are the horizontal displacements (east and north, respectively), and z is the altitude above sea level.
Since the plane flies at a constant height of 7500 meters above the line joining Denver and Bismark, the altitude z remains constant at 7500 meters.
Let's calculate the horizontal displacements x and y:
The eastward displacement x can be found using the cosine of the angle (60°) and the distance to Bismark (850 km):
x = 850 km * cos(60°) ≈ 425 km
The northward displacement y can be found using the sine of the angle (60°) and the distance to Bismark (850 km):
y = 850 km * sin(60°) ≈ 736.6 km
Now, we can write the parametric equations for the plane's motion:
x(t) = x₀ + (x₁ - x₀) * t
y(t) = y₀ + (y₁ - y₀) * t
z(t) = z
where:
x₀ = 0 (initial x-coordinate at Denver)
y₀ = 0 (initial y-coordinate at Denver)
z = 1650 meters (altitude above sea level at Denver)
x₁ = 425 km (x-coordinate at Bismark)
y₁ = 736.6 km (y-coordinate at Bismark)
The parameter t represents the time in hours.
The plane's motion is constant, so t will vary from 0 to the time it takes to travel from Denver to Bismark at a speed of 625 km/hour.
To find the time it takes, we can use the distance formula:
Distance = Speed * Time
850 km = 625 km/hour * Time
Time = 850 km / 625 km/hour ≈ 1.36 hours
A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters).
It travels at 625 km/hour at a constant height of 7500 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60∘ north of east from Denver.
Assume the origin is at sea level beneath Denver, that the x-axis points east and the y-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours.
So, the time it takes for the plane to travel from Denver to Bismark is approximately 1.36 hours.
The final parametric equations describing the plane's motion are:
x(t) = 0 + (425 km - 0) * t = 425t
y(t) = 0 + (736.6 km - 0) * t = 736.6t
z(t) = 1650 meters
where t varies from 0 to 1.36 hours.
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Write this as a power of 2. ex ( 2^n) requires knowledge of negative exponents
Answer:
22.627417Step-by-step explanation:
[tex] \frac{32}{ \sqrt[8]{16} } \\ [/tex]
Simplify
[tex] \frac{32}{1.414213562} \\ \\ = 22.627417[/tex]
Method 2 :
By rationalizing the denominator
3(8p-1)- 17p simplify please????????????
Answer:
7p - 3
Step-by-step explanation:
The length of the hypotenuse, line segment GH, in triangle GJH measures 6 cm. Line segment JH measures 2 cm. Which is the approximate measure of angle JGH? 18.4° 19.5° 70.5° 71.6°
Answer:
b. 19.5
Step-by-step explanation:
The approximate measure of angle JGH is 70.529°.
Analysis of a right triangle
According to this question, we have a right triangle in which lengths of its hypotenuse ([tex]GH[/tex]), in centimetres, and one leg ([tex]JH[/tex]) are known and we must determine the measure of an angle ([tex]m\angle JGH[/tex]), in degrees. A representation of this triangle is included in the image attached below.
By trigonometry we have the following expression for the required angle:
[tex]\cos m\angle GJH = \frac{HJ}{GH}[/tex] (1)
([tex]HJ = 2[/tex], [tex]GH = 6[/tex])
[tex]m \angle GJH = \cos ^{-1} \frac{2}{6}[/tex]
[tex]m \angle GJH \approx 70.529^{\circ}[/tex]
The approximate measure of angle JGH is 70.529°. [tex]\blacksquare[/tex]
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Augh please help quick
Answer:
it is 0.5
Step-by-step explanation:
Answer:
0.5
Step-by-step explanation:
quick maths
What is the remainder of the following division problem? x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
Answer:
1 is your remainder
Step-by-step explanation:
I just the test
Answer:
1
Step-by-step explanation:
i took the test :)
how to calculate the total distance from distance time graph
Answer:
Just calculate the area
fine the value of x.
x = 20
Step-by-step explanation:Hi there !
we have opposite angles =>
2 + 3x = 62
3x = 62 - 2
3x = 60
x = 60 : 3
x = 20
Good luck !
Write the equation of the scenario.
Tony's father is thinking of buying his son a six-month movie pass for $40. With the
pass, movies cost $3.00 each.
A y = 30+4x
B y = 40+ 3x
C y= 3 + 40x
D y=4 + 30x
IM IN A HURRY
One gram of sugar(S) contains 4 calories and one gram of fat(F) contains 9 calories. If one serving of a food contains 160 calories and has 7 grams of sugar , how many grams of fat are if this serving?
Round your answer to 1 decimal place.
Answer: 14.7 grams of fat.
Step-by-step explanation:
The data we have is:
1g of sugar contains 4 cal
1g of fat contains 9 cal.
Let's define:
S = # of grams of sugar.
F = # of grams of fat.
We know that:
A serving has 160 calories:
S*4cal + F*9cal = 160 cal.
S = 7.
Then we can replace the second equation into the first one, and get:
7*4cal + F*9cal = 160cal
F*9cal = 160cal - 28cal = 132 cal.
F = 132cal/9cal = 14.66...
Now we want to round it to the first decimal place, the next decimal after it is a 6, so we must round up.
F = 14.7
This means that the serving has 14.7 grams of fat.
"What are common multiples of 5 and 8" (common multiple, not least common multiple)
Answer:
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, etc.
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, etc.
Step-by-step explanation:
Common multiples are found as you multiply like how i got a common multiple of five and it was 20 we simply multiply 5 times 4 and get 20.
find all the points (x,6) that are 10 units from the point P (-17,-2)
Answer:
The points that are 10 units from P(-17,-2) are (-23,6) and (-11,6)
Step-by-step explanation:
Distance Between Points in the Plane
Given two points A(x,y) and B(w,z), the distance between them is:
[tex]d=\sqrt{(z-y)^2+(w-x)^2}[/tex]
It can be also expressed as:
[tex]d^2=(z-y)^2+(w-x)^2[/tex]
Substituting the values of both points, and knowing the distance is 10:
[tex]10^2=(6-(-2))^2+(x+17)^2[/tex]
[tex]100=8^2+(x+17)^2[/tex]
Swapping both sides:
[tex]64+(x+17)^2=100[/tex]
Moving the constants to the right side:
[tex](x+17)^2=100-64=36[/tex]
Taking the square root:
[tex]x+17=\pm 6[/tex]
We get two possible answers:
[tex]x=-17-6=-23[/tex]
[tex]x=-17+6=-11[/tex]
Thus the points that are 10 units from the point P(-17,-2) are (-23,6) and (-11,6)
Complete the tasks and answer the questions. Use the 2SD method to estimate the true proportion of the population of your city that dislikes the taste of cilantro. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation. Write the interpretation of this confidence interval. Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with a 95% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation. Write the interpretation of this confidence interval. Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with an 88% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation. Write the interpretation of this confidence interval. Your initial post should be made before the end of the fourth day (Saturday) of the module to receive full credit. Return at least once later in the module to comment on at least one classmate's posts. Do NOT "post and run" – making all of your posts on the same visit. You need multiple visits to the Discussions to gain multiple perspectives by reading all of the posts and replies.
Complete Question
The complete question is shown on the first uploaded image
Answer:
Using 2SD Method
The confidence interval is
The interval notation : [tex](0.108 , 0.212 )[/tex]
The interval notation and the sample proportion ± the margin of error
notation:[tex]0.16 \pm 0.052[/tex]
The interpretation
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper(0.212) and the lower(0.108) limit of the calculate confidence interval
Using theory-based method
The 95% confidence interval is
The interval notation : [tex](0.109 , 0.211 )[/tex]
The interval notation and the sample proportion ± the margin of error
notation:[tex]0.16 \pm 0.051[/tex]
The interpretation
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper(0.211) and the lower(0.109) limit of the calculate confidence interval
Using theory-based method
The 88% confidence interval is
The interval notation : [tex](0.120 , 0.200 )[/tex]
The interval notation and the sample proportion ± the margin of
error notation: [tex]0.16 \pm 0.040[/tex]
The interpretation is
There is 88% confidence that the true proportion of those that dislike cilantro lie within the upper(0.200 ) and the lower(0.120) limit of the calculate confidence interval.
Step-by-step explanation:
From the question we are told that
The number sample size is n = 200
The number of people that dislike cilantro is k = 32
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{N}[/tex]
=> [tex]\r p = \frac{32}{200}[/tex]
=> [tex]\r p = 0.16[/tex]
Generally 2SD confidence interval is mathematically represented as
[tex]\r p \pm 2\sqrt{\frac{\r p(1 - \r p)}{n} }[/tex]
substituting value
[tex]0.16 \pm 2\sqrt{\frac{0.16(1 - 0.16)}{200} }[/tex]
=> [tex]0.16 \pm 0.052[/tex]
This can also be represented as
[tex](0.16 - 0.052 , 0.06 + 0.052)[/tex]
=> [tex](0.108 , 0.212 )[/tex]
Generally this confidence interval can be interpreted as
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper and the lower limit of the calculate confidence interval
Using theory-based method estimate 95% confidence interval
Generally from the question the confidence level is 95% hence the level of significance is calculated as
[tex]\alpha = (100 - 95)\%[/tex]
=> [tex]\alpha = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the confidence level using theory base method is
[tex]0.16 \pm 1.96 \sqrt{\frac{0.16 (1- 0.16)}{200} }[/tex]
=> [tex]0.16 \pm 0.051[/tex]
This can also be represented as
[tex](0.16 - 0.051 , 0.06 + 0.051)[/tex]
=> [tex](0.109 , 0.211 )[/tex]
Generally this confidence interval can be interpreted as
There is 95% confidence that the true proportion of those that dislike cilantro lie within the upper(0.211) and the lower(0.109) limit of the calculate confidence interval
Using theory-based method estimate 88% confidence interval
Generally from the question the confidence level is 95% hence the level of significance is calculated as
[tex]\alpha = (100 - 88)\%[/tex]
=> [tex]\alpha = 0.12[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.12 }{2} } = 1.55[/tex]
Generally the confidence level using theory base method is
[tex]0.16 \pm 1.55 \sqrt{\frac{0.16 (1- 0.16)}{200} }[/tex]
=> [tex]0.16 \pm 0.040[/tex]
This can also be represented as
[tex](0.16 - 0.040 , 0.06 + 0.040)[/tex]
=> [tex](0.120 , 0.200 )[/tex]
Generally this confidence interval can be interpreted as
There is 88% confidence that the true proportion of those that dislike cilantro lie within the upper(0.200 ) and the lower(0.120) limit of the calculate confidence interval
How do you Simplify this expression5(x+1)-5x
Answer:
5
Step-by-step explanation:
Begin by removing the brackets.
5x + 5 - 5x
Notice that there are two 5xs. They are of opposite signs so they cancel
Answer 5
Answer:
5
Step-by-step explanation:
5(x+1) -5x
multiply the 5 into the ()
5x+5 -5x
add like terms
5x-5x=0
but their is still the leftover 5
Sorry if this is confusing.
Which equation has the same solution as 7x - 14 = 21?
Answer: 7 x 3 = 21
Step-by-step explanation:
The solution for the given equation is x=5.
The given equation is 7x - 14 = 21.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here,
7x - 14 = 21
⇒ 7x=35
⇒ x=35/7
⇒ x=5
Therefore, the solution for the given equation is x=5.
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- Maria's dog weighs 6 times as much as her rabbit. Together
the pets weigh 56 pounds. What does Maria's dog weigh?
Draw a model. Let n represent the unknown.
Write an equation to find the value of n.7×n=___.n is ___ pounds.
multiply to find how much Maria's dog weighs .8×6=___
So Maria's dog weighs ___ pounds.
plz tell the correct answers
Step-by-step explanation:
6n+n=56. (combine like terms)
7n = 56
÷7. ÷7. (divide both sides, isolate variable)
n. = 8 (rabbit weight)
56-8. =48 (dog weight) or 8x6=48 (6 x rabbit weight)
Solve the following inequality:
55 - 59 > 4(7-9)
Answer:
True.
Step-by-step explanation:
55-59 > 4(7-9)
Simplify 55-59: -4
Simplify again for 4(7-9): -8
Therefore,
-4> -8 The solution is true.
. What is the justification for each step in the solution of the equation?
Fill in the empty boxes with the justification.
15x – 8 = −6 (2+8x) + 42
15x – 8 = −6 (2+8x) + 42 Given
15x – 8 = −12 − 48x + 42 a.
15x − 8 = 30 − 48x b.
63x – 8 = 30 Addition Property of Equality
63x = 38 c.
x = 38/63 Division Property of Equality
Answer:
Step-by-step explanation:
A. Distributive property.
B. Combine like terms.
C. Addition property of equality.
Answer:
a,d,f
Step-by-step explanation:
The purchase price of a condominium is $123,500. A down payment of 23% is made. The bank charges $725 in fees plus 3 1/2 points. Find the total of them down payment and the closing costs. Round your answer the the nearest cent.
Answer:A down payment of 25% is made. The bank charges $725 in fees plus $$3 \frac { 1 } { 2 }$$ points. Find the total of the down payment and the closing costs. ... The bank charges $725 in fees plus 312. points. Find the total of the down payment and the ... We found a book related to your question. ... Round to the nearest cent.
Step-by-step explanation: i hope it helps your qestion
If the purchase price of a condominium is $123500, down payment of 23%, then the total of down payment and the closing costs is $166725.
What is percentage?Percentage is the number or ratio that is expressed in fraction of 100. It is expressed as %. It shows some part of large quantity.
How to find total?We have been given that the price of condominium is $123500. Down payment is 23% of the total price , it is 23%*123500=$28405
Left out amount will be 123500-28405=$95095.
Points=(2*3+1)/2=7/2
let the percentage of fees be x% then fees percentage will be :
7/2=x/100
x=35%
Fees will be 123500*35%=$43225.
Closing cost=95095+43225=$138320
Total will be 28405+138320
=$166725
Hence the total of down payment and closing cost will be $166725.
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Can someoneplzzz do this???
Domain:
Range
Greetings! Hope this helps!
Answer
D {-3, 5}
R: {0,4}
Have a good day!
_______________
A brainliest would help tons! :D
Which equation represents a constant rate of change of 25?
A) x + 25 = y
B) 25x = y
C) x - y = 25
D) 5x = y
The equation that has a constant rate of change of 25 is
25x = y
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
A)
x + 25 = y
When x = 1, y = 26
When x = 2, y = 27
The constant rate of change.
= (27 - 26)/(2 - 1) = 1/1 = 1
B)
25x = y
When x = 1, y = 25
When x = 2, y = 50
The constant rate of change.
= (50 - 25)/(2 - 1) = 25/1 = 25
C)
x - y = 25
When x = 1, y = -24
When x = 2, y = -23
The constant rate of change.
= (-23 + 24)/(2 - 1) = 1/1 = 1
D)
5x = y
When x = 1, y = 5
When x = 2, y = 10
The constant rate of change.
= (10 - 5)/(2 - 1) = 5/1 = 5
Thus,
25x = y has a constant rate of change of 25.
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Plzz help me I put pics I need it asap
I need to find an equation of the line satisfying the following condition.
if possible, write the equation in slope-intercept form.
through (4,3), parallel to 5x+9y= -7
Answer:
-5/9x+47/9=y
Step-by-step explanation:
Ruben puts $40,600 in an account that earns 0.9% interest compounded annually. If
he leaves his investment in the account how much will be in his account after 10
years?
Answer:
[tex]a = 40600(1 + \frac{0.009}{1} ) {}^{10} = 40600 \times 1.0937 = 44405.6[/tex]
The equation x3 + 3x2 + 5x + 15 = 0 has real and imaginary solution(s).
need help really fast
Which pair of lines have the same slopes and y-intercepts?
Answer:
parallel lines have the same slopes
Use the functions f(x) = 3x2 +1 and g(x) = 5x – 3 to evaluate or find the composition
function as indicated and its domain
f(g(x)) =
Domain:
Answer:
f(g(x)) = 75x^2 -90x + 28
Domain: (-∞,∞)
Step-by-step explanation:
fog = f(5x-3)
f(5x-3) = 3( 5x - 3 )^2 +1
3( 5x - 3 )^2 +1 = 75x^2 -90x + 28
Find the distance between (-4,-3) and (6,2).
Answer:
(about) 11.18034
Step-by-step explanation:
Use the distance formula to find the distance:
d = sqr (x2 - x1) + (y2 - y1)
Fill in the variables with what you know:
d = sqr ((6 - (-4)) + (2 - (-3)))
(Honestly it doesn't matter what order you put the x and y, as long as x2 and y2 make up the coordinates of one point and x1 and y1 make up the coordinates of the other)
= sqr ((6 + 4)^2 + (2 +3)^2)
= sqr ((10)^2 + (5)^2)
= sqr (100 + 25)
= sqr (125)
= (about) 11.1803
Dilating a triangle changes the angles and side length of the triangle
A.True
B.False
Answer:
it's false; dilating a triangle won't change the angles
Step-by-step explanation:
A line of best fit for this data is C = 51m + 4.4, where Cis the cumulative cell phone cost and m is the number of months.
Using this data, which value is the best prediction of the cumulative cell phone cost after 18 months?
Answer:
cumulative cell phone cost after 18 months = 922.4
Step-by-step explanation:
We are given the line of best fit for the data as;
C = 51m + 4.4
where;
C is the cumulative cell phone cost
m is the number of months.
Now, we are told that m = 18 months
Thus;
C = 51(18) + 4.4
C = 918 + 4.4
C = 922.4
Tthe best prediction of the cumulative cell phone cost after 18 months is 922.4
Given the equation for the line of best fit expressed as C = 51m + 4.4,
where
C is the cumulative cell phone cost
m is the number of months.
We need to predict the cost after 18 months. Substitute m = 18 into the function to get C
C = 51m + 4.4
C = 51(18) + 4.4
C = 918 + 4.4
C = 922.4
Hence the best prediction of the cumulative cell phone cost after 18 months is 922.4
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