The problems relate to airspeed and altitude in avionics and involve using mathematical concepts such as differential equations and differentials. The differential pressure when the indicated airspeed is 157 knots can be found by rearranging the given equation. Changes in airspeed can be determined based on differences in differential pressures. The equation for true airspeed in terms of altitude and differential pressure can be found by substituting the equation for indicated airspeed into the equation for true airspeed.
Explanation:The subject of these problems is differential calculus, which deals with differential equations and differentials. We're using these mathematical concepts to solve problems related to airspeed and altitude in avionics.
Given the airspeed relationship S=136.4p√+4.5, we can solve for the differential pressure 'p' when S is given 157 knots. We rearrange the equation for 'p': p = (S - 4.5) / 136.4.When the aeroplane slows down from 218 knots to 195 knots, the change in the differential pressure Δp can be found by first calculating the forces at both speeds and then taking the difference.We know that true airspeed T can be modelled by T=(1+A/50,000) ⋅ S, where A is the altitude and S is the indicated airspeed. In this case, we should substitute the relationship S=136.4p√+4.5 into the equation for T, obtaining the equation T = (1 + A/50000) * (136.4p√+4.5).Given that T=280 and A=20,000, we can substitute these values into the equation T = (1 + A/50000) * (136.4p√+4.5) to find 'p'. This will give us the estimated differential pressure.Learn more about Calculating Airspeed here:https://brainly.com/question/29597908
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To find differential pressure at 157 knots, solve the equation S = 136.4√p + 4.5, yielding p ≈ 1.25. For changes in pressure from 218 to 195 knots, calculate both pressures then find the difference: Δp ≈ 0.50 in Hg. For true airspeed in terms of altitude and differential pressure, use T = (1 + A/50,000) ⋅ (136.4√p + 4.5). Estimating differential pressure for a true airspeed of 280 knots at 20,000 feet involves solving the combined equation to find p ≈ 2.05.
Let's tackle each problem step-by-step.
Problem 1
Given the indicated airspeed, S, of 157 knots, we need to find the differential pressure p.
The relationship is given by:
S = 136.4√p + 4.5
Substitute S = 157 into the equation:
157 = 136.4√p + 4.5
Subtract 4.5 from both sides:
152.5 = 136.4√p
Divide both sides by 136.4:
√p = 152.5 / 136.4 ≈ 1.118
Square both sides to solve for p:
p ≈ 1.118² ≈ 1.25 inches of mercury
Problem 2
We need to find the change in the differential pressure when the airplane slows down from 218 knots to 195 knots.
First, find the differential pressure at 218 knots:
218 = 136.4√p + 4.5
213.5 = 136.4√p
√p = 213.5 / 136.4 ≈ 1.565
p1 ≈ 1.565² ≈ 2.45 inches of mercury
Next, find the differential pressure at 195 knots:
195 = 136.4√p + 4.5
190.5 = 136.4√p
√p = 190.5 / 136.4 ≈ 1.397
p2 ≈ 1.397² ≈ 1.95 inches of mercury
Change in differential pressure:
Δp = p1 - p2 ≈ 2.45 - 1.95 ≈ 0.50 inches of mercury
Problem 3
We need to write the equation for true airspeed T in terms of altitude A and differential pressure p.
From the given formulas:
S = 136.4√p + 4.5
T = (1 + A/50,000) ⋅ S
Combining these, we get:
T = (1 + A/50,000) ⋅ (136.4√p + 4.5)
Problem 4
An airplane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. We need to estimate the differential pressure p.
First, express the indicated airspeed S in terms of true airspeed T:
T = (1 + A/50,000) ⋅ S
280 = (1 + 20,000/50,000) ⋅ S
280 = 1.4S
S = 280 / 1.4 ≈ 200 knots
Next, solve for p using S = 136.4√p + 4.5:
200 = 136.4√p + 4.5
195.5 = 136.4√p
√p = 195.5 / 136.4 ≈ 1.433
p ≈ 1.433² ≈ 2.05 inches of mercury
This estimate is correct because it falls within the logical range for differential pressure at this indicated airspeed.
A store owner bought hats for 6.50 each and sold them for 12.00 the overhead was 2.50. What was the profit on each hat?
Arrange the following fractions in order from smallest to largest.
3/4, 1/8, 9/16, 1, 1/4, 3/8
Answer:
1/8, 1/4, 3/8, 9/16, 3/4, 1
Step-by-step explanation:
The fractions have been arranged in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.
How to compare fractions with different denominators?Fractions with different denominators can be compared by making the denominators the same. For example, take 1/4 and 1/2. The LCM of these fractions is 4. Now we can alter the fractions so that they have the same denominators as follows:
1/4 and 2/4
We can see that 2/4 is greater than 1/4.
We can arrange the given fractions in order from smallest to largest as shown below:The given fractions are: 3/4, 1/8, 9/16, 1, 1/4, 3/8
The lowest common multiple of these fractions is 16.
We can convert the fractions as shown below:
12/16< 2/16< 9/16< 16/16< 4/16< 6/16
Now we can arrange them in ascending order easily as shown below:
2/16, 4/16, 6/16, 9/16, 12/16, 16/16
or 1/8< 1/4< 3/8< 9/16< 3/4< 1
Therefore, we have arranged the fractions in order from smallest to largest as 1/8< 1/4< 3/8< 9/16< 3/4< 1.
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a fruit punch recipe requires 12 teaspoons of sugar for every 3 quarts of water. at this rate how much sugar is needed for 9 quarts of water
36 teaspoons. since the number of quarts is multiplied by 3, multiply the number of teaspoons as well. 12 × 3 = 36
The sum of three numbers is 89 The second number is 6 times the first. The third number is 15 less than the second. What is the first number?
The first number is 8
Solution:
Let the first number be "x"
The second number is 6 times the first
Second number = 6x
The third number is 15 less than the second
Third number = second number - 15
Third number = 6x - 15
The sum of three numbers is 89
Therefore,
First number + second number + third number = 89
[tex]x + 6x + 6x - 15 = 89\\\\13x - 15 = 89\\\\13x = 89+15\\\\13x = 104\\\\Divide\ both\ sides\ by\ 13\\\\x = 8[/tex]
Thus the first number is 8
Solve for x and y
5x + 3y = 7
y = 4
Answer: x= -1 y= 4
Step-by-step explanation:
We are going to solve this using substitution.
Here is the work...
5x+3(4)=7
That is what it woud look like because y is equal to 4.
3 times 4 is 12.
So now we have...
5x+12=7
Now we want to get All the common factors together...
To do this we will subtract 12 from 7 and we get -5.
Here is our equation now...
5x=-5
Now we divide x by 5 to get x alone, but we also divide -5 by 5.
x=-1
Now all we have to do to solve for y is put x in an equation.
In this case here is what we will do...
5(-1)+3y=7
Multiply...
-5+3y=7
Now we need to get the common factors together so lets add 5 to 7.
3y=12
3y/3=y
12/3=y
y=4
But that is already in your problem...OOF.Dont worry its still correct.
To solve the system, substitute y=4 into the first equation, leading to x=-1. Thus, the solution is x=-1 and y=4.
Explanation:To solve the system of equations 5x + 3y = 7 and y = 4, we can start by substituting the value of y from the second equation into the first equation. We are given y directly, so the substitution is straightforward.
Substituting y = 4 into the first equation:
5x + 3(4) = 75x + 12 = 75x = 7 - 125x = -5x = -1So, the solution to the system of equations is x = -1 and y = 4. We can say that x and y are variables, and in this case, y is dependent on x in other linear equations but is given directly here.
3x-15=2x+3 Find QR
It says the answer is 39 but I can’t figure out how they got 39. Please help
Answer:
look at the picture shown
the sum of a number z divided by three and the number
Answer:
z ÷ 3 + z
Step-by-step explanation:
8 1/5 + (4 2/5 + 3 3/10)
Answer:
15.7
Step-by-step explanation:
8 1/5= 8.2
4 2/5= 4.4
3 3/10= 3.1
4.4 + 3.1 = 7.5
7.5 + 8.2 = 15.7
Answer:
Step-by-step explanation:
Combine fractions with similar denominators
81/5 + 42/5 + 33/10
Add 81 and 42
123/5 + 33/10
To write 123/5 as a fraction with a common denominator, multiply by 2/2
123/5 >2/2 + 33/10
Write each expression witha common denominator of 10
123 . 2/10 + 33/10
Common numerator over denominator
123 . 2 + 33/10
Simplify
279/10
Thus answer = 279/10 0r 27.9
What is the area of this figure?
Enter your answer in the box.
m²
Area of the figure is 532 m².
Solution:
In the given image the shape is splitted into 2 shapes.
First shape is the square.
In square 4 sides are equal.
Area of the square = side × side
= 18 m × 18 m
Area of the square = 324 m²
Second shape is the triangle in the bottom.
Base of the triangle = 18 m + 8 m = 26 m
Height of the triangle = 16 m
Area of the triangle = [tex]\frac{1}{2}\times{\text{base}}\times{\text{height}}[/tex]
[tex]$=\frac{1}{2}\times16\times26[/tex]
Area of the triangle = 208 m²
Area of the given shape = area of the square + area of the triangle
= 324 m² + 208 m²
Area of the given shape = 532 m²
Hence area of the figure is 532 m².
Answer: 532 is answer
Hope u get a good grade
Which algebraic expression is equivalent to the expression below? 9(2x - 6) A. 9x - 3 B. 18x - 54 C. 9x - 8
Answer:
B
Step-by-step explanation
multiply 2 and 6 by 9
Answer:
its b
Step-by-step explanation:
(c) Mez bought 9 tubes of paint. She
received $16 change from $70.
How much did each tube of
paint cost?
Answer:
$6
Step-by-step explanation:
9 tubes of paint costs
$70 - $16 = $54
1 tube of paint cost
$54 : 9 = $6
What the answer is to question number 4
HELP!! PLEASE... ANSWER
5. Determine whether each pair of triangles is similar. Justify your answer.
Answer:
A
Step-by-step explanation:
Consider Δ JKL and Δ GDF
If the ratios of corresponding sides are equal then the triangles are similar.
[tex]\frac{JK}{GD}[/tex] = [tex]\frac{24}{20}[/tex] = [tex]\frac{6}{5}[/tex]
[tex]\frac{xJL}{GF}[/tex] = [tex]\frac{18}{15}[/tex] = [tex]\frac{6}{5}[/tex]
[tex]\frac{KL}{DF}[/tex] = [tex]\frac{12}{10}[/tex] = [tex]\frac{6}{5}[/tex]
Since the ratios are equal then Δ JKL and Δ GDF are similar by SSS postulate.
(a,1/b) and (b,1/a) find the slope of the line joining the points whose coordinates are
Answer:
[tex]m=\frac{1}{ab}[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
(a,1/b) and (b,1/a)
substitute
[tex]m=\frac{1/a-1/b}{b-a}[/tex]
[tex]m=\frac{\frac{b-a}{ab}}{b-a}[/tex]
[tex]m=\frac{1}{ab}[/tex]
The slope of the line joining the points (a,1/b) and (b,1/a) is calculated using the slope formula and is found to be 1 divided by the product of a and b, assuming a and b are not equal and neither is zero.
Explanation:To find the slope of the line joining the points with coordinates (a,1/b) and (b,1/a), we use the slope formula, which is the change in y divided by the change in x. We can write the formula as:
slope (m) = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula gives us:
slope (m) = (1/a - 1/b) / (b - a)
If we assume that a does not equal b and neither a nor b is zero, the slope can be calculated by simplifying the numerator and the denominator:
slope (m) = ((b - a) / (ab)) / (b - a)
The (b - a) terms cancel out, leaving us with:
slope (m) = 1 / (ab)
Therefore, the slope of the line is the reciprocal of the product of a and b.
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If B=80°, a=4.1, c=7.1, find the area of the triangle.
Answer:
14.2 squared units
Step-by-step explanation:
Always draw a diagram for the question. Capital letters are usually angles, and their opposite side is the same letter as a lowercase. (See diagram) The opposite side of angle B is side b.
The formula for area of a triangle is A = bh/2
"A" is for area.
"b" is for base (usually bottom side)
"h" is for height (perpendicular to base).
We know the measurement for the base c = 7.1. We need to find the height.
Notice when you draw in the height, it form two right triangles. We can use trigonometric ratios for right triangles.
Remember the trigonometric ratios using SohCahToa:
sinθ = opposite/hypotenuse;
cosθ = adjacent/hypotenuse and;
tanθ = opposite/adjacent, where θ means the angle of reference.
Focus on the triangle on the left side. We know one angle (∠B = 80°) and one side (a = 4.1). We can find "h", the missing side.
Since ∠B is our angle of reference, "h" is opposite. Since "a" is a longest side, it's the hypotenuse. Use the sine ratio because it uses the opposite and hypotenuse sides.
sinθ = opp/hyp General sine ratio formula
sinB = h/a Variables you use in this problem
sin80° = h/4.1 Isolate "h". Multiply both sides by 4.1
h = 4.1(sin80°) Multiply with calculator
h = 4.1(0.98480775...) Unrounded sin80
h = 4.03771178... Round this number
Note the number of decimal places given in the question.
h ≈ 4.0 Round to one decimal place
Now we can use the formula for the area of a triangle.
A = bh/2 Don't confuse side "b" with the base in this question
A = (7.1)(4.0)/2 Simplify the division
A = (7.1)(2.0) Multiply
A = 14.2 Final answer for area
Since we don't know what the units are, you can say the answer is:
A = 14.2u² or 14.2 squared units
A Greenland whale can hold its break three times as long as a beaver, and a hippopotamus can hold its breath for five minutes long than a beaver. If you added the time the Greenland whale,beaver and hippopotamus can hold their breath you would get 95 minutes. How long can a beaver hold its break
Answer:
18 minutes
Step-by-step explanation:
the beaver is 18 minutes so multiply that by 3 which equals 54 then add those two together then you get 72 then add 23 qhich then you end up with 95 minutes total.
To solve the problem, we create an equation representing the total time all three animals can hold their breath. Solving it reveals that a beaver can hold its breath for 18 minutes.
Explanation:Let's denote the time a beaver can hold its breath as 'x' minutes. According to the problem, a Greenland whale can hold its breath three times as long as a beaver, so that's '3x' minutes. A hippopotamus can hold its breath for five minutes more than a beaver, making it 'x+5' minutes.
The combined time for all three animals is given as 95 minutes, so we can set up the following equation:
x (beaver) + 3x (Greenland whale) + x + 5 (hippopotamus) = 95
Simplified, it becomes:
5x + 5 = 95
Next, you subtract 5 from both sides:
5x = 90
Finally, divide by 5:
x = 18
So, a beaver can hold its breath for 18 minutes.
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What is the answer to 2/3 (12x-9)
Answer:
8x-6
Step-by-step explanation:
Matthew drew a scale drawing of the elementary school. He used the scale
1 centimeter : 3 meters. The actual width of the school yard is 42 meters. How wide is the
school yard in the drawing?
Answer:
Step-by-step explanation:
candace is at a coffee shop and knows she can spend more than $52 before tax she sees this price list in the coffee shop
[tex]21+7.50p\leq 52[/tex]
Explanation:For inequalities, "a is no more than b" can be written as:
[tex]a\leq b[/tex]
Here we know Candace that can spend no more than $52 before tax. She can spend a certain amount of money in both Dark Roast coffee and Morning Blend coffee. So she spends:
2 pounds of Morning Blend coffee.p pounds of Dark Roast coffeeTherefore:
Amount of money for Morning Blend coffee:
[tex]2\times 10.50=\$21[/tex]
Amount of money for Dark Roast coffee:
[tex]p\times 7.50=\$7.50p[/tex]
So the total amount of money:
[tex]21+7.50p[/tex]
Finally, the inequality becomes:
[tex]21+7.50p\leq 52[/tex]
Besides, in order to know how many pounds she can spend let's solve for p:
[tex]7.50p\leq 52-21 \\ \\ 7.50p\leq 31 \\ \\ p\leq 4.13[/tex]
So she can spend less that 4.13 pounds.
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Final answer:
The correct inequality to determine the possible values for the number of pounds of Dark Roast coffee, p, along with 2 pounds of Morning Blend coffee for $52 or less is 9p + 15.10 ≤ 52. This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p ≤ 4.1.
Explanation:
Calculator Candace wants to determine the number of pounds of Dark Roast coffee, represented as p, she can buy if she purchases 2 pounds of Morning Blend coffee for a total of $52 or less. The price of the Morning Blend coffee is $7.55 per pound. To calculate this, we need to create an inequality that represents the scenario:
The cost for 2 pounds of Morning Blend coffee: 2 x $7.55 = $15.10The maximum amount Candace can spend: $52Now, the inequality will consider the total price of the Morning Blend coffee and add the price of the Dark Roast coffee (which is $9.00 per pound). So the inequality should look like this:
9p + 15.10 ≤ 52
This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p≤4.1.
A small jar of salsa contains 12 1/2 ounces. A large jar of salsa contains 75 ounces. How many small jars of salsa equal the same number of ounces as 1 large jar of salsa?
We can start off by making 12 1/2 to an improper fraction:
12 1/2 = 25/2
Divide the large jar of salsa by the small jar of salsa: 75 / 25/2.
Reciprocal of second and turn divide to multiply:
75 * 2/25.
150/25 = 6.
So 6 jars of small salsa = 1 large jar of salsa.
What is the median value of the data set shown on the line plot?
LMK answer fast!!
Answer:
i cant solve it for you but i will tell you how to do it
Step-by-step explanation:
You add them all up from least to greatest on a piece of paper then use your two fingers starting from the least and the greatest and go down the line if you get more than 1 number you must add them both up and divide by 2.
6a + 3 in Number of Terms
The expression '6a + 3' consists of two terms: '6a' and '3'. In mathematical expressions, terms are separated by addition or subtraction operations.
Explanation:The expression given, 6a + 3, is a mathematical expression that involves operations of addition and multiplication. In this expression, there are two terms separated by a plus sign. To clarify, a term refers to the separated parts of an expression when it is written as a sum or difference. This expression contains one numerical value (3) and one algebraic term (6a).
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What dose 8 1/5 - 3 5/9 =
Answer:1 8/45
Step-by-step explanation:73-20/45
53/45
1 8/45
Answer:
4 29/45
Step-by-step explanation:
What is 5 divided by 25
Answer:
0.2
Step-by-step explanation:
Answer: .2
Step-by-step explanation:
If the question was 25 divided by 5 it'll be 5 but because it's 5 divided by 25 the answer came out as a deciamal.
.2 can also mean it is 2/10 or maybe 20%
Round the following
numbers to the nearest 100.
817 →
368 →
1,4 51 →
Answer:
817 ---- 800
368 ---- 400
1,451 ---- 1500
Which equation can be solved by using this system of equations?
[y= 3x2 - 7x2 + 5
Ly = 7x4 + 2x
Question:
Which equation can be solved by using this system of equations?
y = 3x^3 - 7x^2 + 5
y = 7x^4 + 2x
A.) 3x^3 - 7x^2 +5 = 0
B.) 3x^3 - 7x^2 + 5 = 7x^4 +2x
C.) 7x^4 +2x = 0
D.) 7x^4 +3x^3 -7x^2 +2x + 5 = 0
Answer:
Option B: [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.
Explanation:
The two equations are [tex]y=$3 x^{3}-7 x^{2}+5$[/tex] and [tex]y=$7 x^{4}+2 x$[/tex]
Using substitution method, let us substitute [tex]y=$7 x^{4}+2 x$[/tex] in the equation [tex]y=$3 x^{3}-7 x^{2}+5$[/tex], we get,
[tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex]
Thus, [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.
Hence, Option B is the correct answer.
Answer:
Answer is B. 3x^3-7x^2+5 = 7x^4+2x
Step-by-step explanation:
got it right!
hope this helps
Solve the system of linear equations by substitution.
3x−2y=15
y=2x−11
The solution set is (7,3).
Step-by-step explanation:
Given system of equations is;
3x−2y=15 Eqn 1
y=2x−11 Eqn 2
Substituting value of y from Eqn 2 in Eqn 1
[tex]3x-2(2x-11)=15\\3x-4x+22=15\\-x+22-15=0\\7=x\\x=7[/tex]
Putting x=7 in Eqn 2
[tex]y=2(7)-11\\y=14-11\\y=3[/tex]
The solution set is (7,3).
Keywords: linear equation, substitution method
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Combine 2d + 5d
Answer please ?
Answer:
7D
Step-by-step explanation:
2D + 5D
Add the figures
Find the area of the shape shown below.
Answer: 10
Step-by-step explanation:
2 * 4 = 8
8/2 = 4
2 * 2 = 4
4/2 = 2
4 + 2 = 6
2 * 2 = 4
4 + 6 = 10
Can you find the equation in standard form when given 3 or more orders pairs on a parabola
Answer:
Yes, you can
Step-by-step explanation:
The standard form of the equation of a parabola is [tex]y=ax^2+bx+c[/tex]
When given three points, you substitute each point into the equation to obtain 3 simultaneous linear equations.
You then solve the three equations simultaneously to find the values of the constants a,b, and c.
You then substitute these constants into [tex]y=ax^2+bx+c[/tex]