an aircraft is climbing at 30° angle to the horizontal how fast is the aircraft gaining alitude if it’s speed is 500 mph
Answers
The speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
Since the aircraft is climbing at 30° to the horizontal. it means there will be a vertical component which will be the altitude and also a horizontal component which will be the horizontal distance covered. while the hypotenuse will be how far it has climbed.
Let us call the vertical component x and the hypotenuse component z.
Thus, from trigonometric ratios, we can say that;
sin 30 = x/z
We are looking for how fast the aircraft is gaining altitude. Thus, using Liebniz notation, we can say this rate is; dx/dt. Thus;
sin 30 = (dx/dt)/(dz/dt)
0.5 = (dx/dt)/(dz/dt)
0.5 × (dz/dt) = dx/dt
Its' speed is 500 mph. This means dz/dt = 500
Thus;
dx/dt = 0.5 × 500
dx/dt = 250 mph
Hence, the speed rate at which the aircraft is gaining altitude is;
dx/dt = 250 miles per hour
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Related Questions
number 8 only please help
Answers
Answer:
14/70
Step-by-step explanation:
Translate this sentence into an equation. The product of Mabel's age and 4 is 56. Use the variable m to represent Mabel's age.
Answers
Answer:
4m = 56
Step-by-step explanation:
4 * m = 56
4m = 56
4/4m = 56/4
m = 14
The distance from Leeds to London is 210 miles. The train
travels at an average speed of 90 mph. If I catch the 9.30 am
train in London, at what time should I expect to arrive in
Leeds?
Answers
Distance = speed x time
Rearrange the formula
Time = Distance/speed
D = 210 miles; S = 90
Time = 210/90 = 2.33 hours
First add 2 hr and then add 0.33333 hr
9:30 + 2 hr = 11:30
Converting 0.33333 into min
0.33 x 60 = 20 min
11:30 + 20 min = 11:50 am
I cant solve please help me
Answers
Answer:
Let us set up a ratio to find the relationship between side lengths of the two triangles.
25:10
5:2
We can divide both sides by two, but there's no need as the smaller triangle has multiples of two.
So, if XZ is 6, let's place it into the ratio and find what "x" is.
5(3) : 2(3)
15 : 6
x = 15
COLLEGE MATH! HARD!
NO LINKS OR YOU WILL BE REPORTED!!!!!!!!!
Find the formula for the function of the form w(x)= Asin(Bx)+C with an (i) a maximum (3,6),(i) a minimum at (-9,6), and (iii) no critical points between these two points
Answers
Answer : W (x) = - cos (Bx) A / B + cx+C
(If confused (written out) : Negative cos (Bx) A over B then + cx + C
I’m not sure if this is what you were looking for , Just tryna help.
can you help
thank you
Answers
Answer:
In first box: top left __7, in top right __4, on left top __9, left bottom __6.
In second box: top left __7, in top right __3, on left top __3, left bottom __5.
Step-by-step explanation:
Answer:
Here you go! I believe this is correct.
Two rock climbing gyms offer a two-month “trial period” training program. The first gym charges $4 per climbing session plus a one-time $50 fee. The second gym charges $6 per climbing session plus a one-time $30 fee. For what number of sessions is the cost of the program the same for each gym?
Write a system of equations you can use to find at what number of sessions the cost of the trial period program at each of the gyms is exactly the same.
Answers
Answer:
the second one
Step-by-step explanation:
Use Newton’s Method to find the solution to the equation
-x^2+18=0 use x_1=3 and find x_4 accurate to six decimal places.
Answers
\(f(x) = - x {}^{2} + 18 \\ f'(x) = - 2x\)
\(x_{n + 1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})} \)
\(x_{2} = 3 - \frac{f(3)}{f'(3)} = 4.5\)
\(x _{3}= 4.5 - \frac{f(4.5)}{f'(4.5)} = 4.25\)
\(x_{4} = 4.25 - \frac{f(4.25)}{f'(4.25)} ≈4.242647\)
\(x_{5} = 4.242647 - \frac{f(4.242647)}{f'(4.242647)} ≈4.242640 \\ \)
f:0,1 +0,1?. f(x) is obtained by removing the second bit from x and placing the bit at the end of the string. For example, f(101) = 110. Select the correct description of the function f. a. Neither one-to-one nor onto b. One-to-one and onto c. One-to-one but not onto d. Onto but not one-to-one Answer = Submit
Answers
Onto but not one-to-one. is f(x) which is obtained by removing the second bit from x and placing the bit at the end of the string.
The function f is said to be "onto" because it maps every element in its codomain (the set of possible output values) to at least one element in its domain (the set of possible input values). In this case, the codomain is the set of all binary strings of length 3, and the domain is the set of all binary strings of length 2. However, the function is not one-to-one, because there are multiple elements in the domain that are mapped to the same element in the codomain. For example, both "10" and "01" are mapped to "100". This means that the function f is not one-to-one, meaning that it doesn't map every element in its domain to a unique element in its codomain. A function is said to be one-to-one if every element in its domain (the set of possible input values) is mapped to a unique element in its codomain (the set of possible output values). In other words, no two elements in the domain have the same image (output) under the function. A function is said to be onto if every element in the codomain is mapped to by at least one element in the domain. In other words, every element in the codomain has at least one pre-image (input) under the function. In the case of the function f described in the previous question, it is onto because every binary string of length 3 can be obtained as the output of the function for some binary string of length 2. However, it is not one-to-one because there are multiple binary strings of length 2 that are mapped to the same binary string of length 3. For example, both "10" and "01" are mapped to "100".
So, the function f is described as "onto but not one-to-one".
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PLS HELP I DONT REMEMBER HOW TO DO THIS
Answers
Answer:
oh lord...ill try my best
Step-by-step explanation:
Let's start b writing down coordinates of all points:
A(0,0,0)
B(0,5,0)
C(3,5,0)
D(3,0,0)
E(3,0,4)
F(0,0,4)
G(0,5,4)
H(3,5,4)
a.) When we reflect over xz plane x and z coordinates stay same, y coordinate changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.
A(0,0,0)
Reflecting
A(0,0,0)
B(0,5,0)
Reflecting
B(0,-5,0)
C(3,5,0)
Reflecting
C(3,-5,0)
D(3,0,0)
Reflecting
D(3,0,0)
b.)
A(0,0,0)
Moving
A(-2,-3,1)
B(0,-5,0)
Moving
B(-2,-8,1)
C(3,-5,0)
Moving
C(1,-8,1)
D(3,0,0)
Moving
im sorry think this is wrong I TRIED MY BESTTTT!!!!!!!! give me credit this is tiring
A violin is 100$
What is the price when it's marked down 10%
Answers
Answer:
90
Step-by-step explanation:
Answer:
it should be 95.40
Step-by-step explanation:
Find the 23rd term of the sequence: 77,65,53,41
Answers
Answer:
The 23rd term is -187
Step-by-step explanation:
U₂₃=??, a=77, d=-12, n=23
U₂₃=a+(n-1)d
U₂₃=77+(23-1)(-12)
U₂₃=77+22(-12)
U₂₃=-187
U₂₃=-187
∴U₂₃=-187
A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
Answers
From the problem, we know that:
2(x + 1) + x^2 = 13
Simplifying and rearranging:
x^2 + 2x - 11 = 0
Using the quadratic formula:
x = (-2 ± sqrt(2^2 - 4(1)(-11))) / (2(1))
x = (-2 ± sqrt(48)) / 2
x = (-2 ± 4sqrt(3)) / 2
x = -1 ± 2sqrt(3)
Since the problem states that the numbers are positive, we can ignore the negative solution. Therefore, the smaller number is:
x = -1 + 2sqrt(3)
And the larger number is:
x + 1 = 2sqrt(3)
So the two numbers are -1 + 2sqrt(3) and 2sqrt(3).
Mireya has breakfast at a restaurant. Her bill was $9.00. Mireya plans to leave a 20% tip. How much does she need to leave for the tip?
Answers
9 * .20 = 1.80
Question 9/30 If ADD = 81, BAD = 49, and CAD = 64. then what is the value of ADA?
Answers
The value of ADA is 36
The question could be approached as a quantitative reasoning exercise :
Assigning each alphabet a numeric value corresponding to its position in the English alphabet :
A has a value of 1
B has a value of 2
C has a value of 3
D has a value of 4
ADD could be interpreted as :
ADD = (1 + 4 + 4) = 9
Taking the square of the sum ; 9² = 81
ADD = 81
BAD could be interpreted as :
BAD = (2 + 1 + 4) = 7
Taking the square of the sum ; 7² = 49
CAD could be interpreted as :
CAD = 3 + 1 + 4 = 8
Taking the square of the sum ; 8² = 64
Therefore ;
ADA could be interpreted as :
ADA = 1 + 4 + 1 = 6
Square of the sum ; 6² = 36
Hence, the value of ADA is 36
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Please help!! Find the solution for t in the equation:
Answers
Answer:
t = 1.322
Step-by-step explanation:
4×(2^t) = 10
2^t = 10/4 = 2.5
t = log2(2.5)
now, the logarithm to the base 2 of 2.5 must be larger than 1, as 2.5 is larger than 2.
so, it can be only the 4th answer option.
now, to actually calculate it :
log2(2.5) = log10(2.5) / log10(2) = 1.321928095... ≈
≈ 1.322
we were correct.
Answer:
t = 1.322
Step-by-step explanation:
Given equation:
\(4(2^t)=10\)
Divide both sides by 4:
\(\implies \dfrac{4(2^t)}{4}=\dfrac{10}{4}\)
\(\implies 2^t=2.5\)
Method 1Take natural logs of both sides:
\(\implies \ln 2^t = \ln 2.5\)
\(\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x\)
\(\implies t \ln 2 = \ln 2.5\)
Divide both sides by ln 2:
\(\implies \dfrac{t \ln 2}{\ln 2} = \dfrac{\ln 2.5}{\ln 2}\)
\(\implies t= \dfrac{\ln 2.5}{\ln 2}\)
\(\implies t=1.321928095...\)
Method 2\(\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c\)
\(\implies \log 2 (2.5)=t\)
\(\implies t=1.321928095...\)
SolutionTherefore, the solution that is nearest to the exact solution is t = 1.322
1. Which of the following is equivalent to 6/10? 5/9 9/15 8/12 36/100
Answers
HELP! PLEASEEEEE
IMAGE BELOW!
Answers
Answer:
Quadrant I and Quadrant II
Step-by-step explanation:
Quadrant I has both positive x and y coordinates,Quadrant II has a negative x coordinate but the y coordinate is positive.
MATH EXPERTS I NEED YOU! Is it graph A, B, C, or D?
Answers
Answer:
Its the first graph ok kid
Step-by-step explanation:
You are finding a measure of center in the data sets below using either the mean or the median. In which of the data sets should you find the median? Select all that apply.
A) 68, 73, 77, 75, 23, 62 B) 84, 73, 28, 91, 93, 77 C) 24, 22, 21, 19, 23, 25 D) 18, 13, 56, 21, 12, 19 E) 77, 15, 81, 83, 84, 72
Answers
The whole given data sets can have their median calculated after being arranged either in an ascending or descending order. That is option A,B,C,D and E.
What is median of a data set?The median of a data set is defined as the data that is found at the center, otherwise known as the measure of center of a data set, after being arranged in ascending or descending order.
For example the median of option A) is calculated as follows:
Data set= 23,62,68,73,75,77
Median = 68+73/2 = 70.5
Therefore the median is between 68 and 73 which is = 70.5
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Guys Help!! I Don´t Know How To Do This!!
Answers
Answer:
Frank
Step-by-step explanation:
First let's start by calculating the speed of each runner.
Let's use feet per second
Frank's speed is already given in feet per second: 14 feet/second
We are given that Jake runs 382 feet in 38 seconds. To bring this down to feet/second we need to divide both numbers by 38.
382/38=10.05 feet/second (about)
We are given that Will runs 1 mile in 394 seconds. 1 mile is equivalent to 5280 feet. Now we divide both numbers by 394 to bring it down to feet/second.
5280/394=13.401 feet/second (about)
We are given that Ron runs 555 feet in 1 minute. 1 minute is equivalent to 60 seconds. Now we divide both numbers by 60 to bring it down to feet/second.
555/60=9.25 feet/second
After comparing all the speeds, we can conclude that Frank runs the fastest
help me please i would appreciate it so so much
Answers
Answer:
w = 120
x = 60
y = 120
z = 60
Step-by-step explanation:
w = 120 (vertically opposite angles)
sum of co interior angles is 180
⇒ w + x = 180 and x + y = 180
w + x = 180
⇒ 120 + x = 180
⇒ x = 180 - 120
⇒ x = 60
x + y = 180
⇒ 60 + y = 180
⇒ y = 180 - 60
⇒ y = 120
z = x (corresponding angles)
z = 60
Gate posts are parallel and m<4 =47, what is m<1
Answers
The value of angle 1 given the value of angle 4 as 47° will be 133°
How to explain parallel linesParallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.
Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.
The value will be:
= 180° - 47°
= 133°
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PLEASE PLEASE HELP MEEE :(
Select the correct point on the coordinate plane.
Which point can be used to form a right triangle to derive the distance formula to find the length of the line segment?
Answers
(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment
Determining the distance between two points.Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.
The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:
D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63
Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)
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Answer: It’s -1,-3
Step-by-step explanation:
got 100 on the test
Please help with math question.
Answers
9514 1404 393
Answer:
C
Step-by-step explanation:
Multiply numerator and denominator by the conjugate of the denominator.
\(\displaystyle\frac{7}{-4-\sqrt{x}}=\frac{7(-4+\sqrt{x})}{(-4-\sqrt{x})(-4+\sqrt{x})}=\frac{-28+7\sqrt{x}}{16-x}=\boxed{\frac{7\sqrt{x}-28}{16-x}}\)
Write a two-digit number ...
a
that has 9 tens and 1 ones;
.
Answers
Answer: 91
Step-by-step explanation:
9 tens= 90
1 ones= 1
90+1=91
Solve: + 12x = 9
Ox=3/5 :: 6
O x= 6 745
O=-6+ 745
O *=-6_315
Answers
Answer:
\(x = \frac{3}{4} \)
Step-by-step explanation:
\(12x = 9\)
Divide both sides by 12:
\( \frac{12x}{12} = \frac{9}{12} \)
Simplify the fraction:
\(x = \frac{9}{12} \)
Find the greatest common factor of the numerator and denominator:
\(x = \frac{3.3}{4.3} \)
Factor out and cancel the greatest common factor:
\(x = \frac{3}{4} \)
The radius of a circular clock is 13 centimeters. What is the
area of the clock?
Use 3.14 for pi
Answers
Answer:
452.16
Step-by-step explanation:
A = (3.14)r^2
A=(3.14)12^2
A=452.16
Answer:
530.66 cm
Step-by-step explanation:
A= π r 2
input known values
A= (3.14) (13^2)
Simplify
A= (3.14) 169
A= 530.66
A rectangular piece of tin has an area of 1056 square inches. A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 2052 cubic inches, what were the original dimensions of the piece of tin. PLEASE SHOW WORK
Answers
Answer:
44 inches and 24 inches
Step-by-step explanation:
Let \(l,b\) denotes length and breadth of a rectangle.
\(lb=1056\)
A square of 3 inches is cut from each corner, and an open box is made by turning up the ends and sides.
New length \(=l-6\) inches
New breadth \(=b-6\) inches
Height of box \(=3\) inches
Volume of box = length × breadth × height
\((l-6)(b-6)3=2052\)
\(lb-6l-6b+36=684\\6(l+b)=408\\l+b=68\\b=68-l\)
Put \(b=68-l\) in \(lb=1056\)
\(l(68-l)=1056\\l^2-68l+1056=0\\l^2-44l-24l+1056=0\\l(l-44)-24(l-44)=0\\(l-24)(l-44)=0\\l=24,44\)
At \(l=24,b=\frac{1056}{24}=44\) inches
At \(l=44,b=\frac{1056}{44}=24\) inches
Find the area of each rhombus-shaped tile. Then find the area of the pattern. If necessary, round to the nearest hundredth
Answers
Answer:3655.29
Step-by-step explanation: