The distance between the planes is increasing at a rate of approximately 252 km/hr when the southbound plane is 34 km from the airport and the westbound plane is 15 km from the airport.
Explanation:Identify the relative motion: We need to find the rate of change of the distance between the planes, which is a relative motion problem.
Calculate individual velocities: Since the planes are approaching from different directions, we need to consider their velocities as vectors. The southbound plane has a southward velocity of 124 km/hr, and the westbound plane has an eastward velocity of 223 km/hr.
Apply Pythagorean theorem: At the given moment, the distance between the planes is the hypotenuse of a right triangle formed by their individual velocities. Using the Pythagorean theorem:
Distance^2 = Southbound velocity^2 + Westbound velocity^2
Distance^2 = (124 km/hr)^2 + (223 km/hr)^2
Distance ≈ 258.5 km
Differentiate distance equation: To find the rate of change of the distance, we need to differentiate the distance equation with respect to time. This gives us the relative velocity between the planes.
Calculate relative velocity: Taking the derivative of the distance equation and plugging in the individual velocities:
Rate of change of distance = (Southbound velocity * Eastward velocity) / Distance
Rate of change of distance ≈ (124 km/hr * 223 km/hr) / 258.5 km ≈ 252 km/hr
Therefore, the distance between the planes is increasing at a rate of approximately 252 km/hr when the southbound plane is 34 km from the airport and the westbound plane is 15 km from the airport.
write 42.5% as a fraction in simplest form
The fraction of 42.5% in its simplest form is 17/40.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
42.5%
= 42.5/100
= 425/1000
= 85/200
= 17/40
Thus,
The fraction is 17/40.
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42.5% can be expressed as the fraction 17/40 in simplest form.
To express 42.5% as a fraction in the simplest form, we need to convert the percentage to a fraction with the numerator and denominator in their simplest form. Here's the step-by-step process:
Recognize that a percentage is a fraction out of 100. In this case, 42.5% can be written as 42.5/100.
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 42.5 and 100 is 2. Dividing both the numerator and denominator by 2 gives us 21.25/50.
Continue simplifying the fraction by dividing both the numerator and denominator by any common factors. In this case, we can divide both by 25: 21.25/50 = 0.85/2.
Finally, express the fraction in simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 5 in this case: 0.85/2 = 17/40.
Therefore, 42.5% can be expressed as the fraction 17/40 in simplest form.
This means that 42.5% is equivalent to 17 parts out of 40 parts.
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what is the slope of 3x + 4Y = 24
The slope of the line 3x + 4y = 24 is -3/4.
The slope of a line is determined by the coefficient of x in the equation of a line written in the form y = mx + b, where m represents the slope.
In the equation 3x + 4y = 24, rearranging it to the slope-intercept form y = mx + b gives 4y = -3x + 24, and then y = -3/4x + 6. Thus, the slope is -3/4.
It took morry 2 and 5/6 hours to drive to the beach. it took jason twice as long. about how long did it take jason to drive to the beach?
A hummingbird beats its wings about 75 times in one second. Based on this rate, what is the number of times a hummingbird beats its wings one minute?
What are the different mathematical relationships in data?
Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yard pieces can she cut and still have 1 1/4 yards left?
The difference of two numbers is more than 12,and one of the numbers is 3
Inequality for the other number x > 15.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The most frequent application is to size-compare two numbers on a number line.
Given,
Difference of two numbers is greater than 12
One number is 3
Let the other number be x
Then, inequality becomes
x - 3 > 12
Adding 3 on both sides
x > 12 + 3
x > 15
Hence, x>15 represents the other number so that difference of two numbers is greater than 12.
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The sum of three consecutive integers is 303. If n is the smallest of the three, which equation represents this situation?
Answer:
The correct equation is 3n + 3 = 303
Correct value of n is 100
Step-by-step explanation:
The sum of three consecutive integers is 303.
Consecutive integer is next number of previous one.
Let n be smallest integer.
Next two integer: n+1, n+2
Sum of n, n+1 and n+2 is 303
Therefore,
n + n + 1 + n + 2 = 303
3n + 3 = 303
3n = 300
n = 100
Hence, The correct equation is 3n + 3 = 303
There are 6 female goldfish for every 10 male goldfish in the aquarium. there are 216 female goldfish in the aquarium. how many male goldfish are in the aquarium?
If there are 6 female goldfish for every 10 male goldfish in the aquarium and if there are 216 female goldfish in the aquarium then there are 360 male goldfish in the aquarium.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Let us use a proportion to represent the relationship between the number of female and male goldfish in the aquarium
6 female goldfish / 10 male goldfish = 216 female goldfish / x male goldfish
We know that there are 216 female goldfish in the aquarium, so we can substitute that value into the equation:
6 / 10 = 216 / x
Let us solve for x by cross-multiply:
6x = 10 × 216
6x = 2160
Divide both sides by 6
x = 360
Therefore, there are 360 male goldfish in the aquarium.
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0.87 written as a fraction is _____.
The decimal 0.87 can be written as the fraction 87/100, which cannot be simplified further.
Explanation:The decimal 0.87 can be written as a fraction by placing the decimal over 100 and then simplifying the fraction if possible. In this case, 0.87 can be written as 87/100. However, this fraction can be simplified further. Both 87 and 100 can be divided by 1, making the simplified fraction 87/100.
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Divide the complex number: 7i/8+i
(i= imaginary #)
show step-by-step solution
Choose the best verbal statement for the following inequality: m > 13
you randomly draw a marble from a bag of marbles that contains 7 blue marbles, 2 green marbles, and 1 red marble. what is the probability not draw a blue marble
Answer:
0.3
Step-by-step explanation:
It is given that,
Number of blue marbles = 7
Number of green marbles = 2
Number of red marbles = 1
Total number of marbles = 7+2+1=10
We need to find the probability that we do not draw a blue marble.
[tex]P=\dfrac{\text{Number of non-blue marbles}}{\text{Total number of marbles}}[/tex]
[tex]P=\dfrac{2+1}{10}[/tex]
[tex]P=\dfrac{3}{10}[/tex]
[tex]P=0.3[/tex]
Therefore, the required probability is 0.3.
If Y is between X and Z, then X, Y, and Z are collinear?
A) Always true
B) Sometimes true
C) Never true ...?
Yes, its always true that if Y is between X and Z, then X, Y and Z are collinear.
Here,
Given that;
Y is between X and Z.
We have to find X, Y and Z are collinear.
What is Collinear points?
Two or more points are Collinear points if they are lie in one straight line.
Now,
Y is between X and Z.
Clearly, XZ is a line and Y is lie in between X and Z.
So, X, Y and Z are Collinear points.
Therefore, its always true that if Y is between X and Z, then X, Y and Z are Collinear.
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what is the difference between all real numbers and no solution how do you know when these situations occur
The difference between 'all real numbers' and 'no solution' is that the former means any real number satisfies the equation while the latter means no real number satisfies it. These concepts are essential in understanding and solving mathematical problems, which is a skill developed through practice.
Explanation:The difference between 'all real numbers' and 'no solution' in mathematical equations is significant. When an equation has all real numbers as its solution, it means that any real number can be substituted for the variable and the equation would still hold true. This situation typically occurs when both sides of the equation are identical after simplification. For example, if we simplify an equation and end up with a statement like 5 = 5, it implies that all real numbers are solutions since the statement is always true, regardless of the value of the variable.
On the other hand, 'no solution' means that there are no real numbers that satisfy the equation, often arising when a statement is made that is logically false after simplification, such as 0 = 5. Identifying knowns and unknowns and checking if an answer is reasonable are part of the problem-solving process, where we also look for unreasonable results that might suggest 'no solution'.
The occurrence of these situations during problem solving reflects the complexity of real-world problems, where we must determine which information is relevant and sort out the possible from the impossible. This discernment can be developed through consistent practice in evaluating and solving various types of problems. In some cases, particularly in systems of equations, if the number of unknowns is larger than the number of equations, it may indicate that there could be infinite solutions or no unique solution.
Peaches are being sold for $2 per pound if X represents the number of pounds of peaches bought and Y represents the total cost for the peaches which best describes the value of X and Y
Answer:
Y = 2X is the expression which describes the value of X and Y.
Step-by-step explanation:
Peaches are being sold at the rate = $2 per pound
If X represents the number of pounds of peaches purchased then the total cost of the peaches = 2X
Total cost of the peaches is represented by Y, then the expression will be
Y = 2X
Therefore, expression which shows the relation between X and Y is
Y = 2X
Find the equation of a line with the gradient 5 passing through the point (2,-5)
What is the sum of the arithmetic sequence 151, 137, 123,..if there are 26 terms?
A. -676
B.-650
C.-624
D.-598
Answer:
option C -624
Step-by-step explanation:
One angle has 10 degrees more than another angle. The sum of the angles us 90 degrees . How many degrees are in each angle? Please Explain.
The smaller angle is 40 degrees and the larger angle is 50 degrees.
Explanation:Let's represent the smaller angle by x degrees. According to the problem, the larger angle is 10 degrees more than the smaller angle, so it can be represented by x + 10 degrees. The sum of these two angles is 90 degrees, so we can set up the equation:
x + (x + 10) = 90
Simplifying the equation, we get:
2x + 10 = 90
Subtracting 10 from both sides, we have:
2x = 80
Finally, dividing both sides by 2, we find:
x = 40
So, the smaller angle is 40 degrees and the larger angle is 40 + 10 = 50 degrees.
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A tortoise is walking in the desert. It walks for 4 minutes at a speed of 10.24 meters per minute. For how many meters does it walk?
Final answer:
To find the total distance a tortoise walked in the desert, use the formula distance = speed x time. In this case, the tortoise walked 40.96 meters by walking for 4 minutes at a speed of 10.24 meters per minute.
Explanation:
A tortoise is moving laboriously-khwanya-khwanya-khwanya! To calculate the total distance the tortoise walked, we use the formula: distance = speed x time. Given the tortoise walks for 4 minutes at a speed of 10.24 meters per minute, the calculation is 10.24 m/min x 4 min = 40.96 meters. Therefore, the tortoise walked a distance of 40.96 meters.
The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).
At which points could the vertex of the right angle in the triangle be located? Check all that apply.
(–1, 1)
(4, –2)
(1, 1)
(2, –2)
(4, –1)
(–1, 4)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Let
(x,y) ----> the coordinates of point C
Applying the Pythagoras Theorem
[tex](-1-4)^2+(-2-1)^2=(x-4)^2+(y-1)^2+(x+1)^2+(y+2)^2[/tex]
step 1
Find the possibles values of x
[tex](-1-4)^2=(x-4)^2+(x+1)^2\\\\25=x^{2}-8x+16+x^{2}+2x+1\\\\2x^{2}-6x-8=0[/tex]
Simplify
[tex]x^{2}-3x-4=0[/tex]
Solve the quadratic equation
[tex]x^{2}-3x-4=(x+1)(x-4)[/tex]
The values of x are
x=-1 and x=4
step 2
Find the possibles values of y
[tex](-2-1)^2=((y-1)^2+(y+2)^2\\\\9=y^{2}-2y+1+y^{2}+4y+4\\\\2y^{2}+2y-4=0[/tex]
Simplify
[tex]y^{2}+y-2=0[/tex]
Solve the quadratic equation
[tex]y^{2}+y-2=(y+2)(y-1)[/tex]
The values of y are
y=-2, y=1
therefore
The possibles coordinates of point C are
(-1,1),(4,-2)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Given that the hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2), then two triangles can be formed (see figure attached).
The vertex of the right angle in each triangle are on points (-1, 1) and (4, -2), as can be seen in the figure.
you can buy an 8 pack of paper towels for $7.92 or 12 pack for $11.64, which is a better buy?
Prove triangle dih is congruent to triangle egh
P= $975, r=5.5%, t=60 days
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
The expression representing the total number of letters that Julia wrote after 'y' months is '14y', as she writes 14 letters each month.
Explanation:This is a mathematics problem related to writing algebraic expressions. In this case, Julia has written 14 letters each month for 'y' months. Hence, the expression to determine the total number of letters Julia has written is '14y'. Let's break this down:
Julia writes 14 letters each month. This is a constant, represented by the number 14. The time period over which she continues this action is variable, represented by 'y'. So, for every month 'y', she writes 14 letters. We multiply 14 (letters per month) by 'y' (number of months) to get the total number of letters, hence the expression 14y.Learn more about Algebraic Expression here:
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The expression to show how many total letters Julia wrote is 14y.
Explanation:To find the total number of letters Julia wrote, we need to multiply the number of letters she wrote each month (14) by the number of months she wrote letters (y). So, the expression to show how many total letters she wrote is 14y.
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If $7,000 is placed in an account with an annual interest rate of 5.5%, how long will it take the amount to triple if the interest is compounded annually? Round your answer to two decimal places.
...?
find the derivative of y=(2x-7)^3
To find the derivative of y=(2x-7)^3, use the power rule and chain rule. Differentiate each term individually and apply the chain rule. Add all the terms together to get the derivative.
Explanation:To find the derivative of y=(2x-7)^3, we can use the chain rule. First, we can rewrite the equation using the power rule: y = (2x - 7)(2x - 7)(2x - 7). Next, we differentiate each term individually using the power rule and then apply the chain rule. The derivative of the first term will be 2(2x - 7)(2), the derivative of the second term will be 2(2x - 7)(2), and the derivative of the third term will be 2(2x - 7)(2). Finally, we add all these terms together to get the derivative of the original equation.
Find the key number to the equation, the intervals into which the key numbers divide the number line, and the sign of y over each of these intervals. y=x+1/(x-1)^2
You drop a rock off a bridge. The rock’s height, h (in feet above the water), after t seconds is modeled by h = -16t2 + 541. What is the height of the rock after 2 seconds?
From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2.8% each year. What will the population be in 2040? Round to the nearest whole number. Enter your answer in the box.
actually i just took the test and it said the answer was 9384