One airplane is approaching an airport from the north at 124 km/hr. A second airplane approaches
from the east at 223 km/hr. Find the rate at which the distance between the planes changes when
the southbound plane is 34 km away from the airport and the westbound plane is 15 km from the
airport.
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.
Which of these numbers has the least value?
a. 7.2 x 10
b. 8.1 x 10
c. 9,100,000
d. 9.5 x 10
As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
The digit 5 acts as a limit.
After solving we get.
a. 7.2 x 10 will gives 72.
b. 8.1 x 10 will gives 81.
c. 9,100,000
d. 9.5 x 10 will gives 95.
As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.
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A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
A. True
B. False
Answer:
statement is true .
Step-by-step explanation:
Given : Statement A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
To find : Statement is true or false.
Solution : By polynomial theorem if x-a divide the polynomial P(x) and we get reminder zero then a would be the factor.
Therefore, statement is true .
Answer:
true
Step-by-step explanation:
Which graph best represents the solution to the following system?
5x - 2y < (less than or equal to) 10
x + y < 5
The graph that best represents the solution to the given system is:
Graph A.
Step-by-step explanation:We are given a system of inequalities as:
[tex]5x-2y\leq 10[/tex]
and [tex]x+y<5[/tex]
i.e. the graph of first inequality is a solid straight line( since the inequality is not strict) that passes through (2,0) and (0,-5) and the shaded region is towards the origin( since it passes the zero point test)whereas the graph of second inequality is a dotted straight line(since the inequality is strict) that passes through (0,5) and (5,0) and the shaded region is towards the origin( since it passes the zero-point test)Hence, the graph is:
Graph A.
Average speed of Car 1 = 35 mph. Average speed of Car 2 = 55 mph. Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.
How long before Car 2 overtakes Car 1? ___________ hour.
Answer:
.525
Step-by-step explanation:
35(t+18/60) = 55t
35t +10.5 = 55t
10.5 = 20t
0.525 = t
$250 at 5% simple interest for 3 years
Find the difference. (-ab+8a-5)-(-8ab-4)
Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to walk toward you at the bus stop and then passes you. He walks at a speed of 4 ft/s. His distance d from you after t seconds is given by d = |120 − 4t|. After how many seconds is your neighbor 30 ft from you?
To find the amount of time it takes for your neighbor to be 30 ft from you, you set up and solve an equation using the given information.
Explanation:To find the amount of time it takes for your neighbor to be 30 ft from you, we need to set up an equation and solve for t. The distance d is given by d = |120 - 4t|. The absolute value represents the distance in one direction, so it does not matter if your neighbor is walking towards you or past you. We want to find when the distance is 30 ft, so we set up the equation 30 = |120 - 4t|.
Solving this equation gives us two possibilities: 30 = 120 - 4t and 30 = -(120 - 4t). We can solve each equation separately.
For the first equation, 30 = 120 - 4t, we subtract 120 from both sides to get -90 = -4t. Dividing both sides by -4 gives us t = 22.5.
For the second equation, 30 = -(120 - 4t), we multiply both sides by -1 to get -30 = 120 - 4t. Subtracting 120 from both sides gives us -150 = -4t. Dividing both sides by -4 gives us t = 37.5.
So your neighbor is 30 ft from you after 22.5 seconds and 37.5 seconds.
A country's population in 1991 was 136 million. In 2000 it was 141 million. Estimate the population in 2016 using the exponential growth formula. Round your answer to the nearest million. ...?
"A 23kg kg child goes down a straight slide inclined 38∘ above horizontal. The child is acted on by his weight, the normal force from the slide, kinetic friction, and a horizontal rope exerting a 30N force as shown in the figure.(Figure 1)
How large is the normal force of the slide on the child?"
Force is simply the pull or push that acts on an object.
The normal force acting on the child is 159.12 N
The forces acting on the child are
The 30 N force at 38 degreesThe weight of the childThe weight of the child along the vertical component is:
[tex]\mathbf{Weight = mg \times cos(theta)}[/tex]
So, we have:
[tex]\mathbf{Weight = 23 \times 9.8 \times cos(38)}[/tex]
[tex]\mathbf{Weight = 177.62}[/tex]
The horizontal component of the 30 N force is:
[tex]\mathbf{F_2 = 30 \times sin (38)}[/tex]
So, we have:
[tex]\mathbf{F_2 = 18.50}[/tex]
The normal force (F) on the child is:
[tex]\mathbf{F = Weight - F_2}[/tex]
[tex]\mathbf{F = 177.62N - 18.50N}[/tex]
[tex]\mathbf{F = 159.12N}[/tex]
Hence, the normal force is 159.12 N
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Three fractions that are equivalent to:
12/36
4/5 and
3/12 ...?
The momentum of a system before a collision is 2.4 × 103 kilogram meters/second in the x-direction and 3.5 × 103 kilogram meters/second in the y-direction. What is the magnitude of the resultant momentum after the collision if the collision is inelastic?
A. 1.7 × 103 kilogram meters/second
B. 2.1 × 103 kilogram meters/second
C. 3.4 × 103 kilogram meters/second
D. 4.2 × 103 kilogram meters/second
E. 5.7 × 103 kilogram meters/second ...?
Answer:
Option D - [tex]4.2\times 10^3[/tex] kilogram meters/second.
Step-by-step explanation:
Given : The momentum of a system before a collision is [tex]2.4 \times 10^3[/tex] kilogram meters/second in the x-direction and [tex]3.5 \times 10^3[/tex] kilogram meters/second in the y-direction.
To find : What is the magnitude of the resultant momentum after the collision if the collision is inelastic?
Solution :
In inelastic,
The magnitude of the resultant momentum after the collision (and before) can be determined by using the Pythagorean theorem.
[tex]c^2 = a^2 + b^2[/tex]
Where, a is the momentum before collision [tex]a=2.4 \times 10^3[/tex]
b is the momentum after collision [tex]b=3.5 \times 10^3[/tex]
c is the total amount of momentum before and after collision.
Substitute the value,
[tex]c^2 = (2.4\times10^3)^2 + (3.5\times10^3)^2[/tex]
[tex]c^2 =5760000+ 12250000[/tex]
[tex]c=\sqrt{18010000}[/tex]
[tex]c=4243.819[/tex]
[tex]c=4.2\times 10^3[/tex] kg m/s
Therefore, Option D is correct.
The magnitude of the resultant momentum after the collision if the collision is inelastic is [tex]4.2\times 10^3[/tex] kilogram meters/second.
On a certain map 3/4 inch represents one mile, what distance, in miles is represented by 1 3/4 inches
a system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions. is this statement true?
Always
Sometimes
Never
I think the answer is Sometimes . X=Y and X^2-Y^2=0 Has infinitely Solutions
Answer:
The statement that says that a system constructed by a linear and a quadratic equation, has infinitely solutions is never true.
Step-by-step explanation:
This situations can be explained more easy by the graphic solution of the system of equations. As we know, a cuadratic equation represents a parabola and the linear equation a line, so the solution of the system can be understood as the interseption od the parabola and the line.
In the attached figure above we expouse the three different cases could hapend. In the first case, we have two interceptions, so 2 solutions. For the second case, we have 1 interseption, which represents one solution. In the third case the line doesnt touch the parabola in any point thus we get no solution.
Therefore in none of the cases explained we found infinite solutions, this situacion can never happens.
In the example the second equation doesnot represents a quadratic equation. A quadratic equation has the form of:
Y = aX^2 + BX + C
Thus the given system cannot be understood as a the example of the kind.
f(x)=2x- 1 what is odd number
In the function y=-2(x-1)^2+4, what effect does the number 4 have on the graph, as compared to the graph of the function y=x^2?
A. It shifts the graph 4 units to the right.
B. It shifts the graph down 4 units.
C. It shifts the graph up 4 units.
D. It shifts the graph 4 units to the left. In the function y=-2(x-1)^2+4, what effect does the number 4 have on the graph, as compared to the graph of the function y=x^2?
A. It shifts the graph 4 units to the right.
B. It shifts the graph down 4 units.
C. It shifts the graph up 4 units.
D. It shifts the graph 4 units to the left.
Answer:
it shifts the graph up four units
Step-by-step explanation:
it shifts the graph up four units because its outside of the phranthasies, in y=a(x+h)k k is the shift vertically
In the function y=-2(x-1)²+4, the number 4 represents a vertical translation, shifting the graph up by 4 units when compared to the function y=x². Option C) is the correct answer.
In the function y=-2(x-1)²+4, the number 4 acts as a vertical translation of the graph. Comparing this function to the standard parabola y=x², the addition of 4 to the equation represents shifting the entire graph of the parabola upwards by 4 units. Therefore, the correct answer to the effect of the number 4 on the graph, as compared to the graph of the function y=x² is: C. It shifts the graph up 4 units.
Understanding graph transformations is key in analyzing how different parts of the function equation affect the function's graphical representation.
A positive constant added to a function results in a vertical shift of the graph in the upward direction. This means that every point on the graph y=x² is moved 4 units higher on the y-axis to create the graph of y=-2(x-1)²+4.
Evaluate the expression –0.4(3x – 2) + for x = 4
Answer:
Step-by-step explanation:
=0
According to Edge. the answer is 0 :)
assume 1 card is drawn from a standard deck of 52 cards.find the probability of drawing a 6 or a face card
I included a photo with the information! Here are the questions. A thorough explanation and diagram would help IMMENSELY. Thank you so much!
Question 1: reate a labeled diagram of the Brick. Use x to represent the length of a side of the base of the candle. Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Question 2: Create a labeled diagram of the Egyptian. Use x to represent the length of a side of the base of the candle. Then write an equation for the volume of the candle in terms of x. Write the polynomial in standard form.
Question 3: 1. To impress management, you decide to propose your own original candle design based on solid figures. Make your candle design attractive and make sure it will be practical to manufacture. Draw the candle in the space below and label the drawing with dimensions. Then write an equation for the volume of the candle in terms of x, where x is a dimension that defines the area of the candle’s base. Write the polynomial in standard form.
Answer:
1) Labeled diagram in the first figure attached
Volume of the rectangular prism: x^2*(x-1) = x^3 - x^2 ; x in cm, volume in cm^3
2) Labeled diagram in the second figure attached
Volume of the right square pyramid: (1/3)*(x^2)*21 = 7*x^2, x in cm, volume in cm^3
3) A cylinder is proposed, where x is the radius of the base and the height is 4 times the radius. Labeled diagram in the third figure attached .
Volume of the cylinder: π*x^2*(4*x) = 4*π*x^3, x in cm, volume in cm^3
help with 8th grade math! will upvote!! <33
Which of these is a simplified form of the equation 8p + 4 = − p + 7 + 2p + 3p?
A. 14p = 11
B. 8 = 4
C. 4p = 3
D. 12 = 13
Which of the statements about the following quadratic equation is true?
6x2 - 8 = 4x2 + 7x
The discriminant is greater than zero, so there are two real roots.
The discriminant is greater than zero, so there are two complex roots.
The discriminant is less than zero, so there are two real roots.
The discriminant is less than zero, so there are two complex roots.
If the discriminant of a quadratic equation is positive then, there are two real roots. Here, the discriminant obtained is 113 which is greater than zero. Hence, option a is correct.
What is quadratic equation ?A quadratic equation are polynomial equation with one variable having the degree of 2. This general form a quadratic equation is written as follows:
ax² - b x + c = 0
The discriminant for a quadratic equation is the term b² - 4ac.
Given the quadratic equation is 6x² - 8 = 4x² + 7 x
it can be rearranged as: 2x² - 7x - 8 =0
If the discriminant of the equation is greater than zero, then there will be two real roots.
solving the discriminant here:
b² - 4ac = (-7)² - 4× 2×(-8) = 113
Here, the discriminant is greater than zero. Therefore, there are two real roots.
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Which expression is equivalent to 3x(-4x^2+5x-8)-6(x^2-5x+7)?
A. 12x^3-9x^2+6x-42
B.-12x^3-54x^2+6x-42
C.-12x^3+9x^2+6x-42
D.-27x^3-6x^2+6x-42
name the property of real numbers illustrated by the equation step by step
-10+4=4+(-10)
Which equation does the graph of the systems of equations solve? It's a quadratic graph opening down and quadratic graph opening up. They intersect at (0,3) and (2,-5).
(a)x2 - 2x + 3 = 2x2 - 8x - 3
(b)x2 - 2x + 3 = 2x2 - 8x + 3
(c)-x2 - 2x + 3 = 2x2 - 8x - 3
(d)-x2 - 2x + 3 = 2x2 - 8x + 3
Answer:
D. [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex]
Step-by-step explanation:
We are given that,
The graph of the system of equations is a 'quadratic graph opening down and a quadratic graph opening up'.
This means that one quadratic equation will have leading co-efficient positive and other will have leading co-efficient negative.
So, we get that options A and B are discarded.
Further it is provided that the graph intersect at ( 0,3 ) and ( 2,-5 ).
This means that the pair of points must satisfy the given system of equations.
So, according to the options:
C. [tex]-x^{2} -2x+3=2x^{2} -8x-3[/tex]
Putting x = 0, gives 3 = -3, which is not possible.
So, option C is dicarded.
D. [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex]
Putting x = 0 gives 3 = 3 and x = 2 gives -5 = -5.
Hence, the graph of the given system solves the equation [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex].
Answer:
(d)-x2 - 2x + 3 = 2x2 - 8x + 3
Step-by-step explanation:
The area of a rectangle is 48 square centimeters and the length of the rectangle is 8 centimeters longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
8w = 48
w + 8 = 48
w(w+8)=48w(w+8)=48
w + 8w = 48
the slope of the line below is 0.8 write the equation of the line in point slope form using the coordinates of the coordinates of the labeled point do not use parenthesis on the y side
Final answer:
The equation of the line in point-slope form is y - y1 = 0.8(x - x1), where the point on the line and the slope are given.
Explanation:
To write the equation of a line in point-slope form, we need the slope of the line and the coordinates of a point on the line. In this case, the slope is given as 0.8. Let's assume the labeled point has coordinates (x, y). The equation in point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the labeled point. Substituting the given slope and the coordinates of the point, the equation becomes:
y - y1 = 0.8(x - x1)
Remember to not use any parentheses on the y side of the equation.
What is the length of arc AB if the radius is 14
How do you solve this one 10x^2-25=x^2
Given the vector "v" and its inital point, find the terminal point:
"v"=<-1,3>;Initial Point:(4,2) ...?
What is the principle for f)? The math is Simple Interest
Answer:
E
Step-by-step explanation: