By using the concept of kinetic energy, it is obtained that
Kinetic energy of the airplane when its velocity is 300 m/s is 20250 megajoule
What is Kinetic energy?
Kinetic energy is the energy possessed by the body by virtue of its motion
If m is the mass of the body and v is the velocity of the body, then kinetic energy is given by the formula
Kinetic energy = [tex]\frac{1}{2} \times m \times v^2[/tex]
Let the mass of the airplane be m kg
Velocity = 220 m/s
Kinetic energy = [tex]\frac{1}{2} \times m \times (220)^2[/tex]
By the problem,
[tex]\frac{1}{2} \times m \times (220)^2 = 10890\times 10^6[/tex]
[tex]m = \frac{10890\times 10^6\times 2}{220\times 220}[/tex]
m = [tex]0.45 \times 10^6[/tex] kg
Now,
Velocity = 300 m/s
Kinetic energy = [tex]\frac{1}{2} \times 0.45 \times 10^6 \times 300 \times 300[/tex]
= [tex]20250 \times 10^6[/tex] J
= 20250 mega joules
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answer the question please i would appreciate it man
The scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
What is scientific Notation?Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
Given:
(0. 00032) (5.2 x [tex]10^6[/tex])/ 6.4 x [tex]10^5[/tex]
Now, solving the above expression
= 0.001664 x 10² / 6.4
= 0.00026 x 10²
= 2.6 x [tex]10^{-2}[/tex]
Hence, the scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
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Heidi thinks the rule for the table below is y = x + 3.
Is she correct?
X
-2
-1
0
1
2
y
-7
-4
-1
2
5
a supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. to do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards. what size should the squares be in order to create a box with the largest possible volume?
The size of the squares should be 3 inches in order to create a box with the largest possible volume.
If squares of equal sizes are to be cut out from the four corners so the four sides can be bent upwards, then the length of these squares will be the height of the box. Also twice of this length subtracted from the initial length and width of the material will be the new length and width of the box, respectively.
let x = length of square to be cut = height of the box
length of the box = 30 - 2x
width of the box = 14 - 2x
The volume of the box, which is a rectangular prism, is the product of the length, height and width.
V = l x w x h
V = (30 - 2x)(14 - 2x)(x)
V = 420x - 88x² + 4x³
To obtain the largest volume possible, the first derivative of the volume should be equal to zero.
V'(x) = 0
V = 420x - 88x² + 4x³
420 - 176x + 12x² = 0
Simplify and solve for the value of x.
12x² - 176x + 420 = 0
3x² - 44x + 105 = 0
(3x - 35)(x - 3) = 0
x = 35/3 ; x = 3
Check each value.
When x = 35/3 = h
l = 30 - 2x = 20/3
w = 14 - 2x = -28/3 ( length should be positive)
When x = 3 = h
l = 30 - 2x = 24
w = 14 - 2x = 8
Hence, the length of square to be cut is 3 in.
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what is the future amount of 12,000 invested for 5 years at 14% compounded monthly?
The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest.
what is compound interest?To begin, change R from a percentage to a decimal, using the formula:
r = R/100 r = 14/100
r = 0.14 rate per year;
Next, find A by solving
A = P(1 + r/n)nt A = 12,000.00(1 + 0.14/12)(12). (5)
A = 12,000.00(1 + 0.011666666666667)(60) (60)
A = $24,067.32
Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.
The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest. You will then be left with the loan balance plus compound interest.
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you have 600 ft of fencing material to construct a rectangular pen for cattle. what are the dimensions (in feet) of the pen that maximize the area (enter number only)?
The dimension of pen that maximize the area is 150 ft by 150 ft.
What is the dimension of a area?
In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
Given the perimeter of the rectangular is 600 ft.
Assume that the length of the rectangular be l and the breadth be b.
The perimeter of the rectangular is 2(l+b).
According the question:
2(l+b) = 600
Divide both sides by 2:
(l+b) = 300
l = 300 - b
The area of rectangular is A = lb
Substitute the value of l in the above equation:
A = (300 - b) b
A = 300b - b^2
The maximum value of a quadratic polynomial Ax^2+BX+C is at x = - B/(2A).
Compare Ax^2+BX+C with 300b - b^2:
A = -1 and B = 300.
Putting A = -1 and B = 300 in b= - B/(2A).
b= - 300/(2×(-1))
b = 150.
Putting b =150 in l = 300 - b
l = 300 - 150
l = 150
The dimension is 150 ft × 150 ft.
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4. The temperature of the water in a pot on the stove is taken every 2 minutes, as shown in the
following chart.
Time (Minutes)
0
2
4
6
8
10
12
14
16
18
20
Temperature (°C)
23.2
25.1
29.2
36.8
42.5
47.6
55.9
62.7
72.4
86.1
98.3
Based on an exponential model of the data, what is the predicted temperature of the water at 7
minutes? Use the Desmos calculator to find your answer. Round your answer to the nearest tenth
of a degree.
(1 point)
Based on an exponential model of the data, the predicted temperature of the water at 7 minutes is 39.7 °C using desmos graphing calculator.
What is an exponential model of the data?Similar to how you discovered linear and quadratic models in prior chapters, exponential models can be found by fitting data to them. As you may already be aware, exponential functions take the form y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time. Based on an equation like this one, the exponential model represents the degradation failure process: Y = deterioration; T = time; A and B = parameters to be calculated using the regression approach based on historical data. An expansion within a population that happens at the same pace across time is represented by the function of exponential growth. It is reasonable to suppose that data grows exponentially as populations double or triple in size.
Graph all the points on a graph. Then from the graph, we can find that at 7 minutes the temperature is 39.7°C.
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Answer: 38.2 degrees
Step-by-step explanation:
enter into desmos
use y1 ~ abx2
then input numbers provided
(22.9178)1.07564^7
equals 38.18049
round 38.2
What is the additive in verse of 16 5/7?
Answer:
the additive inverse of 16 5/7 IS 26/7
engineers must consider the diameters of heads when designing helmets. the company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 0.9-in. due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 1.4% or largest 1.4%. what is the minimum head diameter that will fit the clientele? min
The largest head diameter that can accommodate the clientele is 8.5743
Mean, u = 6.4
Standard deviation = 0.9
We must utilize the inverse of the common normal table to obtain our values.
the smallest head width possible.
P(Z < z) = 1.4%
P(Z < z) = 0.014
P(Z < -2.0749) = 0.014
z = -2.0749
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
We already have:
z = -2.0749
u = 6.5
s.d = 1
Replacing numbers,
x = (-2.0749 × 1) + 6.5
x = 4.4251
The clientele requires a minimum head breadth of 4.4251.
The largest head width that can be accommodated.
P(Z > z) = 1.4%
1 - P(Z < z) = 0.014
P(Z < z) = 1 - 0.014 = 0.981
P(Z < 2.0749) = 0.981
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
z = 2.0749
u = 6.5
s.d = 1
Substituting figures,
x = (2.0749 × 1) + 6.5
x = 4.4251
x = 8.5743
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Which number is greatest?
57
10
O 5. 84
51
√33, 5. 84,
0 5. 7
OV33
51
9
The greatest number among the given numbers is= 57
What are greatest numbers?largest and smallest number formation We are aware of how to list the numbers in both ascending and descending order. The highest number is created by placing the specified digits in ascending order, and the lowest number is created by placing them in descending order, as we have already learned.. A number has more places when the digit at the very left is in that position. Therefore, to increase the value of the number, the largest digit should be positioned at the very left of the number.The digit 0 is never written at the very leftmost position when one of the given digits is 0, but rather in the second place from the left to obtain the smallest number.learn more about greatest numbers click here:
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50 points
Please help
Graph -8+x=4y-16
Equation of the line - 8 + x = 4y - 16
In order to graph the line, find its x- and y- intercepts, then connect the two pointsx- intercept, at y = 0:
- 8 + x = 0 - 16x = - 16 + 8x = - 8y- intercept, at x = 0:
- 8 = 4y - 164y = 16 - 84y = 8y = 2The points are (0, 2) and (- 8, 0), plot them and connect to get the graph.
The graph that connects points (-8,0) and (02) is shown below
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
-8+x=4y-16
x- intercept, at y = 0:
- 8 + x = 4(0) - 16
x = - 16 + 8
x = - 8
y- intercept, at x = 0:
- 8 + 0 = 4y - 16
4y = 16 - 8
4y = 8
y = 2
The points are (-8,0) and (02)
So, the graph that connects points (-8,0) and (02) is shown below
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help meeeeeeeeeeeeeee pleaseee
The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2
The curve opens downward.
from, the graph, the roots of the equation are -4 and 0
so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = [tex]x^{2}[/tex] + 4x
the x coordinate of the vertex = -b/2a = axis of symmetry
where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
substitute x = -2 into y = [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex
y = [tex](-2)^{2}[/tex] + 4(-2)
y = 4 -8
y = -4
vertex is (-2, -4)
The axis of symmetry is -b/2a which is -2
The curve opens downward as the vertex is at -4
In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward
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please give me the right answer on this so I can turn it in to my math teacher
Answer: 16/18 and 10/16
Step-by-step explanation: The least common denominator would be 18 and 16 because you would multiply by 2.
Hoped This Helped!
Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
The equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
According to the question,
We have the following information:
Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
Now, we have the following arithmetic progression with common difference, denoted by d:
22, 22.5, 23, 23.5, ...
Formula used to find the nth term:
an = a+(n-1)d where a is the first term
A) 22+(d-1)0.5 = 30
B) The plant still have to grow 8 cm because the difference between 30 and 22 is 8 cm.
C) Value of d:
22+(d-1)0.5 = 30
22+0.5d-0.5 = 30
21.5+0.5d = 30
0.5d = 30-21.5
0.5d = 8.5
d = 8.5/0.5
d = 17
Hence, the equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
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Kenneth has c toy cars. Jennifer has 3 times as many toy cars as Kenneth. Write an expression that shows how many toy cars Jennifer has.
Answer:
3c
3c mean 3xc
but just write 3c
Referring to the figure, find the perimeter of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Referring to the Fig. in Question #1, find the area of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Answer:
Perimeter = 18√3 = 18SQR(3)
Area = 27√3 = 27SQR(3)
Step-by-step explanation:
The sides of a regular polygon are congruent.
Therefore, as the triangle is a regular polygon, it is an equilateral triangle since its sides (and interior angles) are congruent.
The interior angles of a triangle sum to 180°. Therefore, each interior angle of the equilateral triangle is 60°.
Therefore, the right triangle formed inside the equilateral triangle by the perpendicular bisectors is a 30-60-90 triangle with hypotenuse of 6 units.
The ratio of the side lengths of a 30-60-90 triangle is b : b√3 : 2b, where:
b = shortest side opposite the 30° angle.b√3 = side opposite the 60° angle.2b = longest side (hypotenuse) is opposite the right angle.As the hypotenuse of the 30-60-90 right triangle is 6 units:
[tex]2b = 6 \implies b=3[/tex]
Therefore, the length of the longest leg of the right triangle is 3√3.
As this is half the length of one side of the equilateral triangle:
[tex]\implies \sf Perimeter = 6 \times 3 \sqrt{3}=18\sqrt{3}\; units[/tex]
Heron's Formula allows us to find the area of a triangle in terms of its side lengths.
Heron's Formula
[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
where:
a, b and c are the side lengths of the triangle.s is half the perimeter.Given:
Each side length = 6√3 unitsHalf perimeter = 9√3 unitsSubstitute these values into the Heron's formula to calculate the area of the equilateral triangle:
[tex]\begin{aligned}\implies \sf Area &= \sf \sqrt{9\sqrt{3}(9\sqrt{3}-6\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(3\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(81\sqrt{3})}\\&=\sf \sqrt{2187}\\&=\sf \sqrt{729 \cdot 3}\\&=\sf \sqrt{729}\sqrt{3}\\&=\sf 27\sqrt{3} \;\;units^2\end{aligned}[/tex]
State the value of the two square numbers closest to 55. Hence, show that 55 is not a square number.
Answer:
7.416 is the answer
Please Help!
Solve the inequality and graph it’s solution.
Answer:
Step-by-step explanation:
You have to multiply both sides by 3 so its -9>-5+n. Then add each side by 5. The answer is n<-4 (D)
Answer:
D) n<-4
Step-by-step explanation:
Convert 17 weeks into days
Answer:
119days
Step-by-step explanation:
1 week= 7 days
take week as w
so 1w=7 or w=7
now 17 weeks=??
17w=??
w=7 so input in above statement:
17(7)=119days
Answer: 119 days
Step-by-step explanation:
We can set up a dimensional analysis problem to solve.
[tex]\displaystyle 17 \;\text{weeks}\;(\frac{7\;\text{days}}{1\;\text{week}} )[/tex]
The units of [tex]\frac{weeks}{weeks}[/tex] cancel out, leaving us with days. Since we are being asked to find days, this will leave us at the right point.
[tex]\displaystyle \frac{17*7}{1} =119\;\text{days}[/tex]
The Venn diagam represents the
information from the following sets.
= {Prime numbers less than 38}
R = {2, 3, 5, 17, 19, 37}
S = {3, 5, 7, 11, 13, 37}
R
17 5
2
19 37
3/13
S
11
231 23
Find P(RUS)
P(RUS) =
=======================================================
Explanation:
The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.
R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 17, 19, 37, 3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}
This list of values consist of items in set R, set S, or both.
There are 9 items in set R U S.
This is out of 12 items total in the universal set rectangle.
The probability of randomly selecting something from set R U S is 9/12 = 3/4
a campus radio station surveyed 500 students to determine the types of music they like. the survey revealed that 206 like rock, 161 like country, and 118 like jazz. moreover, 30 like rock and country, 27 like rock and jazz, 22 like country and jazz, and 11 like all three types of music. what is the probability that a randomly selected student likes jazz or country but not rock? note: a venn diagram may be useful here. a) 0.400 b) 0.300 c) 0.522 d) 0.262 e) 0.422 f) none of the above.
The probability that a randomly selected student likes neither rock nor country is taken as;
P(R' ∩ C') = 0.326
Let us denote them as follows;
Number that like to be rock music be - R
Number that like to be Country music be - C
Number that like to be Jazz music be - J
Thus, as we are given and we have;
R is equal to 206
C is equal to 161
J is equal to 118
P(R') =206
P(C') =161
P(R' ∩ C') = 0.326
So, now P is removed
R ∩ C = 30 - 11 = 1
Hence the answer is none of the above
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Karl bought 1.6 pounds of oranges and 2.4
pounds of pears. They each cost $1.48 per pound
Use properties to find the total cost.
Answer:
$5.92
Step-by-step explanation:
1.6 lbs. + 2.4 lbs. = 4 lbs.
4 x 1.48 = 5.92
Since it doesn't specify whether the oranges and apples cost differently you can add both of them. Then you multiply it by 1.48 because that's the cost per pound.
help ? please, thank you !
Answer:
3 feet
1ft:2ft
Step-by-step explanation:
3ft/12 inches
12 inches= 1 foot
We can simplify the denominator by turning 12 inches into 1 foot
3/1
And then we divide to make 3 feet
The width of the rectangle is 12 inches and the length is 2 feet so the ratio is
12 in.:2 ft
12 inches can be simplified to 1 foot
1 ft: 2 ft
And it is simplified as much as possible
Hopes this helps please mark brainliest
Write this ratio another way.
120/150
The ratio 120/150 represented in the simplest form is 4 : 5 .
The given ratio is 120 /150 .
Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.
The HCF of the number is 30. Hence the ratio in simplest form will be
120÷30 : 150÷30 = 4 : 5 .
By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.
Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.
Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.
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According to a report for veterinarians in the united states, 36. 5 percent of households in the united states own dogs and 30. 4 percent of households in the united states own cats. If one household in the united states is selected at random, what is the probability that the selected household will own a dog or a cat?.
I NEED HELP PLEASEEEEE ASAPPPPPPP
Answer:
7x+40=180
Step-by-step explanation:
(5x+40)+(2x)=180
7x+40=180
if you were to solve
subtract 40 from each side
7x=140
divide both sides by 7
x=20
check your answer
5(20)+40+2(20)=180
100+40+40=180
this is correct
hope this helps..and with future questions if you need to solve it
To find BCD
we know that C is 40 degrees and we know that triangle is also 180
we can also see that B is a right triangle or 90 degree
so 90+40+A=180
130+A=180
subtract 130 from 180
A=50
Help me for this question
can you give me an answer i don't know how to do this
Answer:
It should be ≈ 6,6
calculated the angle <CAB and both are 90°. But that would mean BC is wrong
Jamie has a table top that he wants to cover in contact paper. The table top has the following dimensions. Length: 3.5 ft. Width: 3.5 ft. Height: 0.25 ft. How many square feet of contact paper does he need to cover the entire table top?
The area of the contact paper required to cover the entire tabletop is 12.25 square feet.
Jamie has a tabletop that he wants to cover with contact paper. The length, width, and height of the tabletop are 3.5 feet, 3.5 feet, and 0.25 feet, respectively. We need to calculate the area of the contact paper required to cover the entire tabletop.
Let the area of the tabletop be represented by the variable "A". We need to calculate the area of only the top surface of the table. The table is rectangular in shape. The area of the tabletop must be the product of the length and the width of the table.
A = 3.5×3.5
A = 12.25
Hence, the area of the tabletop is 12.25 square feet.
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hi i need some help with this math problem
1 is value of x in given function.
What is the definition of a function?
An association between a value from the set of the first components of the ordered pairs and a specific value from the set of the second components is known as a function. a relationship between a set of inputs and a set of potential outputs, where each input is connected to only one possible output.f(x) = 2x + 4/6
put x = - 2 in equation
f(-2) = 2 * -2 + 4 /6
= -4 + 4 /6
= 0/6
= 1
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1 can go on saturday and 14 can go on sunday; some of them can go on both days. how many people can only go to the game on saturday? 6
Answer:
No solution
Step-by-step explanation:
The reason why I say this problem has no solution is due to the fact that it says only one person may go on Saturday yet some fraction of the people between the numbers 1 - 14 can go. We have no idea what this fraction is, leading to a paradox of multiple equations and guesses desperately trying to figure out the number. Thus, the problem has no solution.
Hope this helps.