Answer:
10cm/s²
Step-by-step explanation:
Acceleration is the change in velocity of an object with respect to time.
Given velocity v(x) to be x³-2x+6
Acceleration = ∆v/∆x
Differentiating the velocity function to get acceleration we have,
Acceleration = dv/dt = 3x²-2
Acceleration of the particle at x = 2 will give;
dv/dt @ x = 2 is 3(2)²-2
= 12-2 = 10cm/s²
Based on their standard deviations, compare the tomatoes produced by the two varieties. Choose the correct answer below. A. Both varieties of tomatoes have similar consistency in their weights. B. The old tomatoes are more consistent in their weights than the new tomatoes. C. The new tomatoes are more consistent in their weights than the old tomatoes. D. While the new tomatoes are more consistent in their weights than the old tomatoes, the distribution of weights of the new tomatoes is left skewed.
Answer:
C. The new tomatoes are more consistent in their weights than the old tomatoes.
Context:
Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that averages 74 grams, but 11% of the tomatoes are too small. It is reasonable to assume that a Normal model applies.
The question is asking to compare the consistency of weights in two types of tomatoes based on their standard deviation. Select the option that best fits the standard deviation calculated for each group.
Explanation:In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of values. A lower standard deviation means that the values tend to be close to the mean (average) value of the set, while a higher standard deviation implies that the values are spread out over a wider range. The question asks you to compare the consistency in weight between two types of tomatoes, determined by their standard deviations.
If the standard deviation of the old tomatoes' weight is lower than that of the new ones', option B ('The old tomatoes are more consistent in their weights than the new tomatoes') would be accurate. On the other hand, if the opposite is true, option C ('The new tomatoes are more consistent in their weights than the old tomatoes') would be correct. Option A would be right if the standard deviations are similar, indicating similar consistency, and option D would apply if along with the new tomato weights being more consistent, their weight distribution is left skewed.
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A three-phase lesson format provides a structure for students to have inquiry on a topic, engage in the content through action and discussion and time to reflect and make connections. What statement below demonstrates the Before related agendas?
A) Be sure the task is understood.
B) Let go
C) Provide extensions.
D) Identify future problems.
Answer:
A) Be sure the task is understood.
Step-by-step explanation:
The principle "Make sure the mission is understood, performed, and achieved."
Another way we talk about this principle in the Navy is through the idea of "intrusive leadership." In some respects both "micromanagement" and "intrusive leadership" sound terrible.
Think about certain great managers and leaders you have had in your career yet again. Probability are they will be the ones who asked you those difficult questions, too.
They moved everyone to new technical levels, and eye for detail. When you said you knew what you were doing or when you announced the progress of a project, they didn't necessarily take it to face value.
A pizza chain was willing to pay $1 to each person interviewed about his or her likes and dis- likes of types of pizza crust. Of the people interviewed, 200 liked thin crust, 270 liked thick crust, 70 liked both, and 50 did not like either type of crust. What was the total cost of the survey?
Answer:
Total cost of the survey = $450
Step-by-step explanation:
Given:
Cost for each person = $1
Liked thin crust = 200 people
Liked thick crust = 270 people
Both crust like = 70 people
50 people did not like either type of crust.
We need to find the total cost of the survey.
Solution:
Number of people who like thin crust or thick crust.
⇒ 200 + 270 - 70
⇒ 470 - 70
⇒ 400
So, 400 people likes thin crust OR thick crust.
And, also 50 peoples did not likes either thin crust OR thick crust.
So, we add 50 people who did not like any type of pizza.
⇒ 400 + 50
Therefore, total cost of the survey = $450
A certain solution of salt water is 10% salt and weighs 50 pounds. more salt must be added to produce a solution that is 25% salt. if x represents the pounds of salt to be added, which of the following expressions represents the number of pounds of salt in the 25% solution?
a) 0.25 (x+50)
b) 0.25x
c) 1.25 (x+50)
Answer
7.5 pounds
Step-by-step explanation:
Since adding x grams of salt will bring th percentage of the salt to 25
Hence. 10% of the 50 gram gives. 5 gram initial salt before it is added.
5+ x/ 50 * 100= 25/
5+x /50 = 0.25
5+x = 12.5
X= 12.5- 5
X= 7.5pounds
Ethan went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 35 grams of sugar. Ethan purchased a total of 19 bottles of juice and soda which collectively contain 755 grams of sugar. Determine the number of bottles of soda purchased and the number of bottles of juice purchased.
9 bottles of soda and 10 juice bottles are purchased
Solution:
Given that,
Sugar contained by each soda bottle = 45 grams
Sugar contained by each juice bottle = 35 grams
Let,
x be the number of soda bottles
y be the number of juice bottles
Given that,
Ethan purchased a total of 19 bottles of juice
Therefore, we get,
x + y = 19 ---------- eqn 1
Ethan purchased a total of 19 bottles of juice and soda which collectively contain 755 grams of sugar
Therefore, we frame a equation as:
[tex]45 \times x + 35 \times y = 755[/tex]
45x + 35y = 755 --------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 19 - y --------- eqn 3
Substitute eqn 3 in eqn 2
45(19 - y) + 35y = 755
855 - 45y + 35y = 755
10y = 100
y = 10
Substitute y = 10 in eqn 3
x = 19 - 10
x = 9
Thus 9 bottles of soda and 10 juice bottles are purchased
Study Island: Gina has 24 more barrettes than Holly. The equation g = 24 + h, where g represents the number of barrettes Gina has, and h represents the number of barrettes Holly has, shows this relationship. If Gina has 51 barrettes, how many barrettes does Holly have?
See picture for solution and answer.
If 6 is added to twice a number and this sum is multiplied by 5, the result is the same as if the number is multiplied by negative 3 and 4 is added to the product
Answer:
-2
Step-by-step explanation:
We assume you want to find the number. Let it be represented by x.
(6+2x)·5 = -3x +4 . . . . . the meaning of the problem statement
30 +10x = -3x +4 . . . . . eliminate parentheses
26 +13x = 0 . . . . . . . . . add 3x-4 to both sides
2 + x = 0 . . . . . . . . . . . . divide by 13
x = -2 . . . . . . . . . . . . . . subtract 2
The number is -2.
If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur.
P(A) =0.54
P(B)= 0.68
P'(A)= 1-0.54 = 0.46
P'(B)= 1- 0.68 = 0.32
The probability of neither of both event will occur:
= P'(A)×P'(B)
=0.46 × 0.32
=0.1472
the recommended daily intake rdi a nutrients supplement for a certain age group is 800 mg per day actully supplements needs vary from person to person which absolute value inequality expresses the rdi plus or minus 50 mg
a. |x-800|≥50
b. |50-x|≤800
c. |x-800|≤50
d. |x-50|≤800
Answer:
C
Step-by-step explanation:
The recommended daily intake of a nutrients supplement for a certain age group is 800 mg per day.
Actully supplements needs vary from person to person plus or minus 50 mg.
This means the minimum value is 800 - 50 = 750 mg per day and the maximum value is 800 + 50 = 850 mg per day.
Let x mg be a possible daily amount of nutrients supplement. Then
[tex]750\le x\le 850[/tex]
Subtract 800:
[tex]750-800\le x-800\le 850-800\\ \\-50\le x-800\le 50[/tex]
This inequality can be rewritten using absolute value notation as
[tex]|x-800|\le 50[/tex]
Suppose you are choosing between two roads. The first route is 40 miles at 25 mph, and the second road is 65 miles at 55 mph. Which route would get you there faster, and in what amount of time?
The second route, in 1.6 hours
B. The first route, in 1.6 hours
C. The first route, in 1.18 hours
D. The second route, in 1.18 hours
Answer:
D. The second route, in 1.18 hours
Step-by-step explanation:
The appropriate relation is ...
time = distance/speed
The time required on the first route is ...
time1 = (40 mi)/(25 mi/h) = 40/25 h = 1.6 h
The time required on the second route is ...
time2 = (65 mi)/(55 mi/h) = 65/55 h = 1 2/11 h ≈ 1.18 h
__
The second route requires a shorter time, so will get you there faster. The second route will get you there in 1.18 hours.
A graduated cylinder with 10.0 mL of water ha mass of 25.0 g. 51 paper clips are added to the graduated cylinder . The total mass is 28 and the total volume is 14.7. What is the density of the paper clips? (Calculate your answer to 2 decimal places)
Answer: The density of the paper clips is 0.64 g/ml.
Step-by-step explanation:
Given : Volume of water = 10.0 mL
mass of water = 25.0 g
After 51 clips added to water , the total mass = 28 g
Total volume = 14.7
Mass of clips = total mass - mass of water
= 28 g-25g = 3g
Volume of clips = Total volume- Volume of water
= 14.7- 10.0 = 4.7 ml
Density of paper clips =[tex]\dfrac{\text{Mass of paper clips}}{\text{Volume of paper clips}}[/tex]
[tex]=\dfrac{3}{4.7}=0.638297\approx0.64\ g/ml[/tex]
Hence, the density of the paper clips is 0.64 g/ml.
Answer:
The density of the paper clips is 0.64 g/m
Step-by-step explanation:
hope this helps :)
A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the smaller Ghirardelli's bar?
Answer:A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the - 1468665…
Step-by-step explanation:A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the smaller Ghirardelli's bar?
The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3,945. If an airline charges passenger a fare of $95 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. P(x) = Specify the domain. 0 lessthanorequalto x lessthanorequalto infinity 0 lessthanorequalto x lessthanorequalto 295 0 < x < 295 295 lessthanorequalto x lessthanorequalto infinity What is the least number of passengers it must carry to make a profit? The Metropolitan Company sells its latest product at a unit price of $3. Variable costs are estimated to be 50% of the total revenue, while fixed costs amount to $6,600 per month. How many units should the company sell per month to break even, assuming that it can sell up to 5,000 units per month at the planned price? units
Answer:
42 passengers 4400 unitsStep-by-step explanation:
Please refer to the picture below
a. Is the statement "Every elementary row operation is reversible" true or false? Explain. A. True, because interchanging can be reversed by scaling, and scaling can be reversed by replacement. B. False, because only scaling and interchanging are reversible row operations. C. True, because replacement, interchanging, and scaling are all reversible. D. False, because only interchanging is a reversible row operation.
The statement "Every elementary row operation is reversible" is true because interchanging can be reversed by scaling, and scaling can be reversed by replacement (Option A is correct).
The statement "Every elementary row operation is reversible" is true.
The correct choice is: A. True, because interchanging can be reversed by scaling, and scaling can be reversed by replacement.
- Interchanging rows (row swapping) can be reversed by another interchange.
- Scaling a row by a non-zero scalar can be reversed by scaling it by the reciprocal of that scalar.
- Replacement operations (adding or subtracting multiples of one row from another) can also be reversed by adding or subtracting the same multiples in the opposite direction.
So, all three elementary row operations (replacement, interchanging, and scaling) are reversible, which makes option A the correct choice.
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The statement 'Every elementary row operation is reversible' is true. All the three types of elementary row operations, i.e., scaling, interchanging, and replacement, can be reversed using appropriate methods.
Explanation:The statement 'Every elementary row operation is reversible' is indeed true. The three types of elementary row operations, i.e., scaling, interchanging, and replacement, are all reversible. Scaling can be reversed by multiplying the row by the reciprocal of the scale factor. Interchanging rows can be undone by simply interchanging them again. Replacement can be reversed by applying a replacement operation with the opposite sign.
For example, if you multiply a row by a factor of 3 (scaling), you can reverse this by multiplying the row by 1/3. If you interchange row 1 and row 2, you can reverse this by interchanging these two rows again. Finally, if you replaced row 1 by adding 2*row 2 to it, you could reverse this by replacing row 1 by subtracting the same 2*row 2 from it.
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Write a formula that describes the value of an initial investment of $1,200, growing an interest rate of 4% compounded continuously.
Continuous compound is e^rate x time
The formula would be D. 1200e^0.04t
Answer: OPTION D A = 1200.e(0.04)(t)
Step-by-step explanation:
If the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by:
A = P. e rt
P =$1200, r = 4% , t = t years
A = 1200.e(0.04)(t)
A garden supply store sells two types of lawn mowers. Total ales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.
Write and solve a system of equations to find the number sold of each type of mower.
Answer:
The number of small mowers are 19 and the large mowers are 11.
Step-by-step explanation:
Given:
A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.
Now, to find the number of each type of mower sold.
Let the number of small mower be [tex]x.[/tex]
And the number of large mower be [tex]y.[/tex]
So, total number of mowers are:
[tex]x+y=30[/tex]
[tex]x=30-y\ \ \ ....(1)[/tex]
Now, the total sales of mowers are:
[tex]249.99(x)+329.99(y)=8379.70[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]249.99(30-y)+329.99y=8379.70[/tex]
[tex]7499.7-249.99y+329.99y=8379.70[/tex]
[tex]7499.7+80y=8379.70[/tex]
Subtracting both sides by 7499.7 we get:
[tex]80y=880[/tex]
Dividing both sides by 80 we get:
[tex]y=11.[/tex]
The number of large mower = 11.
Now, to get the number of small mowers we substitute the value of [tex]y[/tex] in equation ( 1 ):
[tex]x=30-y\\x=30-11\\x=19.[/tex]
The number of small mower = 19.
Therefore, the number of small mowers are 19 and the large mowers are 11.
What is the pressure difference Δp=pinside−poutside? Use 1.28 kg/m3 for the density of air. Treat the air as an ideal fluid obeying Bernoulli's equation.
This is an incomplete question, here is a complete question.
A hurricane wind blows across a 7.00 m × 12.0 m flat roof at a speed of 150 km/h.
What is the pressure difference Δp = p(inside)-p(outside)? Use 1.28 kg/m³ for the density of air. Treat the air as an ideal fluid obeying Bernoulli's equation.
Answer : The pressure difference will be, [tex]1.11\times 10^3Pa[/tex]
Step-by-step explanation :
As we are given:
Speed = 150 km/h = 41.66 m/s
Density = [tex]\rho=1.28kg/m^3[/tex]
Area = A = 7.00 m × 12.0 m
Formula used :
[tex]\Delta P=\frac{1}{2}\times \rho \times v^2[/tex]
Now put all the given values in this formula, we get:
[tex]\Delta P=\frac{1}{2}\times (1.28kg/m^3)\times (41.66m/s)^2[/tex]
[tex]\Delta P=1.11\times 10^3Pa[/tex]
Thus, the pressure difference will be, [tex]1.11\times 10^3Pa[/tex]
Please help!!! I will mark you brainliast
Answer:5 sqrt(2)
Step-by-step explanation:
All the sides of the square are congruent by the markings. Therefore they all measure 5 and because all 4 sides are congruent it is a square. Because it is a square the corners are right angles and you can use the Pythagorean Theorem. a^2 +b^2 = c^2.
5^2 + 5^2 = x^2
25 + 25 = x^2
50= x^2
X = square root of 50
X= square root of 25 Times Square root of 2
X= 5square root of 2
Answer: 5 sqrt (2)
Step-by-step explanation:
ABCD is a square
BCD is a triangle
BC=DC=5
To find DB
Let BC= a, DC=b, BD=c.
using Pythagoras Theorem in Triangle BCD
c2 = a2+b2
c2 = 52+52
c2= 25+25
c= √(50)
c2= √(25)×√ (2)
c= √(5× 5) √(2)
c= 5√(2) or c=5sqrt(2)
Rmbr, Let BC= a, DC=b, BD=c.
The point P(21,35) is on the terminal side of an angle in standard position. What is the distance from P to the origin?
Answer:
The distance from P to origin is approximately 40.82 units.
Step-by-step explanation:
We are given the following in the data:
The point P(21,35)
We have to find the distance of point P from the origin.
Coordinates of origin: (0,0)
Distance formula:
[tex](x_1,y_1),(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Putting the values, we get,
[tex](21,35), (0,0)\\\\d = \sqrt{(0-21)^2 + (0-35)^2} = \sqrt{1666} = 7\sqrt{34} \approx 40.82\text{ units}[/tex]
The distance from P to origin is approximately 40.82 units.
Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can't recall the brand name and does not wish to return home to find the old can of paint. So she selects two of the three brands of paint at random and buys them. Her husband also goes to the paint store and fails to remember what brand to buy. So he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband's selections independent of his wife's selections
The probability that both the woman and her husband fail to get the correct brand of paint is 4/9.
Explanation:To determine the probability that both the woman and her husband fail to get the correct brand of paint, we need to consider the probability of each event happening independently. Since the woman selects two brands at random out of the three available, the probability of her not getting the correct brand is 2/3. Similarly, the husband also selects two brands at random out of the three, so his probability of not getting the correct brand is also 2/3. Since the events are independent, we can multiply the probabilities together to get the probability that both fail to get the correct brand. Therefore, the probability is (2/3) * (2/3) = 4/9.
The husband's selections are independent of his wife's selections because each brand he chooses is not influenced by the brands his wife chooses. Regardless of what she selects, he still has three brands to choose from and selects two at random. This means that his probability of not getting the correct brand is the same regardless of his wife's choices.
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How does the Pythagorean Theorem relate to trigonometric ratios? What is important to remember about coterminal angles and their trigonometric function values?
Answer:
How Pythagoras theorem relates to Trigonometry ratios
For a right angled triangle ∆ABC,
Let a = hypothenus
b = opposite
c = adjacent
Sin²θ + Cos²θ = 1
Provided that a² + b² = c²
To prove this divide through by c²
Tongive
a²/c² + b²/c² = c²/c²
Sinθ = a/c , Cosθ = b/c
So, the above equation becomes
(Sinθ)² + (Cosθ)² = 1
Sin²θ + Cos²θ = 1
Coterminal Angles
Coterminal Angles are angles who share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.
Final answer:
The Pythagorean Theorem and trigonometric ratios are related through the relationships between the sides of a right triangle. The theorem helps to calculate the sides involved in defining the sine, cosine, and tangent functions. Coterminal angles share the same trigonometric values despite having different measurements.
Explanation:
The Pythagorean Theorem is intimately related to trigonometric ratios, as it provides the fundamental relationship between the sides of a right-angled triangle. In trigonometry, the ratios of these sides define sine, cosine, and tangent functions. The Pythagorean theorem states that a² + b² = c², where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse of a right triangle. For example, given an angle θ within the right triangle, the cosine of θ is the adjacent side over the hypotenuse (cos(θ) = a/c), which implicitly uses the Pythagorean relationship when solving for the hypotenuse 'c'.
It's also important to remember coterminal angles in trigonometry, which are angles that share the same terminal side. Coterminal angles can be found by adding or subtracting whole multiples of 360° (or 2π radians). Although coterminal angles are different in measure, they have the same sine, cosine, and tangent values because these trigonometric functions are based on the position of the terminal side, not the actual angle measurement. Hence, coterminal angles have identical trigonometric function values.
Which of the following represents a direct variation?
y=2/x
y = -3x
y = x2 – 2x + 5
y=square root x
Answer:
Direct variation is constantly proportional (constant multiple)
Answer:
a) y = - 1/2 x
Step-by-step explanation:
The equation that represents a direct variation is y = -3x. So, correct option is B.
A direct variation is a relationship between two variables where one is a constant multiple of the other. In other words, as one variable increases or decreases, the other also increases or decreases in a consistent manner. The equation for direct variation is typically of the form y = kx, where k is the constant of variation.
Let's analyze each given equation:
y = 2/x - This equation does not represent a direct variation because y is not a constant multiple of x.
y = -3x - This equation does represent a direct variation because y is a constant multiple of x. Here, k (the constant of variation) is -3.
y = x² - 2x + 5 - This equation is a quadratic equation, not a direct variation, as it involves x raised to a power greater than 1.
y = √x - This equation does not represent a direct variation as y is not a constant multiple of x.
So, the equation that represents a direct variation is option 2) y = -3x. It has a direct relationship between y and x with a constant of variation of -3.
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The sketch shows the floor plan of a bathroom. The shower tray is 2'6" square and is
fixed to the floor. The toilet and washbasin are both wall mounted.
14) Allowing for 15% wastage, approximately how many square yards of floor tiles should
be ordered?
A
7.25
B
6.25
C
9.25
D
5.50
E
8.50
1.
A 0.40 kg football is thrown with a velocity of 15 m/s to the right. A stationary receiver
catches the ball and brings it to rest in 0.20 s. What is the force exerted on the ball by
the receiver?
Yo sup??
From Newton's 2nd law of motion
F*t=Δp
=mv-mu
mu=0.4*15
=6
t=0.2
mv=0
Therefore
F*0.2=6
F=30 N
Hope this helps.
A snail starts at the bottom of a well 20 feet deep and crawls up 4 feet each day. However, each night as it sleeps, the poor snail slips back 3 feet. How long will it take the snail to get out of the well?
Answer:
20days
Step-by-step explanation:
The daily progress is 4ft - 3ft = 1ft
20ft/1ft = 20days
The snail will take 20 days to get out of the well.
Explanation:To find out how long it will take the snail to get out of the well, we need to determine how many days it takes for the snail to climb a distance of 20 feet. Each day, the snail climbs 4 feet but slips back 3 feet at night. So, the net distance the snail covers each day is 4 - 3 = 1 foot.
Dividing the total distance of 20 feet by the net distance covered each day (1 foot), we find that it will take the snail 20 days to get out of the well.
Hence, the snail will take 20 days to get out of the well.
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HELP ASAP!!! will give brainliest to best answer!!
What proportional segment lengths verify that XZ¯¯¯¯¯∥PQ¯¯¯¯¯ ?
Fill in the boxes to correctly complete the proportion.
Answer:
[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]
or
[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]
Step-by-step explanation:
we know that
If two figures are similar then the ratio of its corresponding sides is proportional
In this problem
triangle YPQ and triangle YXZ are similar by AA Similarity Theorem
so
[tex]\frac{YP}{YX}=\frac{YQ}{YZ}[/tex]
substitute the given values
[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]
Rewrite
[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]
The boxes should be filled with [tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]
The calculation is as follows:As we know that
In the case when two figures are similar so the ratio of its corresponding sides is proportional
In this given situation
triangle YPQ and triangle YXZ are similar by AA Similarity Theorem
So,
[tex]\frac{YP}{YX} = \frac{YQ}{YZ}[/tex]
[tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]
It can be any of the both.
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A plane travels 240 miles on a bearing of N 10° E and then changes its course to N 67° E and travels another 180 miles. Find the total distance traveled north and the total distance traveled east. (Round each answer to the nearest whole number.)
Answer:
Step-by-step explanation:
Given
Plane travels 240 miles [tex]10^{\circ}[/tex] East of North
Position vector [tex]\vec{r_1}=240(\cos(10)\hat{j}+\sin (10)\hat{i})[/tex]
Then the plane travels 180 miles [tex]67^{\circ}[/tex] East of North
[tex]\vec{r_{21}}=180(\cos(67)\hat{j}+\sin (67)\hat{i})[/tex]
[tex]\vec{r_2}=\vec{r_{21}}+\vec{r_1}[/tex]
[tex]\vec{r_2}=\left ( 240\sin (10)+180\sin (67)\right )\hat{i}+\left ( 240\cos (10)+180\cos (67)\right )\hat{j}[/tex]
[tex]\vec{r_2}=\left ( 207.36\right )\hat{i}+\left ( 306.68\right )\hat{j}[/tex]
Total distance traveled in North direction is given by coefficient of \hat{j}
i.e. North[tex]=306.68\ miles\approx 307\ miles[/tex]
Total distance traveled in East direction is given by coefficient of \hat{i}
East [tex]=207.36\ miles\approx 207\ miles[/tex]
A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 24 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible?
To maximize the area of the Norman window, solve for the dimensions of the rectangle. Substitute the expression for 'h' in terms of 'w' into the area formula. Take the derivative of A with respect to 'w', set it equal to zero, and solve for 'w'.
Explanation:To maximize the area of the Norman window, we need to find the dimensions of the rectangle. Let's denote the width of the rectangle as 'w' and the height as 'h'. The perimeter of the rectangle can be expressed as 2w + h + πh = 24 feet. Rearranging the equation, we have (2 + π)h + 2w = 24. Since we want to maximize the area, we can solve for 'h' in terms of 'w' using this equation.
Next, we can substitute the expression for 'h' in terms of 'w' into the area formula for the window, which is A = wh + (π/4)w^2. Simplifying this expression, we get A = (w(2 + πw))/4. To find the dimensions that maximize the area, we can take the derivative of A with respect to 'w', set it equal to zero, and solve for 'w'. This will give us the width of the rectangle. Once we have the width, we can substitute it back into the equation for 'h' to find the height.
By solving these equations, we can find the dimensions of the rectangle that will maximize the area of the Norman window, allowing in as much light as possible.
having trouble with this and 3 others (part 3)
Answer:
a.) 23
b.) y=14
c.) 23
d.) -23
e.) T=8
f.) f=1/8
Step-by-step explanation:
a.) general equation is Asin((2π/T))
A is the amplitude. It's A value is 23
b.) Midline = vertical_shift = 14
c.) max = positive amplitude value = 23
d.) min = negative amplitude = -23
e.) Factor out 2π from your angular frequency to get the period.
ω = π/4 = (2π)/8 = (2π)/T
Period = 8
f.) Frequency is just the inverse of the period.
f = 1/T = 1/8
What is the area of this figure? Enter your answer in the box. units² points on graph are (-2,3) (-4,5) (-5,3) (-3,-3) (4,-3) (3,4) (4,3) WILL MARK BRAINLIEST 50 POINTs
Answer:
A: -4,3 The x coordinate of the vertex is given by x = -b/2a and the y coordinate of the vertex is given by y= f( -b/2a), we need to transform the equation to the form ax^2 + bx + c We have: 5(x+4)^2+3 = 5x^2+ 20x + 23 Then we substitute x= -20/2*5 y= f(-20/2*5) = -4 = f(-4) =3 So V(-4,3)
Step-by-step explanation:
Answer:
I still dont get what the answer is
Step-by-step explanation: