To find the span of the bridge, or the length of its minor axis, we use the equation for an ellipse with the given dimensions and solve for 'b'. Then, we multiply 'b' by 2 to find the total span.
To determine the span of the bridge, or the length of its minor axis, we know that the top of the arch (which coincides with the semi-major axis) is 35 feet above the ground and the height is 15 feet above the ground at a distance of 27 feet from the center. The equation for an ellipse with a vertical major axis is:
(x^2/b^2) + (y^2/a^2) = 1where 'a' is the semi-major axis and 'b' is the semi-minor axis. Since the total height is 35 feet, the semi-major axis, 'a', is 35/2 = 17.5 feet. The distance of 27 feet from the center to the point where the height is 15 feet can be plugged into the equation with 'y' being the remaining height from that point to the top of the arch:
(27^2/b^2) + ((35-15)^2/(17.5)^2) = 1Upon calculating and rearranging the terms, we have:
b^2 = 27^2 / (1 - 400/306.25)Rounding 'b', the semi-minor axis, to two decimal places will give us the span of the bridge which is twice 'b' because it's a complete minor axis.
To find the span of the bridge (the length of its minor axis), we first need to determine the equation of the ellipse.
The standard equation of an ellipse with the center at the origin and the major axis along the x-axis is:
[tex]\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \][/tex]
Where \( a \) is the semi-major axis (half of the major axis) and [tex]\( b \)[/tex] is the semi-minor axis (half of the minor axis).
Given that the top of the arch is 35 feet above the ground (the major axis) and the height 27 feet from the center is to be 15 feet above the ground, we can set up the following system of equations:
1. When [tex]\( y = 0 \)[/tex] (ground level), [tex]\( x = a \)[/tex]
2. When [tex]\( y = 27 \)[/tex] (height above the center), [tex]\( x = 15 \)[/tex]
Using these conditions, we can solve for [tex]\( a \) and \( b \):[/tex]
[tex]1. \( \frac{a^2}{a^2} + \frac{0}{b^2} = 1 \)2. \( \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \)[/tex]
Solving equation 1 for[tex]\( a \):[/tex]
[tex]\[ \frac{a^2}{a^2} = 1 \]\[ a = a \][/tex]
Solving equation 2 for [tex]\( b \):[/tex]
[tex]\[ \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \]\[ \frac{225}{a^2} + \frac{729}{b^2} = 1 \]\[ \frac{729}{b^2} = 1 - \frac{225}{a^2} \]\[ b^2 = \frac{729a^2}{a^2 - 225} \]\[ b = \sqrt{\frac{729a^2}{a^2 - 225}} \][/tex]
We already know that [tex]\( a = 35 \)[/tex](since it's the distance from the center to the top of the arch).
[tex]\[ b = \sqrt{\frac{729 \times 35^2}{35^2 - 225}} \][/tex]
Now we can calculate [tex]\( b \):[/tex]
[tex]\[ b = \sqrt{\frac{729 \times 1225}{1225 - 225}} \]\[ b = \sqrt{\frac{893025}{1000}} \]\[ b ≈ \sqrt{893.025} \]\[ b ≈ 29.88 \][/tex]
So, the span of the bridge (the length of its minor axis) should be approximately 29.88 feet, rounded to two decimal places.
Allie is waiting to be tall enough to ride the thunder dragon roller coaster. You have to be at least60 inches to ride. Write this situation as an inequality
Answer:
[tex]x\geq 60[/tex] where x denotes height of Allie
Step-by-step explanation:
An inequality compares two values. One value is less than, greater than, or not equal to another value.
Given: Allie is waiting to be tall enough to ride the thunder dragon roller coaster. You have to be at least 60 inches to ride.
To write: an equality
Solution:
Let the height of Allie be x inches.
As a person has to be at least 60 inches to ride,
the inequality can be [tex]x\geq 60[/tex]
QUICK FIRST GETS BRAINLIEST!!!!! Use the interactive spinner to model who among Elisondra and her three friends will order first.
Then answer the questions:
What is the theoretical probability of the spinner landing on Elisondra’s section?
Spin the spinner.
Who orders first?
Answer: The chance of Elisondra getting picked is 25%
Step-by-step explanation:
Now you spin the spinner and whoever it lands on is the one who orders first.
Good Luck!
Answer:
It depends if Elisondra and her friend's share of the wheel is the same but if it is the same, then it is a 1/4 chance because there are 4 people.
In order to answer the following question, please use the following image down below:
Find the value of x.
X=(Blank)
What is the value of X? Please show all the work on how you got your answer.
(If you can't explain your work, then it's fine. The only thing that I'm asking for is for you to show the work alongside your answer)
Answer:
4
Step-by-step explanation:
(x+8)(8) = (10+6)(6) -->
8x + 64 = 60 + 36 -->
8x = 32 -->
x = 4
Which statement is true about the data point 84? It is within 1 standard deviation of the mean. It is within 2 standard deviations of the mean. It is exactly 3 standard deviations from the mean. It is exactly 4 standard deviations from the mean.
Answer: It is within 2 standard deviations of the mean
Step-by-step explanation:
In the figure below, hln. Find the values of z and y.
To find y:
[tex]3y-14=180[/tex]
[tex]3y=194[/tex]
[tex]y=64.7[/tex]
To find z:
[tex]180 - 64.7 = z[/tex]
[tex]z = 115.3[/tex]
(1 point) The revenue, in dollars, from selling x items is R(x)=400x−x2, and the total cost, in dollars, is C(x)=50+9x. Write a function that gives the total profit earned, and find the quantity which maximizes the profit.
Answer:r=400 because the x is 72(6)
Step-by-step explanation:
Please helppp can someone please help me I am so confused on how to answer these
Answer:
A; D; A; C; C
Step-by-step explanation:
1. S29 means the sum of the first 29 terms. Because it's an arithmetic sequence, the sum of the first x terms is (the first term + xth term)(x)/2
That means the answer to the first question is (7+70)(29)/2 = 1116.5 (A)
2. The sum of the first 18 terms is (56 + 5)(18)/2 = 549 (D)
3. The common difference is 3.5, making the 26th term 87.5. That makes the sum of the first 26 terms (7+94.5)(26)/2 = 1319.5 (A)
4. The question is asking for the sum of the first 28 terms. The first term is 50-4(1) = 46. The 28th term is 50-4(28) = -62. That makes the sum of the first 28 terms (46+(-62))(28)/2 = -224 (C)
5. The first x terms of a geometric sequence is the (first term - (x+1)th term)/(1-(ratio)).
That makes the sum ((1/3)-(729))/(1-3) = -(2186/3)/-2 = 1093/3 = 364 1/3 (C)
It's been so hot out lately that you are thinking of throwing a bucket of water over your brother's head. You have a 2 gallon bucket, 7 quart bucket and an 18 pint bucket. Which bucket holds the most water to splash your brother with? (1 gallon = 8 pints, 1 gallon = 4 quarts, 1 quart = 2 pints)
Answer: The 18 pint bucket.
Step-by-step explanation: If you convert all of the units to gallons, you will find that the 7 quart bucket contains 1.75 gallons and the 18 pint bucket contains 2.25 gallons. Since 2.25 is the greatest amount, the 18 pint bucket contains the most water.
Seo-Yun hosted a party. She had 50 party
favors to give away, and she gave 3 party
favors to each of her guests as they arrived at
the party.
Let g(n) be the number of party favors Seo-
Yun had before the nth guest arrived.
g is a sequence. What kind of sequence is it?
Answer: It’s an arithmetic sequence
g(n)=50-3•(n-1)
Step-by-step explanation:
Answer:
it’s a arithmetic sequence and answer is 50-3(n-1) please give brainliest anyway bye have a good day but I don’t think u are because u probably bored of khan academy anyway bye have a good day! :D
Step-by-step explanation:
Estimate the result by rounding the numbers to the second decimal before performing the operation. Then also round your answer to the second decimal. 8123÷0.211 How do you do it?
Answer:
40615
Step-by-step explanation:
Note, rounding off decimals involves observing if the said decimal is up to the value of 5. If it is, then it can be rounded up, if not, its rounded off.
Since we need to round the numbers to the second decimal before performing the operation, we will have, 8123÷0.2
Note, 8123 has no decimal so we ignore
But 0.211 has a second decimal which is the first 1 so because it's not up to 5, we round it off to 0.
Hence we have 8123 ÷ 0.2= 40615.0
Since our answer has no decimal, we leave it like that.
Answer:
38680.95
Step-by-step explanation:
Solution:-
- We will round the denominator of the fraction " 0.211 " to two decimal places.
0 . 2 1 1
1st 2nd 3rd
3rd digit = 1 < 5 ... "Truncate the 3rd decimal value and on wards"
ans: 0.21
- Now perform the division:
8123 / 0.21 = 38680.95238
- Now again round the resulting answer to 2nd decimal place:
38680. 9 5 2
1st 2nd 3rd
3rd digit = 2 < 5 ... "Truncate the 3rd decimal value and on wards"
- The resulting answer will be after rounding to 2nd decimal place:
Answer: 38680.95
The ratio of boys to girls in a group is 2:1. If there are 22 more boys than girls, work out how many people there are in total
Answer:
66 in total. 44 boys and 22 girls
Step-by-step explanation:
you have to multiply 22 by 2 because there is twice as many (half of two is one) boys than there is girls.
Answer:
66
Step-by-step explanation:
There is a 2:1 ratio of boys to girls, and there are 22 more boys than girls. We can assume that 2/3 of the class are boys while 1/3 of the class is girls.
The difference between the two is 1/3. This can be found by taking away the smaller of the two from the larger, in this case it's 2/3 - 1/3. Removing the third, it's 2-1 which can be done by multiplying the two fractions by three. If we add the third back by dividing by three, we get 1/3.
This means that 22 people must be equivalent to 1/3 the total class' population. If x/3 = 22, then 22 * 3 must be x.
22 * 3 = 66, so there must be 66 students in the class.
Analyzing an Oblique Prism
The base area of an oblique pentagonal prism is 15 sq. in. The prism measures 3 inches in height and the edges connecting the bases measure 5 inches each. Which statements about the prism are true? Check all that apply.
The volume of the prism is computed using the expression (15)(3).
The volume cannot be determined because the dimensions of the base are unknown.
The edge length can be used in place of the height of an oblique prism if the height is unknown.
The unit on the volume measure of the prism is cubic inches.
The edge length times the height is the area of the base in any prism.
Answer: A and D
I just worked on this!
Answer:
1 and 4... A and D
Step-by-step explanation:
plz, help I don't know what I'm doing wrong. In the diagram, RSTU, and ABCD. Find the ratio of their perimeters.
Answer:
3 : 2
Step-by-step explanation:
Note that the ratio of perimeters is equal to the ratio of the sides, thus
ratio of corresponding sides = 12 : 8 = 3 : 2
Thus the ratio of perimeters is 3 : 2
The ratio of their perimeters is 3 : 2
calculation of ratio:Since the ratio of perimeters is equivalent to the ratio of the sides,
So,
ratio of corresponding sides = 12 : 8 = 3 : 2
Thus the ratio of perimeters is 3 : 2
Learn more about the ratio here: https://brainly.com/question/13176103?referrer=searchResults
An urn contains 8 balls identical in every aspect except color. There is 1 red ball, 2 green balls, and 5 blue balls. You draw two balls from the urn, and you do not replace the first ball before drawing the second. Find the probability that the first ball is blue and the second is green.
Answer:
P(blue and green) = P(blue)*P(green) = (5/8)(2/8) = 10/64
The probability that the first ball is blue and the second is green, with no replacement, is approximately 0.179 or 17.9%.
Explanation:The subject of this question pertains to probability, specifically the concept of dependent events in the realm of combinatorics. The problem involves an urn with 8 balls of different colors. The question asks us to find the probability that a blue ball is drawn first and a green ball second, with no replacement.
Firstly, we calculate the individual probabilities. The probability of drawing a blue ball first is 5/8, because there are 5 blue balls out of a total of 8. Since the blue ball isn't replaced, there are now 7 balls left in the urn, and therefore, the probability of drawing a green ball next is 2/7. To find the combined probability, we multiply the individual probabilities: (5/8) * (2/7) = 10/56 = 0.1786 (rounded). So the probability that the first ball is blue and the second is green is approximately 0.179 or 17.9%.
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ3
What is the solution to the equation x/3 + 5 = 8?
x = 1
x = 6
x = 7
x = 9
Brainliest if answered correctly.
Answer:
The answer is for sure x = 9
Answer:
x=9
Step-by-step explanation:
x/3+5=8 -5=-5 x/3=3 x=9Which mark on the tape measure is closest to 2.23607 inches?
Answer:
5.7 cm or 2 1/4 in
Step-by-step explanation:
Your tape measure is not shown.
On my tape measure, 5.7 cm is the closest mark. On the inch scale, 2 1/4 inches is the next-closest mark.
_____
On a tape measure graduated in 1/32 inch between 2 and 3 inches, you can find the closest mark by rounding to the nearest 32nd:
2.23607 × 32 ≈ 71.55 ≈ 72 --- 32nds of an inch
72/32 = 2 1/4 . . . . the closest mark on an inch ruler graduated in 32nds
__
For a ruler graduated in millimeters, you can find the closest millimeter in the same way. There are 25.4 mm to the inch.
2.23607 in × 25.4 mm/in ≈ 56.80 mm ≈ 57 mm
57 mm = 5.7 cm . . . closest mark on metric scale
__
When we check the error, we find the metric mark is closer than the inch mark.
5.7 cm ≈ 2.24409 in . . . . error of 0.00802 in
2 1/2 in = 2.25000 in . . . error of 0.01393 in
Final answer:
The mark on the tape measure closest to 2.23607 inches is just above 2 3/16 inches, which can be more precisely measured with a tape measure that features millimeter or half-millimeter markings.
Explanation:
The student has asked which mark on the tape measure is closest to 2.23607 inches. To answer this question, we must consider the precision of the measuring device. When using a ruler without millimeter markings, such as the bottom ruler mentioned, the measurement can be understood in tenths of a centimeter. This would make it difficult to conclusively measure and report on the hundredths digit for a length.
Conversely, using a tape measure with millimeter or even half-millimeter markings (akin to the top ruler), the user can measure more precisely. Given that 1 inch equals 2.54 centimeters, 2.23607 inches would be approximately 5.679818 centimeters. This would be between the 2.5 cm and 2.6 cm marks on a metric tape measure or between 2 3/16 inches and 2 1/4 inches on an imperial tape measure; 2.23607 inches is very close to, but slightly above, 2 3/16 inches, so this would be the mark on an imperial tape measure that is closest to 2.23607 inches.
A pool company claims that for optimal results customers should use 20 cups of 73% chlorine solution to treat their pools unfortunately the company only has an 80% chlorine solution and a 60% chlorine solution In stock how many cups of Each chlorine solution should be mixed to create the optimal solution?
Answer:
13 cups of the 80% chlorine solution + 7 cups of the 60% chlorine solution
Step-by-step explanation:
The pool company recommendation is 20 cups of 73% chlorine to treat their pool
Concentration of chlorine solution in stock = 80% and 60%
Therefore to make 20 cups of 73% solution, we require;
X cups of the 80% chlorine solution and
Y cups of the 60% chlorine solution
That gives 0.8·X + 06·Y = 0.73 × 20
X + Y = 20
Solving gives X = 13 cups
and Y = 7 cups
Therefore to make the optimal solution, 13 cups of the 80% chlorine solution should be mixed with 7 cups of the 60% chlorine solution.
Raj polled 100 students in his class to compare the number of hours that teen boys and girls played video games each week. The results of his survey are shown below. Which gender shows greater variability in their playing time?
Hours of Video Game Time per Week for Teen Boys
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 9 to 17. A line divides the box at 14.5.
Hours of Video Game Time per Week for Teen Girls
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 3 to 15. A line divides the box at 6.
Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.
Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.
Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.
Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.
The gender that shows greater variability in their playing time is females (teen girls).
How can we measure variability in a box-plot?It may depend on conditions. The dispersion can be measured in many ways. We can find range (max value - min. value), or interquartile range(the absolute difference between the first and third quartile ), etc to measure the variability.
How does a boxplot shows the data points?A box plot has 5 data description.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.How to find the interquartile range?IQR(inter quartile range) is the dfference between third and first quartile.
We will use the interquartile range here to find the variability in the playing time taken by different genders.
From the box plots given, we get the data of first and third quartiles from the left and right limits of boxes.
For males (teen boys):
First quartile: left limit of box = 9Third quartile: right limit of box = 17IQR is 17-9 = 8
For females (teen girls):
First quartile: left limit of box = 3Third quartile: right limit of box =15IQR is 15-3 = 12
Thus, there is greater variability in playing time of teen girls (females).
Thus, the gender that shows greater variability in their playing time is females (teen girls).
Learn more about box-plot here:
https://brainly.com/question/1523909
Girls have a larger interquartile range (IQR), indicating more varied playing times compared to boys.
Let's break down the analysis in detail:
1. Interpretation of Box-and-Whisker Plots:
- Box-and-whisker plots provide a visual representation of the distribution of a dataset. They show the median, quartiles, and range of the data.
2. Understanding Interquartile Range (IQR):
- The interquartile range (IQR) is a measure of statistical dispersion, which is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). It represents the spread of the middle 50% of the data.
- A larger IQR indicates greater variability in the dataset.
3. Comparison of IQRs for Boys and Girls:
- For boys:
- Lower quartile (Q1) = 9
- Upper quartile (Q3) = 17
- IQR for boys = Q3 - Q1 = 17 - 9 = 8
- This means that the middle 50% of boys' playing time falls within the range of 8 hours.
- For girls:
- Lower quartile (Q1) = 3
- Upper quartile (Q3) = 15
- IQR for girls = Q3 - Q1 = 15 - 3 = 12
- This indicates that the middle 50% of girls' playing time spans a range of 12 hours.
4. Analysis and Conclusion:
- The interquartile range for girls (12 hours) is larger than that for boys (8 hours).
- Therefore, girls' playing time exhibits greater variability compared to boys'.
- This suggests that there is more diversity in the amount of time girls spend playing video games each week, as indicated by the wider spread of their data points around the median.
5. Reasoning Behind the Conclusion:
- While both groups have the same overall range of possible values (from 0 to 28 hours), the spread of data within the middle 50% (as captured by the IQR) is wider for girls, indicating greater variability in their playing time.
So, based on the analysis of the interquartile ranges, we conclude that girls show greater variability in their playing time compared to boys in this dataset.
The angular velocity of a fan blade is 4.6 radians per second.
Approximately how many revolutions does the fan blade make in 2.4 minutes?
State your answer, rounded to the nearest tenth of a revolution.
Answer:
In 2.4 minutes the fan made 105.5 revolutions.
Step-by-step explanation:
In order to solve this problem we need to convert the speed from radians to revolutions. To do that we can use a rule of three as shown below:
2pi rad/s -> 1 rev/s
4.6 rad/s -> x rev/s
2pi/4.6 = 1/x
2pix = 4.6
x = 4.6/2pi = 2.3/pi rev/s
Now we need to conver the time at which the blade was spinning from minutes to seconds, to do that we need to multiply by 60.
t = 2.4*60 = 144 s
To calculate the number of revolutions we multiply the angular velocity of the fan by the time it was spinning:
rev = (2.3/pi)*144 = 331.2/pi = 105.5 revolutions
Answer:
105.4 revolutions
Step-by-step explanation:
By converting 2.4 min into seconds, we'll have
2.4 minutes = 60 x 2.4 = 144 seconds.
Now, in 2.4 minutes, the fan rotate 4.6 [rad/s] x 144s = 662.4 radians
As the answer is required in revolution
therefore, 1 radian = 0.159155 revolutions
so 0.159155 x 662.4 = 105.4 revolutions
The fan rotated 105.4 revolutions in 2.4 minutes
A rectangle is enlarged by a factor of 1.5. The width is given as w=2 and the length is given as l =7 in. What would be the perimeter of the new rectangle?
Answer:
Hence Perimeter for new rectangle will be 27 units .
Step-by-step explanation:
Given:
A rectangle with enlarged factor of 1.5
L=7 and W=2
To Find:
Perimeter for new rectangle
Solution:
First calculate the new dimensions for new rectangle ,
Given that original length and width as 7 and 2 respectively and it is increasing by 1.5 times of the original ones
So
New length =1.5 *L
=1.5 *7
=10.5 units
And for width,
New width=1.5 *W
=1.5 *2
=3
Hence New dimensions are 10.5 and 3 units .
So perimeter of new rectangle =2(New length + New breadth)
=2(10.5+3)
=2(13.5)
=27 units
What is the volume of wax needed for the candle in the shape of a prism?
Answer:
Step-by-step explanation:
You need answer choices for someone to answer.
What’s the volume of this triangular prism ?
Answer: 157.5
Step-by-step explanation: To get the volume of an object you must multiply the width x height ÷ it by 2 x length
Therefore 7 x 5 = 35 ÷ 2 = 17.5
17.5 x 9 = 157.5
Answer:
157.5
Step-by-step explanation:
The first step is to find the area of the triangular base. The formula for the area of a triangle is bh/2, or in this case 5×7/2=17.5. Multiplying this by the length of the prism, you get 9×17.5=157.5. Hope this helps!
The circumference of a circle is 6π centimeters.What is the radius?
Answer:
37.699cm
Step-by-step explanation:
thank me and rate!!! plz thank you :)
Which function has the same graph as y = 2cos(x + pi/4 )?
y = 2sin(x + pi/4 )
y = 2sin(x - pi/4 )
y = 2sin(x + 3pi/4 )
y = 2sin(x - 3pi/4 )
Answer:
y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) has the same graph of y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) ⇒ 3rd answer
Step-by-step explanation:
Let us revise the rules of the trigonometric compound angles
cos(x + y) = cos x cos y - sin x sin y
sin(x + y) = sin x cos y + cos x sin y
Let us solve the problem using the rules above
y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] )
∵ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = 2[cos x cos [tex]\frac{\pi }{4}[/tex] - sin x sin [tex]\frac{\pi }{4}[/tex] ]
∵ cos [tex]\frac{\pi }{4}[/tex] = [tex]\frac{\sqrt{2}}{2}[/tex] and sin [tex]\frac{\pi }{4}[/tex] = [tex]\frac{\sqrt{2}}{2}[/tex]
- Substitute them in the right hand side
∴ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = 2[ [tex]\frac{\sqrt{2}}{2}[/tex] cos x - [tex]\frac{\sqrt{2}}{2}[/tex] sin x]
- Multiply the bracket in the right hand side by 2
∴ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
∴ y = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
Now let us find the function which give the same right hand side of the function above
y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] )
∵ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = 2[sin x cos [tex]\frac{3\pi }{4}[/tex] + cos x sin [tex]\frac{3\pi }{4}[/tex] ]
∵ sin [tex]\frac{3\pi }{4}[/tex] = [tex]\frac{\sqrt{2}}{2}[/tex] and cos [tex]\frac{3\pi }{4}[/tex] = [tex]-\frac{\sqrt{2}}{2}[/tex]
- Substitute them in the right hand side
∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = 2[ [tex]-\frac{\sqrt{2}}{2}[/tex] sin x + [tex]\frac{\sqrt{2}}{2}[/tex] cos x]
- Multiply the bracket in the right hand side by 2
∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = [tex]-\sqrt{2}[/tex] sin x + [tex]\sqrt{2}[/tex] cos x
- Switch the two terms of the right hand side
∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
∴ y = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
- The same with right hand side of the function above
∴ y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) has the same graph of y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] )
Answer:
y=2sin(x+3pi/4)
Step-by-step explanation:
Answer C
Brooklyn needs to earn $14 more dollars to have $32. How much money does Brooklyn have now?
Identify the steps needed to write and solve an equation to solve the word problem. Select all that apply.
The variable, m, is equal to the amount of money Brooklyn has now.
The variable, m, is equal to the amount of money Brooklyn needs to earn.
The correct equation is 14 + m = 32.
The correct equation is 14m = 32.
To solve the equation, subtract 14 from both sides.
To solve the equation, divide 14 on both sides.
Answer:
its A,C,E
Step-by-step
i got it right on edge
Brooklyn has $18 now.
The correct steps are given below.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called an equation.
Given:
Brooklyn needs to earn $14 more dollars to have $32.
Let m be variable, which is equal to the amount of money Brooklyn has now.
The equation is,
14 + m = 32.
To solve the equation:
Subtract 14 from both sides.
We get,
m = 18
Therefore, the value of m is 18.
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ6
Henry want to know how long his patio is . He said the perimeter of his patio is 48 feet . He knows that one side of his patio is 9 feet long . How many feet long are all the sides
Answer:
Step-by-step explanation:
Perimeter = 48 feet
2*(length + width) = 48
2*(9 + width ) = 48
Divide both sides by 2.
9 + width = 48/2
9+width = 24
Subtract 9 from both sides.
9+width - 9 = 24 - 9
Width = 15 feet
What is the square root of 7? Decimal form please. Person with the most decimal places gets brainliest.
Answer:
2.64575131106 2.6457513110645905905016157536392604257102591830824501803683344592010688232302
83627760392886474543610615064578338497463095743529888627214784427390555880107722
71715072972832389229968959486508726070097805420372382802371594110034193911600157
85255963059457410351523968027164073737990740415815199044034743194536713997305970
05051399692237545616097119027378154991633288287704000657570674651963497752083793
81811461309087647378659562433057994798128163230705483650107715617946361191553454
53647749482059309049484983403398900210478616673327950369392462257170537164925787
54832290732492671346980298949908037748251109227895568897919808814834090831685251
33535829539172211770714414974576907081989444441458972284741400303502353203719487
07382629318519364090832280596462783761021959794197089096354695861341181793067816
21360849101677835321255633463490021898146042255929503669562418692737327715022087
52309966469813203212818945478568020950635962446628550076190504139350447437123488
52233277362510045059621080672334698120004300514490251206257311759115423194459672
60497833404344683725636178255048160879406205511486397833055016369470076387773745
19511658095220474202064982102444056001996590904100285534069110102261166807200774
83070332613842826296809502470794656496344336830519708820348050486447262317930876
95722489377521119788376007845603903658809421599292501057753682356001720074065236
92473209967419778002535708540617794442886681589731184938101638162073015642647016
29841099690071341323798188477647769954391111945967670336972452475367740100245826
51593077528163005479339717508017899520565284447796194304512502890432970610508746
04492966897542257133380633247034508888234275409806214511439553803393190705392738
14520604335238180389333294731479058055670704161068722878104529957696633035133295
04704245502510500789645502552271857923370921821991843932537781386785650143790894
13002099040860186605228131329821735251716419633617853080179022873400337109527257
36428650922035916343820273976336550966714177816292894279884853951076819102168116
99677176780863793410667897509217050421558644370687652934899322442240273649792906
66842070305782257110537944215790013280304078494579431518120466309284152592404683
65282802722458530778415894238973955590959563491357495109757674781975590533726939
36521431268222909570986506137179452721677198255442288046052307455488310813325041
49932783468182066583447383366862454456169497251774270254688591746231942309355060
38899235355634465872922507362228284298215287903623847595555861643755472027361518
00826144981691174794610631845652307625691344410868551999982851633960745717970829
72776495645142655658205126240305961633868338746134237463526431296594527010213721
72174899143552932049575097114259427207988929665230498875939525378121455723193310
30690840194942118708515205734116214105775416917245804962369512932926647583857193
34312550616097509003957512063487575979549295499224726634074018815634940531052960
4465875564620943Step-by-step explanation:
please help fast i am struggling
Answer:
what is the question
Step-by-step explanation:
Which is not a property of countercurrent multiplication?
Answer:
It is opposed by the vasa recta.
Step-by-step explanation:
Question:
Which of these is not a property of the renal counter-current multiplier?
It is opposed by the vasa recta.
It exploits the structure of the nephron loop.
It depends on active ion transport to function.
It creates a hyperosmotic interstitial fluid in the kidney medulla.
Answer:
The correct option is;
It is opposed by the vasa recta
Step-by-step explanation:
Counter current multiplication is the process whereby energy is used to build osmotic pressure gradient in the kidney such that water is reabsorbed from the exit tubular fluids reducing the volume of produced urine by increasing the urine concentration while the vasa recta capillaries slows blood flow rate so as to keep the osmotic pressure gradient constant enabling water to be reabsorbed thus concentrating the urine in line with counter current multiplication.
Ummm help please please
Answer:
120
Step-by-step explanation: