Answers
The figure which has the correct lines of symmetry drawn is figure D.
What is line of symmetry?A line of symmetry refers to the line that divides a shape or an object into two equal and symmetrical parts.
The figure given is a five sided shape referred to as a pentagon.
A pentagon has five lines of symmetry.
Therefore, the correct line of symmetry is 5 lines drawn from each angle respectively.
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Related Questions
The area, a, of an ellipse can be determined using the formula a=TTxy where x and y are half the lengths of the largest and smallest diameters of the ellipse. Which is an equivalent equation solved for y
Answers
To solve for y, divide both sides by [tex]\pi x[/tex]:
[tex]y=\frac{a}{\pi x}[/tex]
Answer:
Area of an ellipse(a), ,having x and y being the lengths of the largest and smallest diameters of the ellipse = π xy
The lengths of the largest and smallest diameters of the ellipse is called Major Axis and Minor axis of the ellipse.
[tex]\rightarrow a=\pi x y\\\\\rightarrow y=\frac{a}{\pi \times x}[/tex]
If a quadratic function has two zeros, 112 and 122, then what is its axis of symmetry?
Answers
[tex]x=117[/tex]
Janelle was trying to find the distance between (3,7) and (9,6) in the coordinate plane. She knew the formula was D=√(9 - 3)^2 + (6 - 7)^2. So she took the square root and got (9-3)+(6-7)=5. Did she get the correct answer? Explain.
Answers
incorrect answer because :
[tex] \sqrt{ a^{2} + b^{2} } \neq \sqrt{ a^{2} } + \sqrt{ b^{2}} \neq a+b[/tex]
but :
[tex] \sqrt{ (a+b)^{2} } = a+b[/tex]........a+b ≥ 0
20 PTS!!!Each month, Matthew gets a $25 allowance and earns $100 mowing lawns. He uses the expression 25x + 100y to keep track of his earnings.
Part A: Identify the variables and coefficients in the expression. (3 points)
Part B: How many terms are in the expression, what are they, and how do you know? (4 points)
Part C: Which term in the expression shows the total earned from mowing lawns? (3 points)
Answers
The variables would be x and y where as the coefficients would be 25 and 100
Part B
There are two terms in the expression, those being 25x and 100y. This is because s plus or minus sign separates terms, and in this case, we only have one plus sign.
Part C
The term that represents the total earnings from mowing lawns in 100y, because the prompt says that he earns $100 mowing lawns.
A store stocked 150 cans of popcorn for a weekend sale.
That weekend, 72 of the cans sold. What percent of the
cans of popcorn stocked were sold that weekend?
Answers
Answer:
48%
Step-by-step explanation:
In order to find the percentage we need to divide the sold cans by total cans and multiply the result by 100.
Total cans = 150
Sold cans = 72
→ 72/150 = 0.48
→ 0.48 * 100 = 48
The percentage of the cans of popcorn stocked were sold that weekend is 48%
The given parameters are:
Total can of popcorn = 150
Sold can of popcorn = 72
The percentage of can sold is then calculated as:
[tex]\%Sold = \frac{72}{150} *100\%[/tex]
Multiply 72 and 100
[tex]\%Sold = \frac{7200}{150}\%[/tex]
Divide 7200 by 150
[tex]\%Sold = \%48[/tex]
Hence, the percentage of the cans of popcorn stocked were sold that weekend is 48%
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What is 345,876 in short word form?
Answers
A baseball is hit with an initial upward velocity of 70 feet per second from a height of 4 feet above the ground. The equation h= −16t^2 +70t + 4 models the height in feet t seconds after it is hit. After the ball gets to its maximum height, it comes down and is caught by another player at a height of 6 feet above the ground. About how long after it was hit does it get caught?
Answers
6 = -16t^2 + 70t + 4
Next put the equation in standard form by subtracting 6 from both sides
-16t^2 + 70t - 2 = 0
This equation can be simplified by dividing by 2
-8t^2 + 35t - 1 = 0
This equation cannot be factored, but we can use the quadratic formula to find a value for x. Using the equation above we can find the values for a=-8, b = 35 and c = -1.
using the quadratic formula we can solve for x
-b +/- sqrt(b^2 - 4ac)
-------------------------------
2a
The solutions are
0.03 and 4.35. as 0.03 seems an unrealistic time to hit and catch a baseball we would expect the time to be 4.35 seconds.
By setting the given height (6 feet) in the height equation and using the quadratic formula to solve for time 't', we get two solutions. Since the ball reaches 6 feet twice in its ascension and decension, the latter value of t = 3.79 seconds would be the time it is caught.
Explanation:The question is regarding the time at which a baseball, hit with an initial upward velocity and caught at 6 feet above the ground, is caught. Firstly, input the given height of 6 feet into the height equation h= -16t^2 + 70t + 4 and solve for
t
. Based on the quadratic formula, we receive two solutions: t = 3.79 s and t = 0.54 s. Since the ball has two points at which it reaches the height of 6 feet during its trajectory - once while going up and once while coming down - the time when it is caught would be the larger value,
t = 3.79 s
. Therefore, approximately 3.79 seconds after being hit, the ball is caught.
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Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 4x2 + 9y2 = 36. cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
Answers
defines an ellipse centered at [tex](0,0)[/tex] with semi-major axis length 3 and semi-minor axis length 2. The semi-major axis lies on the [tex]x[/tex]-axis. So if cross sections are taken perpendicular to the [tex]x[/tex]-axis, any such triangular section will have a base that is determined by the vertical distance between the lower and upper halves of the ellipse. That is, any cross section taken at [tex]x=x_0[/tex] will have a base of length
[tex]\dfrac{x^2}9+\dfrac{y^2}4=1\implies y=\pm\dfrac23\sqrt{9-x^2}[/tex]
[tex]\implies \text{base}=\dfrac23\sqrt{9-{x_0}^2}-\left(-\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac43\sqrt{9-{x_0}^2}[/tex]
I've attached a graphic of what a sample section would look like.
Any such isosceles triangle will have a hypotenuse that occurs in a [tex]\sqrt2:1[/tex] ratio with either of the remaining legs. So if the hypotenuse is [tex]\dfrac43\sqrt{9-{x_0}^2}[/tex], then either leg will have length [tex]\dfrac4{3\sqrt2}\sqrt{9-{x_0}^2}[/tex].
Now the legs form a similar triangle with the height of the triangle, where the legs of the larger triangle section are the hypotenuses and the height is one of the legs. This means the height of the triangular section is [tex]\dfrac4{3(\sqrt2)^2}\sqrt{9-{x_0}^2}=\dfrac23\sqrt{9-{x_0}^2}[/tex].
Finally, [tex]x_0[/tex] can be chosen from any value in [tex]-3\le x_0\le3[/tex]. We're now ready to set up the integral to find the volume of the solid. The volume is the sum of the infinitely many triangular sections' areas, which are
[tex]\dfrac12\left(\dfrac43\sqrt{9-{x_0}^2}\right)\left(\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac49(9-{x_0}^2)[/tex]
and so the volume would be
[tex]\displaystyle\int_{x=-3}^{x=3}\frac49(9-x^2)\,\mathrm dx[/tex]
[tex]=\left(4x-\dfrac4{27}x^3\right)\bigg|_{x=-3}^{x=3}[/tex]
[tex]=16[/tex]
The volume [tex]\( V \)[/tex] of the solid [tex]\( S \)[/tex] is 32 cubic units.
To find the volume [tex]\( V \)[/tex] of the solid [tex]\( S \),[/tex] where the base is an elliptical region defined by the equation [tex]\( 4x^2 + 9y^2 = 36 \),[/tex] and the cross-sections perpendicular to the [tex]\( x \)[/tex]-axis are isosceles right triangles with their hypotenuse lying on the base, we proceed as follows:
The equation [tex]\( 4x^2 + 9y^2 = 36 \)[/tex] represents an ellipse centered at the origin with semi-major axis [tex]\( \sqrt{9} = 3 \)[/tex] along the [tex]\( y \)[/tex]-axis and semi-minor axis [tex]\( \sqrt{4} = 2 \)[/tex] along the [tex]\( x \)[/tex]-axis.
Each cross-section perpendicular to the [tex]\( x \)[/tex]-axis is an isosceles right triangle with its hypotenuse on the elliptical base. The height [tex]\( h(x) \)[/tex] of each triangle at a given [tex]\( x \)[/tex] is determined by the elliptical equation.
For a fixed [tex]\( x \),[/tex] the corresponding [tex]\( y \)[/tex] values on the ellipse satisfy [tex]\( 4x^2 + 9y^2 = 36 \).[/tex] Solving for [tex]\( y \)[/tex], we get:
[tex]\[ y = \frac{2}{3} \sqrt{36 - 4x^2} \][/tex]
The height of the triangle is [tex]\( \frac{2}{3} \sqrt{36 - 4x^2} \).[/tex]
To find the volume [tex]\( V \)[/tex] of the solid [tex]\( S \),[/tex] integrate the area of each triangular cross-section along the [tex]\( x \)[/tex]-axis from [tex]\( x = -3 \) to \( x = 3 \):[/tex]
[tex]\[ V = \int_{-3}^{3} \text{Area of triangle at } x \, dx \][/tex]
The area of each triangle is [tex]\( \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 2h(x) \cdot h(x) = h(x)^2 \).[/tex]
Thus,
[tex]\[ V = \int_{-3}^{3} h(x)^2 \, dx = \int_{-3}^{3} \left( \frac{2}{3} \sqrt{36 - 4x^2} \right)^2 \, dx \][/tex]
[tex]\[ V = \int_{-3}^{3} \frac{4}{9} (36 - 4x^2) \, dx \][/tex]
[tex]\[ V = \frac{4}{9} \int_{-3}^{3} (36 - 4x^2) \, dx \][/tex]
[tex]\[ V = \frac{4}{9} \left[ 36x - \frac{4x^3}{3} \right]_{-3}^{3} \][/tex]
Solving further,
[tex]\[ V = \frac{4}{9} \left[ \left( 36 \cdot 3 - \frac{4 \cdot 27}{3} \right) - \left( 36 \cdot (-3) - \frac{4 \cdot (-27)}{3} \right) \right] \][/tex]
[tex]\[ V = \frac{4}{9} \left[ (108 - 36) - (-108 + 36) \right] \][/tex]
[tex]\[ V = \frac{4}{9} \left[ 72 \right] \][/tex]
[tex]\[ V = \frac{4 \cdot 72}{9} \][/tex]
[tex]\[ V = 32 \][/tex]
Therefore, the volume [tex]\( V \)[/tex] of the solid [tex]\( S \)[/tex] is 32 cubic units.
The ages of Edna,Ellie,and Elsa are consecutive integers. The sum of their ages is 120. What are their ages?
Answers
x+x-1+x+1 =120
3x=120
x=40
40-1=39
40+1 =41
39 +40 +41 = 120
ages are 39 40 & 41
If a number A is a 2 digit number and its digits are transposed to form number B, then the difference between the larger of the two numbers and the smaller of the two numbers must be divisible by:
Answers
so A-B is divisible by 9
The difference is a multiple of 9, so it is always divisible by 9.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The difference between the larger of the two numbers and the smaller of the two numbers.
A - B or B - A (whichever is greater)
If we transpose the digits of a two-digit number A to form B, then:
A = 10a + b, where a is the tens digit and b is the one's digit
B = 10b + a, where b is the tens digit and a is the one's digit
The difference between the two numbers.
= A - B
= (10a + b) - (10b + a)
= 9a - 9b
= 9(a - b)
or
B - A
= (10b + a) - (10a + b)
= 9b - 9a
= 9(b - a)
Either way, the difference is a multiple of 9, so it is always divisible by 9.
Therefore,
The difference is a multiple of 9, so it is always divisible by 9.
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the hypotenuse of a right triangle is 24ft long. The length of one leg is 20ft more than the other. Find the length of the legs.
Answers
h^2=x^2+y^2
We are told that y=x+20 and h=24 so
x^2+(x+20)^2=24^2
x^2+x^2+40x+400=576
2x^2+40x+400=576
2x^2+40x=176
x^2+20x=88
x^2+20x+100=188
(x+10)^2=188
x+10=±√188
x=-10±√188, x>0 so
x=-10+√188 ft
y=10+√188 ft
If you want approximations...
x≈3.71 ft
y≈23.71 ft
We can find the lengths of the legs of the right triangle using the Pythagorean theorem. One leg is x and the other leg is x+20. A quadratic equation can be solved to find x.
Explanation:The problem involves a right triangle, and we are given the length of the hypotenuse and a relationship between the lengths of the legs. We can solve it using the Pythagorean theorem, which for a right triangle with legs of lengths 'a' and 'b' and hypotenuse 'c' is stated as a² + b² = c².
Let's assign 'x' to the shorter leg. Given that the other leg is 20ft longer, it would be 'x + 20'. The hypotenuse is given as 24, hence the equation becomes: x² + (x + 20)² = 24².
By solving this equation, we find two potential values for 'x', but since a length can't be negative, we exclude the negative value. Hence, the length of the shorter leg is 'x' and of the longer leg is 'x + 20'.
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please help! really appreciate it
Answers
rugby 7 has 3 out of 5 sold out = 3/5 = 0.6
Junior Athletics has 3 out of 5 sold out = 3/5 = 0.6
Volley ball has 2 out of 5 sold out = 2/5 = 0.4
Volleyball is the answer for the first part
Part 2 = 3/5 x 3/5 =9/25
What is the volume of the prism? 192 cubic units 200 cubic units 384 cubic units 400 cubic units
Answers
V=xyz, where x,y, and z are the dimensions...
V=16*5*5
V=400 u^3
V=5*5*16=400 cubic units.
A pair of dice are rolled. What is the probability of getting a sum greater then 7?
Answers
The probability of rolling a sum greater than 7 with a pair of dice is [tex]\( \frac{5}{12} \).[/tex]
To find the probability of getting a sum greater than 7 when rolling a pair of dice, let's first list all the possible outcomes when rolling two dice:
1. (1,1)
2. (1,2)
3. (1,3)
4. (1,4)
5. (1,5)
6. (1,6)
7. (2,1)
8. (2,2)
9. (2,3)
10. (2,4)
11. (2,5)
12. (2,6)
13. (3,1)
14. (3,2)
15. (3,3)
16. (3,4)
17. (3,5)
18. (3,6)
19. (4,1)
20. (4,2)
21. (4,3)
22. (4,4)
23. (4,5)
24. (4,6)
25. (5,1)
26. (5,2)
27. (5,3)
28. (5,4)
29. (5,5)
30. (5,6)
31. (6,1)
32. (6,2)
33. (6,3)
34. (6,4)
35. (6,5)
36. (6,6)
Out of these 36 possible outcomes, the sums greater than 7 are:
12, 17, 18, 22, 23, 24, 27, 28, 29, 30, 32, 33, 34, 35 and 36.
There are 15 favorable outcomes. So, the probability of getting a sum greater than 7 is:
[tex]\[ \frac{15}{36} = \frac{5}{12} \][/tex]
on a city map 2.5 inches represents 5 miles the library and the bank are 3 inches apart on the map what is the actual distance between the library and the bank
Answers
3/2.5=1.2
5-1.2=3.8
Thats where I got the answer I hope it is correct and helps.
Answer:
6 miles.
Step-by-step explanation:
We have been given that on a city map 2.5 inches represents 5 miles the library and the bank are 3 inches apart on the map. We are asked to find the actual distance between the library and the bank.
[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{\text{5 miles}}{\text{2.5 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{3 inches}}=\frac{\text{5 miles}}{\text{2.5 inches}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{3 inches}}*\text{3 inches}=\frac{\text{5 miles}}{\text{2.5 inches}}*\text{3 inches}[/tex]
[tex]\text{Actual distance}=\frac{\text{5 miles}}{2.5}*3[/tex]
[tex]\text{Actual distance}=\text{2 miles}*3[/tex]
[tex]\text{Actual distance}=\text{6 miles}[/tex]
Therefore, the actual distance between the library and the bank is 6 miles.
A sealed rectangle or box measuring 8 x 6 x 18 contains 864 Sugar cubes each measuring one by one by one how many sugar cubes are touching the box
Answers
The arrangement of the 864 cubes would be 18 6 by 8 layers.
All 48 would be touching the bottom of the box on the bottom layer and all 48 would be touching the top of the box on the top layer.
The cubes along both lengths would be touching the sides of the box for the remaining 16 layers. That would be16 cubes per layer or 256 cubes after counting both sides.
The cubes along the width would be touching the ends of the box for those 16 layers. Those need to be eliminated from the count since the corner cubes were already counted as part of the ones touching the sides. 4 cubes have not been previously counted for each width of 6 cubes. Both ends of the 16 layers has 8 cubes per layer or 128 cubes.
Therefore, that is 256 (sides) + 128 (ends) + 48 (top) + 48 (bottom) and that totals to 480 cubes touching the box.
which line would best fit the data shown in a scatterplot
Answers
I really, really need help with my Accounting II class! I need 1-4 answered along with the bullet points at the bottom. Thank you in advance if anyone can help, this determines if I graduate!
Your manufacturing company incurs several costs to make the finished product, which are cans of eco-friendly paint. You purchase 100 empty cans at $2.00 each and 200 labels for the cans of paint at $1.00 each. You have two employees who bottle the paint into the cans and one additional employee who places a label on each can. You take a printout from your clock where the employees have entered their time and find that the wages due to these three employees is $2,000.00. You must also pay payroll taxes in the amount of $140.00 total for these three employees. A number of other costs incurred must be taken into consideration as well: depreciation on the factory machine of $150.00, utilities of $200.00, prepaid insurance of $600.00, and property taxes on your building of $2,000.00.
1) Prepare the journal entries to record the purchase of the raw materials, the labor incurred, and the overhead incurred.
2) Assume that $100.00 of the raw materials and $1,000.00 of the indirect materials were used. Prepare the journal entries to assign these materials to the jobs and overhead.
3) Of the $2,140.00 in factory labor, $500.00 was attributed to indirect labor costs. Prepare the journal entry to assign the labor to jobs and overhead.
4) You determine that direct labor cost is the activity base for determining the predetermined overhead rate. The following information is known about the estimated annual costs:
overhead costs: $18,000.00
direct labor costs: $25,000.00
-What is the predetermined overhead rate?
-What is the journal entry to assign overhead to jobs?
-Prepare the journal entry to transfer costs to Finished Goods.
-A sale of the goods takes place. The goods are sold for $5,000.00. Prepare the journal entry to record this sale.
Answers
See the attachments
Hope it helps
What effect does adding a constant have on a exponential function?
Answers
Then your function will be shifted up by x units.
Notice, if x is negative, then shifted up by negative number means shifted down by the absolute value
Adding a constant to an exponential function results in shifting the graph vertically or horizontally, depending on where the constant is added. The shift will be positive for a positive constant and negative for a negative constant.
Explanation:In Mathematics, when dealing with an exponential function, adding a constant can affect the function in two different ways, depending on where the constant is being added. If the constant is added to the exponent, this results in shifting the graph horizontally. However, if the constant is added outside the exponent (as in f(x) = 2x + k), this will result in the entire graph being shifted upward or downward vertically, based on whether the constant is positive or negative.
For example, consider the simple exponential function f(x) = 2x. If a constant 'c' is added - resulting in f(x) = 2x + c, the resulting graph will be the same as the original, but shifted 'c' units upward if 'c' is positive and downward if 'c' is negative. This is a fundamental principle of exponential functions.
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If it takes 0.20 dollars to buy a mexican peso and 0.60 dollars to buy a brazilian real, then it takes _____ pesos to buy one brazilian real.
Answers
1 Brazilian real = 60 cents
so it takes 3 pesos to buy 1 Brazilian real
It will takes 3 mexican pesos to buy one brazilian real .
According to the given condition
It takes 0.20 dollars to buy a mexican peso and 0.60 dollars to buy a brazilian real,
We have to determine that it takes how many mexican pesos to buy one brazilian real.
This question can be solved by applying the principles of unitary method
One peso will be bought in $ 0.20
One real will be bought in $ 0.60
1 dollar is equivalent to
[tex]\rm 1 \; dollar = \dfrac{1}{0.2} peso \\\\\rm 1 \; dollar = \dfrac{1}{0.6 } \; real[/tex]
[tex]\rm 1/0.2\; peso = 1/0.6 \; real \\1 \; real = 0.6/0.2 = 3 \; peso[/tex]
So it will take 3 pesos to buy one real
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A gully can fly at a speed of 22 miles per hour about how many feet per hour can the gull fly?
Answers
A bank withdraw of 50 dollars
Answers
Thanks,
Whiiz
A spinner is divided into many sections of equal size. Some sections are red, some are blue, and the remaining are green. The probability of the arrow landing on a section colored red is 11 over 20. The probability of the arrow landing on a section colored blue is 6 over 20. What is the probability of the arrow landing on a green-colored section?
Answers
blue = 6/20...this tells me there is 6 blue ones and 20 total sections
so if the rest are green, and if there are 20 total spaces and 11 are red and 6 are blue....that leaves (20 - 11 - 6) = 3...so 3 are green.
so the probability of picking a green one is 3/20 <==
h=7 + 29t-16t^2 find all values of t for which the balls height is 19ft
Answers
[tex]\bf h(t)=7+29t-16t^2\qquad h(t)=19\implies 19=7+29t-16t^2 \\\\\\ 16t^2-29t+12=0\impliedby \textit{now, let's use the quadratic formula} \\\\\\ t=\cfrac{-(-29)\pm\sqrt{(-29)^2-4(16)(12)}}{2(16)}\implies t=\cfrac{29\pm\sqrt{841-768}}{32} \\\\\\ t=\cfrac{29\pm\sqrt{73}}{32}\implies t\approx \begin{cases} 1.17\\ 0.64 \end{cases}[/tex]
so hmm check the picture below, thus the ball hits 19 feet of height twice, once on the way up, and once on the way down, at about 0.64 seconds and at 1.17 seconds.
** NEED THIS ANSWERED ASAP**
Find the indicated probability. Round to the nearest thousandth.
In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11, what is the probability that the mixture will test positive?
a. 0.503
b. 0.00000177
c. 1.00
d. 0.497
Answers
How to write two different pairs of decimals whose sums are 14.1. One pair should involve regrouping
Answers
=> Regrouping involves carrying and borrowing during subtraction and addition of the given numbers.
So let us have the non-regrouping decimal number:
=> 8.4
Next, the other regrouping decimal
=> 5.7
So now let us show how it becomes 14.1:
8.4
+5.7
14.1
Starting from the right, 4 + 7 is equal 11, so bring down 1 and carry 1. Now 8+5 = 13, but 13 + carry 1 = 14
Thus, the answer is 14.1
Find the area of the helicoid (or spiral ramp) with vector equation r(u, v) = ucos(v) i + usin(v) j + v k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π.
Answers
[tex]\mathbb r(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+v\,\mathbf k[/tex]
for [tex]0\le u\le1[/tex] and [tex]0\le v\le9\pi[/tex]. The surface area is given by the surface integral,
[tex]\displaystyle\iint_H\mathrm dS=\iint_H\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv[/tex]
We have
[tex]\mathbf r_u=\dfrac{\partial\mathbf r(u,v)}{\partial u}=\cos v\,\mathbf i+\sin v\,\mathbf j[/tex]
[tex]\mathbf r_v=\dfrac{\partial\mathbf r(u,v)}{\partial v}=-u\sin v\,\mathbf i+u\cos v\,\mathbf j+\mathbf k[/tex]
[tex]\implies\mathbf r_u\times\mathbf r_v=\sin v\,\mathbf i-\cos v\,\mathbf j+u\,\mathbf k[/tex]
[tex]\implies\|\mathbf r_u\times\mathbf r_v\|=\sqrt{1+u^2}[/tex]
So the area of [tex]H[/tex] is
[tex]\displaystyle\iint_H\mathrm dS=\int_{v=0}^{v=9\pi}\int_{u=0}^{u=1}\sqrt{1+u^2}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\dfrac{9(\sqrt2+\sinh^{-1}(1))\pi}2[/tex]
The area f the helicoid ramp is:
∫∫A) | r(u) *r( v) | dudv
The solution is:
A = 10.35×π square units
r ( u , v ) = u×cosv i + u×sinv j +v k
To get
r (u ) = δ(r ( u , v ) ) / δu = [ cosv , sinv , 0 ]
r ( v ) = δ(r ( u , v ) ) / δv = [ -u×sinv , u×cosv , 1 ]
The vectorial product is:
i j k
r (u ) * r ( v ) cosv sinv 0
-u×sinv u×cosv 1
r (u ) * r ( v ) = i × ( sinv - 0 ) - j × ( cosv - 0 ) + k ( u×cos²v + u× sin²v )
r (u ) * r ( v ) = sinv i - cosv j + u k
Now
| r (u ) * r ( v ) | = √sin²v + cos²v + u² = √ 1 + u²
Then
A = ∫₀ (9π) dv ∫₀¹ √ 1 + u² du
∫₀¹ √ 1 + u² du = 1.15
A = 1.15 × v |( 0 , 9π )
A = 10.35×π square units
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If the radius of a sphere is doubled, then its volume is multiplied by _____. 2 4 8
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M(6, 6) is the midpoint of mc139-1.jpg. The coordinates of S are (8, 9). What are the coordinates of R?
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(6,6)=((8+x)/2, (9+y)/2)
(12,12)=((8+x), (9+y))
(4,3)=(x,y)
So the coordinates of R are (4,3)
Crystal reads 25 pages in 1/2 hours write an equation to represnets the relationship between the number of pages crystal reads and how much time she spends reading.
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Crystal would read 37.5 pages in [tex]\( \frac{3}{4} \)[/tex] hour.
To represent the relationship between the number of pages Crystal reads and the time she spends reading, we can use the formula:
[tex]\[ \text{Pages Read} = \text{Reading Rate} \times \text{Time Spent Reading} \][/tex]
In this case, Crystal reads 25 pages in 1/2 hour, so her reading rate can be calculated as follows:
[tex]\[ \text{Reading Rate} = \frac{\text{Pages Read}}{\text{Time Spent Reading}} \][/tex]
[tex]\[ \text{Reading Rate} = \frac{25 \text{ pages}}{\frac{1}{2} \text{ hour}} \][/tex]
[tex]\[ \text{Reading Rate} = 25 \times 2 \][/tex]
[tex]\[ \text{Reading Rate} = 50 \text{ pages per hour} \][/tex]
Now, we can substitute this reading rate into the equation to represent the relationship:
[tex]\[ \text{Pages Read} = 50 \times \text{Time Spent Reading} \][/tex]
This equation describes the relationship between the number of pages Crystal reads and the time she spends reading.
To illustrate how to use this equation, let's say Crystal reads for [tex]\( \frac{3}{4} \)[/tex] hour. We can plug this value into the equation to find out how many pages she reads:
[tex]\[ \text{Pages Read} = 50 \times \frac{3}{4} \][/tex]
[tex]\[ \text{Pages Read} = 37.5 \][/tex]
So, Crystal would read 37.5 pages in [tex]\( \frac{3}{4} \)[/tex] hour.