Compute the surface element:
[tex]\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv[/tex]
[tex]\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}[/tex]
[tex]\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}[/tex]
So the integral is
[tex]\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)[/tex]
[tex]=\dfrac23(37^{3/2}-1)[/tex]
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x - 6)2
Answer:
Translate 6 units to the right.
Step-by-step explanation:
The y = x^2 function is a quadratic function with vertex at (0,0). It can be transformed to have a vertex of (6,0) like the function y = (x-6)^2 by shifting it 6 units to the right. It is now the graph of y = (x-6)^2.
The equation y = (x - 6)² represents a transformation of the graph y = x², specifically a horizontal shift 6 units to the right on the 2-dimensional (x-y) plane.
Explanation:To transform the graph of y = x² to the graph of the equation y = (x – 6)², you must understand that these both take the form of a quadratic equation, producing a parabola when graphed. The difference between these two equations is indicated by the term '– 6' in the x of the second equation which corresponds to a horizontal shift in the graph.
In the equation y = (x – 6)², this specifically means that the graph of y = x² is shifted 6 units to the right. This shift doesn't change the shape of the graph, it only moves the location in the 2-dimensional (x-y) plane. So, when you plot data pairs for both y = x² and y = (x – 6)², the second graph would be identical to the first, just moved 6 units to the right.
Learn more about graph transformations here:https://brainly.com/question/19040905
#SPJ3
Simplify -8 + 6(b - 1). answer
Answer:
Step-by-step explanation:
-8 + 6(b - 1) = -8 +6b-6 = 6b -14
The simplified expression is now 6b - 14.
To simplify the expression -8 + 6(b - 1), you need to distribute the 6 to both terms inside the parentheses and then combine like terms. Here's the step-by-step process:
Multiply 6 by both b and -1 inside the parentheses: 6 * b gives 6b, and 6 * -1 gives -6.
Write out the new expression without the parentheses: -8 + 6b - 6.
Combine the like terms, which are the constants -8 and -6: -8 - 6 equals -14.
The simplified expression is now 6b - 14.
Lewis fills his thermos with 2 liter of water. Garret fill his thermos with 1 of water. How many more milliliter of water does lewis have than Garret?
For this case we have to:
Lewis carries 2 liters of water
Garret carries 1 liter of water
So, Lewis has 1 liter of water more than Garret.
By definition we have that 1 liter equals 1000 milliliters.
Thus, Lewis carries 1000 milliliters more water than Garret.
Answer:
1000 milliliters
The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. what is the expected number of students who had scores greater than 60?
Answer:
23 students expected to have scores greater than 60.
Step-by-step explanation:
60 is 2 standard deviations above the mean. This translates into a z-score of +2. According to a table of z-scores, the area under the standard normal curve to the left of z = 2 is 0.9772; that to the right of z = 2 is 1.0000 - 0.9772, or 0.0228. This 0.0228 represents the probability that a given score is greater than 60.
This fraction (0.0228) of 1000 students comes out to 23 (rounded up from 22.75).
Final answer:
To find the expected number of students who had scores greater than 60 on a standardized test, we can calculate the probability using the properties of the normal distribution. The expected number is approximately 23 students.
Explanation:
To find the expected number of students who had scores greater than 60, we can use the properties of the normal distribution. We know that the mean score is 50 and the standard deviation is 5. We want to find the probability of getting a score greater than 60. First, we need to calculate the z-score for a score of 60 using the formula:
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z = (60 - 50) / 5 = 2
Next, we use a z-table or calculator to find the area to the right of z = 2. This represents the probability of getting a score greater than 60. A z-table or calculator will give us a value of approximately 0.0228.
Finally, we multiply this probability by the total number of students (1000) to find the expected number of students who had scores greater than 60:
Expected number = probability * total number of students = 0.0228 * 1000 = 22.8
Therefore, we can expect approximately 23 students to have scores greater than 60.
The functions f(x) and g(x) in the graph below are most likely which two equations?
Answer:
It's C.
Step-by-step explanation:
The red curve pass through the point (0, 1) and also y = 2 when x = 1 , so this is y = 2^x. The inverse is the reflection of f(x) in x = y so the blue curve is y = log2 x.
The two equation shown in the graph are y = e^x and y = lnx.
What is a function?In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable).
The red line shown in the graph represents y = e^x
The graph of y = e^x will never have a negative value of y, as the value of x increases the value of y will keep on increasing till ∞ . The value of y at x = 0 is 1, so the graph will cross the y-axis at (0,1).
The blue line shown in the graph represents y = lnx
The value of y will be negative when the value of x lies between 0 and 1 after that the value of y will keep on increasing and the point (1,0) satisfies the equation so it will cross the X - axis at (1,0)
Learn more about functions on:
https://brainly.com/question/10439235
#SPJ2
Please help with this....
Answer:
i think its 20
Step-by-step explanation:
Answer:
x = 12.8 cm
Step-by-step explanation:
Using the sine ratio in the right triangle to solve for x
sin70° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{12}{x}[/tex]
Multiply both sides by x
x × sin70° = 12 ( divide both sides by sin70° )
x = [tex]\frac{12}{sin70}[/tex] ≈ 12.8
Classify each of the angel (example. right, acute, etc). Then identify each angle as interior or exterior
interior is the angle
Answer:
1 = 139 degrees
Step-by-step explanation:
You can use the corresponding angles theorem
A box contains 17 nickels, 11 dimes and 19 pennies. if a coin is picked at random from the box, what is the average value of the draw in dollars?
Answer: its not possible
Step-by-step explanation: there are 17 nickels, 11 dimes and 19 pennies, NO dollars
Hey,can you find an area of a trapezoid that has 0.2 for base 1 and 0.6 for base 2 and also 0.2 for its height
Answer:
Trapezoid area = ((sum of the bases) ÷ 2) • height
Trapezoid area = (.2 + .6 / 2) * .2
Trapezoid area = (.8 / 2) * .2
Trapezoid area = .4 * .2 = .08
Step-by-step explanation:
A writer earns 8% of total sales dollars as a commission. If 2000 copies of his book are sold at $14.95 each, how much commission does he earn? $119.60 $1.20 $2,392 $160
Answer:
C $2392
Step-by-step explanation:
Which of the following is not a characteristic of the normal probability distribution? Select one: a. Symmetry b. The total area under the curve is always equal to 1. c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean d. The mean is equal to the median, which is also equal to the mode
Answer:
c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean
Step-by-step explanation:
In a normal distribution, the shape is bell-shaped; this means it is symmetric.
The area under a normal distribution will always be equal to 1.
The mean, median and mode in a normal distribution are equal.
However, the data assumes values within 1 standard deviation above or below the mean 68% of the time, not 99.72% of the time. This is the characteristic that doesn't fit.
The statement which is not a characteristic of the normal distribution is:
c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.The area under the normal curve is always equal to 1.The mean, the mode and median are equal.The Empirical Rule states that 68% of the measures are within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3, thus, statement c is false.For more on the normal distribution, you can check https://brainly.com/question/13011828
Dan, Gordon and Malachy share some sweets in the ratio 4:3:5. Dan gets 48 sweets. How many sweets are there altogether?
Answer:
144 sweets
Step-by-step explanation:
Let
x----> number of sweets that Dan has
y----> number of sweets that Gordon has
z----> number of sweets that Malachy has
we know that
x=48
x/y=4/3----> y/x=3/4 ----> y=(3/4)x
Substitute the value of x
y=(3/4)48=36
x/z=4/5 ----> z/x=5/4 ----> z=(5/4)x
Substitute the value of x
z=(5/4)48=60
therefore
altogether there are x+y+z=48+36+60=144 sweets
Veata is buying a new video game for $45. She has $150 in her checking account and $5 in her wallet. Which is the most reasonable way for Veata to pay for the game?
2 bill of 20 and 3 of 1
Answer:
Debit card
Step-by-step explanation:
Find the circumference and the area of a circle with diameter 6 cm Use the value 3.14 for pie , and do not round your answers. Be sure to include the correct units in your answers.
The circumference of the circle is 18.84 cm and the area is 28.26 cm².
Explanation:To find the circumference of a circle, we use the formula C = πd, where d is the diameter. In this case, the diameter is 6 cm, so the circumference is:
C = 3.14 × 6 = 18.84 cm
To find the area of a circle, we use the formula A = πr², where r is the radius. Since the radius is half the diameter, the radius in this case is 6/2 = 3 cm. So the area is:
A = 3.14 × 3² = 28.26 cm²
Learn more about circumference and area of a circle here:https://brainly.com/question/17130827
#SPJ3
The longest river in the UK is the river Severn which has a length of 24 cm on a map. If the map is drawn at a scale of 1:1,500,000, then how many kilometers is the river actually?
Answer:
360 km
Step-by-step explanation:
The length on the ground will be ...
(24·10^-2 m)·(1.5·10^6) = 36·10^4 m = 360·10^3 m = 360 km
Answer:
The length of river is 360km
Explanation:
Length on the map of Severn river = 24cm
Scale on the map = x:y axis
=1:1500000
Where y is the length
Hence 1 cm= 15 km
Therefore
Length of the river
=24[tex]\times[/tex]15
=360 km
Hence the length of river is 360 km
Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.
a. (5 square root 2, 225°), (-5 square root 2, 45°)
b. (5 square root 2, 315°), (-5 square root 2, 135°)
c. (5 square root 2, 135°), (-5 square root 2, 315°)
d. (5 square root 2, 45°), (-5 square root 2, 225°)
Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).
a. y squared over 81 minus x squared over 100 = 1
b. y squared over 81 minus x squared over 19 = 1
c. y squared over 19 minus x squared over 81 = 1
d. y squared over 100 minus x squared over 81 = 1
Answer:
First part
The answer is (5 square root 2, 45°), (-5 square root 2, 225°) ⇒ answer (d)
Second part
The equation in standard form for the hyperbola is y²/81 - x²/19 = 1 ⇒ answer(b)
Step-by-step explanation:
First part:
* Lets study the Polar form and the Cartesian form
- The important difference between Cartesian coordinates and
polar coordinates:
# In Cartesian coordinates there is exactly one set of coordinates
for any given point.
# In polar coordinates there is an infinite number of coordinates
for a given point. For instance, the following four points are all
coordinates for the same point.
# In the polar the coordinates the origin is called the pole, and
the x axis is called the polar axis.
# The angle measurement θ can be expressed in radians
or degrees.
- To convert from Cartesian Coordinates (x , y) to
Polar Coordinates (r , θ)
# r = ± √(x² + y²)
# θ = tan^-1 (y / x)
* Lets solve the problem
- The point in the Cartesian coordinates is (5 , 5)
∵ x = 5 and y = 5
∴ r = ± √(5² + 5²) = ± √50 = ± 5√2
∴ tanФ = (5/5) = 1
∵ tanФ is positive
∴ Angle Ф could be in the first or third quadrant
∵ Ф = tan^-1 (1) = 45°
∴ Ф in the first quadrant is 45°
∴ Ф in the third quadrant is 180 + 45 = 225°
* The answer is (5√2 , 45°) , (-5√2 , 225°)
Second part:
* Lets study the standard form of the hyperbola equation
- The standard form of the equation of a hyperbola with
center (0 , 0) and transverse axis parallel to the y-axis is
y²/a² - x²/b² = 1, where
• the length of the transverse axis is 2a
• the coordinates of the vertices are (0 , ±a)
• the length of the conjugate axis is 2b
• the coordinates of the co-vertices are (±b , 0)
• the coordinates of the foci are (0 , ± c),
• the distance between the foci is 2c, where c² = a² + b²
* Lets solve our problem
∵ The vertices are (0 , 9) and (0 , -9)
∴ a = ± 9 ⇒ a² = 81
∵ The foci at (0 , 10) , (0 , -10)
∴ c = ± 10
∵ c² = a² + b²
∴ (10)² = (9)² + b² ⇒ 100 = 81 + b² ⇒ subtract 81 from both sides
∴ b² = 19
∵ The equation is y²/a² - x²/b² = 1
∴ y²/81 - x²/19 = 1
* The equation in standard form for the hyperbola is y²/81 - x²/19 = 1
Find the center, vertices, and foci of the ellipse with equation 2x2 + 8y2 = 16.
[tex] {2}x^{2} + 8 {y}^{2} = 16 \\ \\ 1. \: {2x}^{2} = - 8 {y}^{2} + 16 \\ 2. \: {x}^{2} = - 4y^{2} + 8 \\ 3. \: x = \sqrt{ - 4y^{2} + 8} \\ x = - \sqrt{ - 4y^{2} + 8 } \\ \\ answer \\ x = \sqrt{ - 4y^{2} + 8 } \\ x = - \sqrt{ - 4y^{2} + 8} [/tex]
Answer:
Step-by-step explanation:
2x² + 8y² = 16
divide both sides of equation by the constant
2x²/16 + 8y²/16 = 16/16
x²/8 + y²/2 = 1
x² has a larger denominator than y², so the ellipse is horizontal.
General equation for a horizontal ellipse:
(x-h)²/a² + (y-k)²/b² = 1
with
a² ≥ b²
center (h,k)
vertices (h±a, k)
co-vertices (h, k±b)
foci (h±c, k), c² = a²-b²
Plug in your equation, x²/8 + y²/2 = 1.
(x-0)²/(2√2)² + (y-0)²/(√2)² = 1
h = k = 0
a = 2√2
b = √2
c² = a²-b² = 6
c = √6
center (0,0)
vertices (0±2√2,0) = (-2√2, 0) and (2√2, 0)
co-vertices (0, 0±√2) = (0, -√2) and (0, √2)
foci (0±√6, 0) = (-√6, 0) and (√6, 0)
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The frequency table was made using a deck of cards in which each card is numbered 1, 2, 3, or 4.
Create a bar graph by dragging the sliders on the horizontal axis to represent the probability distribution.
Answer: 1) 0.10
2) 0.60
3) 0.20
4) 0.10
Step-by-step explanation:
The total frequency is 20+120+40+20 = 200. This means they ran the experiment 200 times. The probability distribution is calculated by the satisfactory number of outcomes (frequency) divided by the total number of experiments/outcomes (total frequency):
[tex]\begin{array}{c|c||lc}\underline{x}&\underline{f}&\underline{f\div 200}&\underline{\text{Probability Distribution}}\\1&20&20\div200=&0.10\\2&120&120\div 200=&0.60\\3&40&40\div 200=&0.20\\4&20&20\div 200=&0.10\end{array}\right][/tex]
A line passes through the point (-8,9) and has a slope of 3/4.
Help pls
Answer:
I have no idea what you're asking for but I got y= -3/4x+3 as the equation for the line.
ANSWER
[tex]y = \frac{3}{4}x + 15[/tex]
EXPLANATION
The given line passes through the point
(-8,9) and has a slope be of
[tex]m = \frac{3}{4} [/tex]
We obtain the equation of this line using
[tex]y-y_1=m(x-x_1)[/tex]
We plug in the values into the formula to get,
[tex]y - 9 = \frac{3}{4} (x - - 8)[/tex]
[tex]y = \frac{3}{4} (x + 8) + 9[/tex]
Expand the parenthesis to get:
[tex]y = \frac{3}{4}x + 6 + 9[/tex]
[tex]y = \frac{3}{4}x + 15[/tex]
What is the solution to the equation below?
3log4x=log432+log42
X=-8
X=-4
X=4
X=8
Answer:
[tex]\large\boxed{x=4}[/tex]
Step-by-step explanation:
[tex]3\log_4x=\log_432+\log_42\qquad\text{use}\ \log_ab^c=c\log_ab\ \text{and}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_4x^3=\log_4(32\cdot2)\\\\\log_4x^3=\log_464\iff x^3=64\to x=\sqrt[3]{64}\\\\x=4[/tex]
Answer: 4
Step-by-step explanation: Its on EDG
The graph of this function is "M" shaped? f(x)=−3x4−7x3+6x2+5 Question 28 options: True False
the answer of this question is 8 bro..........................................................
What are the values of a, b, and c in the quadratic equation 0 = 5x 4x2 2? a = 5, b = 4, c = 2 a = 5, b = 4, c = 2 a = 4, b = 5, c = 2 a = 4, b = 5, c = 2
Answer:
d. 4,-5,-2
Step-by-step explanation:
The values of {a}, {b} and {c} in the quadratic equation are a = 4, b = 5, c = 2 respectively.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c.
Given is the quadratic equation as follows -
5x + 4x² + 2 = 0
The given quadratic equation is -
5x + 4x² + 2 = 0
4x² + 5x + 2 = 0
A quadratic equation is of the form -
ax² + bx + c
So, on comparing, we get -
a = 4, b = 5, c = 2
Therefore, the values of {a}, {b} and {c} in the quadratic equation are a = 4, b = 5, c = 2 respectively.
To solve more questions on quadratic equations, visit the link below -
brainly.com/question/22412845
#SPJ5
Find the parabola of the form y=ax2+b that best fits the points (1,0), (3,4), (4,5) by minimizing the sum of squares, s, given by s=(a+b)2+(9a+b−4)2+(16a+b−5)2
Answer: your mum gay
Step-by-step explanation:
PLEASE HELP ASAP
y coordinate
show work
-3x+2y=6 and 4x-y=2
A. -6
B. 1
C .2
D. 6
ANSWER
D. 6
EXPLANATION
We want to find the y-coordinate of the point of intersection of
-3x+2y=6
and
4x-y=2
Solve for y in equation (2) to get:
y=4x-2
Put y=4x-2 into the first equation:
-3x+2(4x-2)=6
-3x+8x-4=6
-3x+8x-4=6
[tex]5x=10[/tex]
Divide both sides by 5 to get
x=2
This implies that:
y=4(2)-2
y=8-2=6
The total cost for 9 bracelets including shiping is $72.00
The shipping charge is $9.00
How much are the bracelets?
Please show your work (and dont guess this is an important test!)
Answer it depends
Step-by-step explanation: how much are there a pice or how much are all 9 . 72-9= 63
But the cost of 1 bracelet is $7
The library is 3 miles east of the city hall. The mall is 10 miles west of the library. How far and in what direction is the mall from the city hall?
Answer:
7 miles west of the city hall
Step-by-step explanation:
The city hall on a coordinate plane is at the origin (0, 0). That means that if the library is 3 miles straight east, its coordinates are (3, 0). If the mall is 10 miles straight west of the library, we find its coordinates by subtracting 10 from 3, which puts us at the coordinate (-7, 0). That means that the mall is 7 miles west of the city hall.
Answer:
[tex]\boxed{\text{seven miles west}}[/tex]
Step-by-step explanation:
Think of this as a number line in which city hall is at 0.
East of city hall is the positive direction and west is negative.
Start at city hall and go three miles east to the library. You are at +3.
Then go 10 mi west to the mall. You end up at -7.
+3 – 10 = -7
[tex]\text{The mall is \boxed{\textbf{seven miles west}} of city hall.}[/tex]
Please help me out please:)
Answer:
56.1 cm²
Step-by-step explanation:
In any circle the area (A) of a sector is
A = area of circle × fraction of circle
= πr² × [tex]\frac{81}{360}[/tex]
= π × 8.91² × [tex]\frac{81}{360}[/tex]
= [tex]\frac{8.91^2(81)\pi }{360}[/tex] ≈ 56.1 cm²
A veterinarian investigating possible causes of enteroliths in horses suspects that feeding alfalfa may be to blame. she wishes to estimate the proportion of horses with enteroliths who are fed at least two flakes of alfalfa per day. in a sample of 62 horses with enteroliths, she finds 42 are fed two or more flakes of alfalfa. she estimates the standard error to be se = 0.0594. 0.2185. 0.0035. 0.4675.
Final answer:
In this Biology question, a veterinarian is investigating the possible causes of enteroliths in horses and suspects that feeding alfalfa may be responsible. She conducted a study to estimate the proportion of horses with enteroliths who are fed two or more flakes of alfalfa per day.
Explanation:
The subject of this question is Biology. The veterinarian is investigating the possible causes of enteroliths in horses and suspects that feeding alfalfa may be to blame. She wants to estimate the proportion of horses with enteroliths who are fed at least two flakes of alfalfa per day.
She conducted a study where she sampled 62 horses with enteroliths and found that 42 of them are fed two or more flakes of alfalfa. She estimates the standard error to be 0.0594.
Which ordered pair is on the graph of the function y = 8x - 1 ? A (2, 15) B (8, –1) C (8, 1) D (15, 2)
Answer:
A(2,15)
Step-by-step explanation:
Plug it in on the desmos calculator!!! Put the equation first and then add the points and see which one touches the line.
The ordered pair which is on the graph of the given function is (2, 15).
What is a function?It gives the relationship between each element of a set to another non-empty set.It is one of the most important part of the calculus.It is a rule, that gives unique output for the any input we provide.
Given: Function
y = 8x - 1
Now, among the given ordered pair (x, y), the pair that satisfies the given function is the point on the graph.
Option (A): (2, 15)
⇒ y = 8x - 1
⇒ 15 = 8(2) - 1
⇒ 15 = 16 - 1
⇒ 15 = 15
Hence, this ordered pair is on the graph of the given function.
This option is correct.
Option (B): (8, -1)
⇒ y = 8x - 1
⇒ -1 = 8(8) - 1
⇒ -1 = 64 - 1
⇒ -1 ≠ 63
Hence, this ordered pair is not on the graph of the given function.
This option is incorrect.
Option (C): (8, 1)
⇒ y = 8x - 1
⇒ 1 = 8(8) - 1
⇒ 1 = 64 - 1
⇒ 1 ≠ 63
Hence, this ordered pair is not on the graph of the given function.
This option is incorrect.
Option (D): (15, 2)
⇒ y = 8x - 1
⇒ 2 = 8(15) - 1
⇒ 2 = 120 - 1
⇒ 2 ≠ 119
Hence, this ordered pair is not on the graph of the given function.
This option is incorrect.
Therefore, (2, 15) is the only ordered pair on the graph of the given function.
Hence, Option (A) is correct.
Learn more about the Function here: https://brainly.com/question/16406473
#SPJ2
What’s the slope of the line?
Answer:
Y=-3x+4
Step-by-step explanation:
The Slope is -3 and the Y intercept is +4
Answer:
-3
Step-by-step explanation:
We can find the slope of a line by finding 2 points
(0,4) and (2,-2) are two points on the line
m = (y2-y1)/(x2-x1)
= (-2-4)/(2-0)
= -6/2
=-3