Answer:
x-intercept=3
y-intercept=4
z-intercept=2
Step-by-step explanation:
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3 sin^2(t), y = 3 cos^2(t), 0< t<3pi
What is the length of the curve?
The length of the curve (and thus the total distance traveled by the particle along the curve) is
[tex]\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt[/tex]
We have
x(t) = 3 sin²(t ) ==> x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )
y(t) = 3 cos²(t ) ==> y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )
Then
√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|
and the arc length is
[tex]\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt[/tex]
Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.
Now,
• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)
• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)
so we split up the integral as
[tex]\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)[/tex]
which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.
11 10 Find the area of the shaded region. Round your answer to the nearest tenth.
Quadrilateral ABCD has vertices A(–1, –2), B(–1, 3), C(4, 3) and D(4, –2). It’s dilated by a factor of 2 with the center of dilation at the origin. What are the coordinates of the resulting quadrilateral A’B’C’D
9514 1404 393
Answer:
A'(-2, -4)B'(-2, 6)C'(8, 6)D'(8, -4)Step-by-step explanation:
Dilation about the origin multiplies each coordinate value by the dilation factor.
A' = 2A = 2(-1, -2) = (-2, -4)
B' = 2B = 2(-1, 3) = (-2, 6)
C' = 2C = 2(4, 3) = (8, 6)
D' = 2D = 2(4, -2) = (8, -4)
a number has 7 at the tens place .there is zero in the thousand place. the number 5 is at the hundreds place .there is number 1at the ten thousand place..what is the number?
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 185 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m. Equipment damage will occur if the parachute opens at an altitude of less than 100 m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes
Answer:
0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.
Step-by-step explanation:
For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.
To find the probability of damage on a parachute, the normal distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Probability of a parachute having damage.
The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that [tex]\mu = 185, \sigma = 32[/tex]
Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 185}{32}[/tex]
[tex]Z = -2.66[/tex]
[tex]Z = -2.66[/tex] has a p-value of 0.0039.
What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?
0.0039 probability of a parachute having damage, which means that [tex]p = 0.0039[/tex]
5 parachutes, which means that [tex]n = 5[/tex]
This probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193[/tex]
0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.
What is the distance between the following points?
WILL GIVE BRAINLIEST
Answer:
D.√85
Step-by-step explanation:
We can find the distance between two points using the distance between two points formula
Distance between two points formula:
d = √(x2 - x1)² + (y2 - y1)²
Where the x and y values are derived from the given points
We are given the two points (-2,7) and (7,9)
Using these points let's define the variables ( variables are x1, x2, y1, and y2)
Remember points are written as follows (x,y)
The x value of the first point is -2 so x1 = -2
The x value of the second point is 7 so x2 = 7
The y value of the first point is 7 so y1 = 7
The y value of the second point is 9 so y2 = 9
Now that we have defined each variable let's find the distance between the two points
We can do this by substituting the values into the formula
Formula: d = √(x2 - x1)² + (y2 - y1)²
Variables: x1 = -2, x2 = 7, y1 = 7, y2 = 9
Substitute values in formula
d = √(7 - (-2))² + (9 - 7)²
Evaluation:
The two negative signs cancel out on 7-(-2) and it changes to +7
d = √ (7+2)² + (9-7)²
Add 7+2 and subtract 9 and 7
d = √ (9)² + (2)²
Simplify exponents 9² = 81 and 2² = 4
We then have d = √ 81 + 4
Finally we add 81 and 4
We get that the distance between the two points is √85
What's the next number in the sequence 16, 4, 1,
Answer:
0.25
Step-by-step explanation:
16/4 = 4
4/4 = 1
1/4 = 0.25
0.25/4 = 0.0625
0.0625/4 = 0.015625
give me brainliest please:)
Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2).
Answer:
Point-slope form: y-4=2(x+1)
Slope intercept form: y=2x+6
I hope this helps!
Answer:
[tex]y-4=2(x+1)[/tex]
Step-by-step explanation:
Point-slope form is equal to
[tex]y-y_1=m(x-x_1)[/tex]
where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:
[tex]4-2=m(-1-(-2))[/tex]
We can simplify negative one minus negative two as positive 1.
[tex]4-2=m(1)[/tex]
4 minus 2 is 2, so m times 1 is 2. That means m is 2.
Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:
[tex]y-4=2(x+1)[/tex]
Help plz last question
Answer:
224π in^2
Step-by-step explanation:
Just plug in the values,
Surface area=2πr(h+r) [Factoring]
r=7in
h=9in
2πr(h+r)=2π*7(9+7)=14π(16)=224π in^2
In the diagram below, circle O has a radius of 10. If the measure of arc AB is 72°, find the area of shaded sector AOB, in terms of π. Show all your work that leads to the final answer.
Answer:
62.8
Step-by-step explanation:
Area of sector=(pi*r^2)*(theta/360)
Area of sector=(pi*100)*(72/360)=62.8
The area of the shaded sector AOB in terms of π is 20π units squared.
How to find area of a sector?
The area of a sector can be described as follows;
area of sector = ∅ / 360 × πr²
where
r = radius of the circleTherefore,
r = 10 units
∅ = 72°
Hence,
area of the sector = 72° / 360° × π10²
area of the sector = 7200 / 360 π
area of the sector = 20π units²
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Which equation is in standard form?
a. X +3= -5y
b. 5-y=x
c. y =3x + 6
d. -8x+ 3y = 12
选项 (d)
option (d)
!!!!!!!!!
Power Function:
Consider the following graphs (1 and 2), and answer the questions FOR EACH GRAPH:
A) In what interval of the graph is it increasing, decreasing and constant? This answer must be justified by means of the definition
B) What is the domain and range?
C) Is it an odd or even function? This answer must be justified by means of the definition
Graph 1
Part (a)
The function is increasing when x > 0. The function is decreasing when x < 0.
The function is never constant
An increasing portion is when the graph goes uphill when moving left to right. A decreasing portion goes in the opposite direction: it goes downhill when moving left to right.
The reason why the function is never constant is because there aren't any flat horizontal sections. Such sections are when x changes but y does not. No such sections occur.
------------------------
Graph 1
Part (b)
Domain = set of all real numbers
Range = set of y values such that [tex]y \ge 0[/tex]
The domain is the set of all real numbers because we can plug in any value for x without any restriction. There are no division by zero errors to worry about, or square roots of negative numbers to worry about either.
The range is the set of nonnegative numbers as the graph indicates. The lowest y gets is y = 0.
------------------------
Graph 1
Part (c)
The function is even
The function f(x) = 1.6x^12 is an even function due to the even number exponent. For any polynomial, as long as the exponents are all even, then the function itself is even. If all the exponents were odd, then the function would be odd. This applies to polynomials only. A power function is a specific type of polynomial.
Note in the graph, we have y axis symmetry. The mirror line is vertical and placed along the y axis. This is a visual trait of any even function.
We could use algebra to show that f(-x) = f(x) like so
f(x) = 1.6x^12
f(-x) = 1.6(-x)^12
f(-x) = 1.6x^12
The third step is possible because (-x)^12 = x^12 for all real numbers x. It's similar to how (-x)^2 = x^2. You could think of it like (-1)^2 = (1)^2
============================================================
Graph 2
Part (a)
The function is decreasing when x < 0 and when x > 0
The function is never increasing
The function is never constant
In other words, the function is decreasing over the entire domain (see part b). The only time it's not decreasing is when x = 0.
The function is decreasing because the curve is going downhill when moving to the right. You can think of it like a roller coaster of sorts.
At no point of this curve goes uphill when moving to the right. Therefore, it is never increasing. The same idea applies to flat horizontal sections, so there are no constant intervals either.
------------------------
Graph 2
Part (b)
Domain: x is any real number but [tex]x \ne 0[/tex]
Range: y is any real number but [tex]y \ne 0[/tex]
Explanation: If we tried plugging x = 0 into the function, we get a division by zero error. This doesn't happen with any other number. Therefore, the set of allowed inputs is any number but 0.
The range is a similar story. There's no way to get y = 0 as an output.
If we plugged y = 0 into the equation, then we'd get this
y = 17x^(-3)
0 = 17/(x^3)
There's no way to have the right hand side turn into 0. The numerator is 17 and won't change. Only the denominator changes. We can't have the denominator be 0.
------------------------
Graph 2
Part (c)
The function is odd
We can prove this by showing that f(-x) = -f(x)
f(x) = 17x^(-3)
f(-x) = 17(-x)^(-3)
f(-x) = 17* ( -(x)^(-3) )
f(-x) = -17x^(-3)
f(-x) = -f(x)
This is true for nearly all real numbers x, except we can't have x = 0.
Graphic 1:
(A) If f(x) = 1.6x ¹², then f '(x) = 19.2x ¹¹. Both f '(x) and x have the same sign, which means
• for -∞ < x < 0, we have f '(x) < 0, so that f(x) is decreasing on this interval
• for 0 < x < ∞, we have f '(x) > 0, so f(x) is increasing on this interval
f(x) is not constant anywhere on its domain.
(B) Speaking of domain, since f(x) is a polynomial (albeit only one term), it has
• a domain of all real numbers
• a range of {y ∈ ℝ : y = f(x) and y ≥ 0} (in other words, all real numbers y such that y = 1.6x ¹² and y is non-negative)
(C) This function is even, since
f(-x) = 1.6 (-x)¹² = (-1)¹² × 1.6x ¹² = 1.6x ¹² = f(x)
Graphic 2:
(A) Now if f(x) = 17/x ³, then f '(x) = -51/x ⁴. Because x ⁴ ≥ 0 for all x, this means f '(x) < 0 everywhere, except at x = 0. So f(x) is decreasing for (-∞ < x < 0) U (0 < x < ∞).
(B) f(x) has
• a domain of {x ∈ ℝ : x ≠ 0} (or all non-zero real numbers)
• a range of {y ∈ ℝ : y = f(x) and y ≠ 0} (also all non-zero reals)
(C) This function is odd:
f(-x) = 17/(-x)³ = 1/(-1)³ × 17/x ³ = -17/x ³ = -f(x)
A cylinder with a base diameter of x units has a volume of excubic units.
Which statements about the cylinder are true,Select
two options.
1)The radius of the cylinder is 2x units.
2)The area of the cylinder's base is 1/4 piex^2square units.
3)The area of the cylinder's base is 1/2 piex^2 square units.
4)The height of the cylinder is 2x units.
5)The height of the cylinder is 4x units.
Answer:3 and 4
Step-by-step explanation:
The length L of the base of a rectangle is 5 less than twice its height H. Write the algebraic expression to model the area of the rectangle.
Answer:
Area of rectangle = 2H² - 5H
Step-by-step explanation:
Let the length be L.Let the height be H.Translating the word problem into an algebraic expression, we have;
Length =2H - 5
To write the algebraic expression to model the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = L * H
Where;
L is the Length.H is the Height.Substituting the values into the formula, we have;
Area of rectangle = (2H - 5)*H
Area of rectangle = 2H² - 5H
if x and y are linear pair of angel then x +y=
Answer: x + y = 180²
Step-by-step explanation:
A linear pair is a pair of adjacent, supplementary angles.
Adjacent means next to each other.
Supplementary means that the measures of the two angles add up to equal 180 degrees.
Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.
HELP WILL GIVE BRAINLYIST
Answer:
The parent cubic function has been vertically stretched by a factor of 4.
Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]
Answer: Option B
OAmalOHopeO
Let U be a matrix where u_ij = 0 if i > j, and L be a matrix where l_ij = 0 if i < j.
(a) U is called an upper triangular matrix and L is a lower tri-angular matrix. Explain why.
(b) Prove or disprove: The sum of two upper triangular matrices is an upper triangular matrix.
(c) Prove or disprove: The product of two upper triangular matrices is an upper triangular matrix.
Answer:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 )
B) sum of two upper triangular matrices = upper triangular matrix.
C) product of two upper triangular matrices = upper triangular matrix
Step-by-step explanation:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 ) since Lij = 0 if i < j
B) To prove that sum of two upper triangular matrices
attached below
C) Prove or disprove that product of two upper triangular matrices is an upper triangular matrix
attached below
5. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will _____________________ . (5 points)
Answer:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase
Step-by-step explanation:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase.
Aaron uses 18% of the paper in a printer paper package when she print a report for social studies class this is 90 sheets of paper how many sheets of paper are there in the printer paper in a package?
Answer:
percentage of paper used= 18%
Number of papers printed= 90
Total number of papers in the paper package= 'y'
total number of papers
= [tex]\frac{18}{100}[/tex] × y =90
transpose to the other side,
y= 90 ×[tex]\frac{100}{18}[/tex]
y=10 x100
y=1000
hence total number of papers in the package is 1000
Hope this helps
Please mark me as brainliest
I need help on this plzzz I and not the best at math
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]f(x) = \left[\begin{array}{cc}-1&x<-1\\0&-1\le x \le -1\\1&x>1\end{array}\right[/tex]
Required
The graph of the step function
Before plotting the graph, it should be noted that:
[tex]\le[/tex] and [tex]\ge[/tex] use closed circle at its end
[tex]<[/tex] and [tex]>[/tex] use open circle at its end
So, we have:
[tex]f(x) = -1,\ \ \ \ x < -1[/tex]
The line stops at -1 with an open circle
[tex]f(x) = 0,\ \ \ \ -1 \le x \le 1[/tex]
The line starts at - 1 and stops at -1 with a closed circle at both ends
[tex]f(x) = 1,\ \ \ \ x > 1[/tex]
The line starts at 1 with an open circle
The options are not complete, so I will plot the graph myself.
See attachment for graph
In a café, I order a cup of tea and a piece of cake and it costs £1.10. The next time I order 2 cups of tea and one piece of cake and it costs £1.70. Find the cost of a piece of cake.
Answer:
£0.50
Step-by-step explanation:
t = one cup of tea
c = one piece of cake
t + c = £1.10
2t + c = £1.70
the cost increases by £0.60 (£1.70 - £1.10) when you order one more cup of tea which means that one cup of tea costs £0.60
substitute £0.60 into t + c = £1.10
£0.60 + c = £1.10
rearrange to get c = £1.10 - £0.60 = £0.50
so one piece of cake costs £0.50
Trisha bought a carton of orange juice. She drank 1/3 of the carton on Monday and 5/12 of the carton on Tuesday. What fraction of the carton did Trisha drink?
Answer:
9/12 or 2/3
Step-by-step explanation:
Make both fractions have the same denominator by finding their least common multiple
1x12 = 12 1x3 = 3
2x6 = 12 3x1 = 3
3x4 = 12
4x3 = 12
6x2 = 12
12x1 = 12
In which case it would be 12.
1/3 would be 4/12
5/12 + 4/12 = 9/12
which is also 2/3 if your teacher wants the simplest answer
Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. If 390 tickets were sold for a total of $2190.00, how many student tickets were sold
Answer: Therefore 100 student tickets were sold
Step-by-step explanation:
Let the number of student tickets be x
So adult tickets = 390 - x
ATQ
4.5(x) + 6(390-x) = 2190
4.5x + 2340 - 6x = 2190
-1.5x + 2340 = 2190
-1.5x = 2190-2340
-1.5x = -150
x = -150/-1.5
x = 100
Therefore 100 student tickets were sold
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how many ways can this be done. if a committee of 5 people from 7 men and 8 women?
Answer:
3003 ways
Step-by-step explanation:
(7+8)C5
= 15C5
= 15!/(5!10!)
= 3003
what should be added to 4x get 9X please help me in this pic also all
Answer:
[tex]thank \: you[/tex]
[tex]2i+3x=4-ix[/tex]
Show work.
No wrong answers or you will be reported. I will mark Brainliest! Thank you!
Answer:
Step-by-step explanation:
I am assuming i is the imaginary number:
Factor:
(3 + i)x - (4-2i) = 0.
In order for this to equal 0, x must be equal to 1-i.
I don't want to be reported to so take my word for it.
Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.
Using BTS he properties, find the unit's digit of the cube of each of the following numbers
There are10 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, howmany different slates of candidates are possible
Answer:
The answer is "720"
Step-by-step explanation:
The amount of different slates candidates:
[tex]n=\frac{N!}{(N-k)!}\\\\[/tex]
[tex]=\frac{10!}{(10-3)!}\\\\=\frac{10!}{7!}\\\\=\frac{10\times 9 \times 8 \times 7! }{7!}\\\\=10\times 9 \times 8\\\\=90\times 8\\\\=720[/tex]
Which of the following best describes the line that divides a design so that
every point on one side of the line coincides with a point on the other side of
the line?
A. Line of Symmetry
B. Point of Translation
C. Angle of Symmetry
D. Point of congruency
Answer:
Line of Symmetry i think
Line of symmetry best describes the line that divides a design so that every point on one side of the line coincides with a point on the other side of the line.
What is Coordinate Geometry?Coordinate Geometry (or the analytic geometry) describes the link between geometry and algebra through graphs involving curves and lines.
A line of symmetry is a line that divides a figure into two congruent parts such that if one part is folded over the line of symmetry, it will coincide with the other part.
In other words, each point on one side of the line of symmetry is equidistant from the line as the corresponding point on the other side of the line.
The line that divides a design so that every point on one side of the line coincides with a point on the other side of the line is called the Line of Symmetry.
Hence, line of symmetry best describes the line that divides a design so that every point on one side of the line coincides with a point on the other side of the line.
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what are the factor of pair of number?
a.45 and 60
b.45 and 70
c.40 and 80
d.30 and 50
PLEASE gelp me with this, gelp me please oh please gelp me!
Answer:
V = 2143.57 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
The diameter is 16 so the radius is 1/2 of the diameter or 8
V = 4/3 ( 3.14) (8)^3
V =2143.57333
Rounding to the nearest hundredth
V = 2143.57 cm^3
Answer:
2143.57 cm^3
Step-by-step explanation:
V = 4/3 * 3.14 * r^3
r = 1/2 * 16 = 8
So V = 4/3 * 3.14 * 8^3
= 2143.57 cm^3.
