What is the rectangular equivalence to the parametric equations?
x(θ)=2sinθ+1,y(θ)=3cosθ−2 , where 0≤θ<2π .
Drag a term into each box to correctly complete the rectangular equation.
Answers
Notice that
(x - 1)²/4 + (y + 2)²/9 = (2 sin(θ))²/4 + (3 cos(θ))²/9
… = sin²(θ) + cos²(θ)
… = 1
Solve for y in terms of x :
(x - 1)²/4 + (y + 2)²/9 = 1
(y + 2)²/9 = 1 - (x - 1)²/4
(y + 2)² = 9 - 9/4 (x - 1)²
y + 2 = ± √(9 - 9/4 (x - 1)²)
y + 2 = ± 3/2 √(4 - (x - 1)²)
y = -2 ± 3/2 √(4 - (x - 1)²)
In order for the square root to be defined, one needs
4 - (x - 1)² ≥ 0
(x - 1)² ≤ 4
-2 ≤ x - 1 ≤ 2
-1 ≤ x ≤ 3
so x must belong to the interval [-1, 3].
Related Questions
What is the surface area of the cylinder? Express the answer in terms of pi
d = 8 cm
h = 18 cm
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answer ≈ 522.92
working
A= 2πrh+2πr^2
=2 x π x 4 x 18+2 x π x 4^2
≈552.92031
Which inequality is true?
Answers
Answer:
[tex]\boxed{\sf Option \ C \ is \ correct .}[/tex]
Step-by-step explanation:
We need to tell which of the given inequality is true . The given inequalities are ,
[tex]\sf A)\pi + 8 <11\\\\\sf B) \dfrac{\pi}{8} > 2 \\\\\sf C) 3\pi > 9 \\\\\sf D) 2\pi - 1 < 5 [/tex]
Let's check the options one by one .
Option A :-
[tex]\sf\longrightarrow \pi + 8 < 11[/tex]
Subtract 8 to both sides ,
[tex]\sf\longrightarrow \pi < 11 - 8 [/tex]
Simplify ,
[tex]\sf\longrightarrow \pi < 3[/tex]
We know the approximate value of pi 3.14 . But the inequality says pi is less than 3 . Therefore the given inequality is incorrect .
______________________________________
Option B :-
[tex]\sf\longrightarrow \dfrac{\pi}{2} > 2 [/tex]
Multiply both sides by 2 ,
[tex]\sf\longrightarrow \pi > 4 [/tex]
We know the approximate value of pi 3.14 . But the inequality says pi is more than 4 . Therefore the given inequality is incorrect .
______________________________________
Option C :-
[tex]\sf\longrightarrow 3 \pi > 9[/tex]
Divide both sides by 3 ,
[tex]\sf\longrightarrow \pi < 9/3[/tex]
Simplify ,
[tex]\sf\longrightarrow \pi > 3 [/tex]
We know the approximate value of pi 3.14 .And the inequality says pi is more than 3 . Therefore the given inequality is correct .
Option C is correct .
Evaluate function from their graph
Answers
This is because the point (0,5) is shown on the graph. This is the point on the y axis.
We can say that h(x) = 5 when x = 0.
Answer:
5
Step-by-step explanation:
The fellow who expalined it before before me expalined it correctly, so the answer should be 5.
when I add a number to another number four times as big, the result is 30. find the first number
Answers
Answer:
x = 6
Step-by-step explanation:
Let x = first number
x+4x = 30
5x = 30
Divide by 5
5x/5 =30/5
x = 6
Let's assume the number is N
According to the question,
when I add a number to another number four times as big, the result is 30.
[tex]x+4x=30\\\\5x=30\\\\x=\dfrac{30}{5}\\\\x=\frak{6}[/tex]
Changing some of the values in a data set is called transforming the data.
A. True
B. False
Answers
Answer:
The answers is False
Step-by-step explanation:
What is the value of x in the triangle below?
A. 18
B. 15
C. 6
D. 45
Answers
Answer:
it is b I already took it I just checked again
two similar triangular prisms have surface areas of 64cm2 and 144cm2(the 2 means square) respectively. a.find the ratio of their heights. b. The height of the smaller prism is 49cm,find the height of the larger prism.
Answers
Answer:
a.The ratio of the heights is the square roots of the both of them √64 and √144
which is 8 and 12
b.To find the height of the larger prism you use the ratio of the heights,in a ratio and proportion
8 - 49
12-x
8x/8=588/8
x=73.5
I hope this helps
Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years.Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.(a) null hypothesis H0: μ = 2.5 yearsH0: μ = 3 years H0: μ > 3 yearsH0: μ ≥ 2.5 yearsH0: μ = 1.8 years(b) alternative hypothesis Ha: μ ≠ 2.5 yearsHa: μ > 3 years Ha: μ ≥ 1.8 yearsHa: μ ≤ 3 yearsHa: μ > 2.5 years
Answers
Answer:
The null hypothesis is [tex]H_0: \mu = 2.5[/tex].
The alternative hypothesis is [tex]H_1: \mu > 2.5[/tex]
Step-by-step explanation:
Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years.
At the null hypothesis, we test if the mean is of 2.5 years, that is:
[tex]H_0: \mu = 2.5[/tex]
A study was then done to see if the mean time has increased in the new century.
At the alternative hypothesis, we test if the mean has increased, that is, if it is above 2.5 years. So
[tex]H_1: \mu > 2.5[/tex]
(Question is in the image)
please I really need help
Answers
Answer:
c
Step-by-step explanation:
The period is 1 complete cycle of the wave, before repeating.
1 cycle is from - 6 to - 2 , then
period = 4 → c
Instructions: Find the measure of the indicated angle to the nearest degree.
?
Answers
Answer:
? = 14
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan ? = 8/33
Taking the inverse tan of each side
tan ^-1 ( tan ?) = tan ^-1 ( 8/33)
? =13.62699
To the nearest degree
? = 14
Answer:
14
Step-by-step explanation:
We can solve for either x or y first, but we will choose to solve for x first. The side with length of 8 is opposite the angle x and the side with length of 33 is adjacent. Since we have opposite and adjacent sides, we will use the tangent ratio.
tan(x)= opposite/adjacent
tan(x)= 8/33
To find the measure of angle x, we will use the inverse tan function.
x=tan⁻¹(8/33)= 14
which of the following is equivalent to 18-
[tex] \sqrt{ - 25} [/tex]
a 5i
b 18-5i
c 18+5i
d 23
Answers
Answer:
[tex]18-\sqrt{-25}[/tex]
[tex]\sqrt{-25} =5i[/tex]
[tex]=18-5i[/tex]
OAmalOHopeO
A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $10.20 per pound with a Terraza coffee blend that normally sells for $13.50 per pound to create 40 pounds of a coffee that can sell for $10.37 per pound. How many pounds of each kind of coffee should they mix
Answers
Answer:
Rift =37.92 pounds
Terraza=2.08 pounds
9514 1404 393
Answer:
Rift Valley: 37 31/33 ≈ 37.94 lbTerraza: 2 2/33 ≈ 2.06 lbStep-by-step explanation:
Let t represent the number of pounds of Terraza blend required. Then 40-t is the number of pounds of Rift Valley blend needed. The cost of the mix will be ...
13.50t +10.20(40 -t) = 10.37(40)
3.30t = 6.8 . . . . . . . . . . . . . . . . . . . . subtract 408
t = 6.8/3.30 = 68/33 = 2 2/33 ≈ 2.06061 . . . . pounds of Terraza
Then the quantity of Rift Valley blend required is ...
40 -2 2/33 = 37 31/33 ≈ 37.93939 . . . . pounds of Rift Valley
12X12= ___+144-88=___
Answers
Explanation. After you get the 12×12 and get the answer you add the answer to 144 and subtract 88 and that’s your answer
A locker combination has three nonzero digits, with no repeated digits. If the first digit is a 2, what is the probability the second digit is also even?
A. 1/2
B. 1/3
C. 3/7
D. 3/8
Answers
If the product of two numbers is 1800 and its H.C.F. Is 30, find the L.C.M.
Answers
Answer:
LCM = 60
Step-by-step explanation:
Product = HCF × LCM
1800 = 30 × LCM
LCM = 1800/30
∴ LCM = 60
Find the measure of FG.
Answers
Answer:
Choice D, x = 9
Answer:
Step-by-step explanation:
EG = EF + FG = 9 + x - 3 = 6 + x
AG = AH + HG = 6 +x - 2 = 4 + x
Intersecting secant theorem,
FG * EG = HG * AG
(x - 3)*(6 +x) = (x -2)(x + 4)
Use Foil method
6x + x² - 18 - 3x = x² + 4x - 2x - 8
x² + 3x - 18 = x² + 2x - 8
x² - x² + 3x - 2x = -8 + 18
x = 10
What is the surface area of a sphere with a diameter of 14 cm?
Question 6 options:
175.84 cm^2
351.68 cm^2
615.44 cm^2
2461.76 cm^2
Show your work:
Answers
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Answer:
(c) 615.44 cm^2
Step-by-step explanation:
The surface area of a sphere is given by ...
A = 4πr² . . . . where r is the radius, half the diameter
A = 4(3.14)(7 cm)² = 196(3.14) cm² = 615.44 cm²
PLS HELP 10 POINTS!!!
Identify the term whose coefficient is -12 in the expression:
98x – 12xy2 - 15xy2
Answers
Answer:
[tex] - 12xy {}^{2} [/tex]
Step-by-step explanation:
A coefficient is a rational number in front of multiple consecutive terms.
verify a(b-c)=ab-ac for a=1.6;b=1/-2;& c=-5/-7
Answers
Given:
[tex]a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}[/tex]
To verify:
[tex]a(b-c)=ab-ac[/tex] for the given values.
Solution:
We have,
[tex]a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}[/tex]
We need to verify [tex]a(b-c)=ab-ac[/tex].
Taking left hand side, we get
[tex]a(b-c)=1.6\left(\dfrac{1}{-2}-\dfrac{-5}{-7}\right)[/tex]
[tex]a(b-c)=1.6\left(-\dfrac{1}{2}-\dfrac{5}{7}\right)[/tex]
Taking LCM, we get
[tex]a(b-c)=1.6\left(\dfrac{-7-10}{14}\right)[/tex]
[tex]a(b-c)=\dfrac{16}{10}\left(\dfrac{-17}{14}\right)[/tex]
[tex]a(b-c)=\dfrac{8}{5}\left(\dfrac{-17}{14}\right)[/tex]
[tex]a(b-c)=-\dfrac{68}{35}\right)[/tex]
Taking right hand side, we get
[tex]ab-ac=1.6\times \dfrac{1}{-2}-1.6\times \dfrac{-5}{-7}[/tex]
[tex]ab-ac=-\dfrac{16}{20}-\dfrac{8}{7}[/tex]
[tex]ab-ac=-\dfrac{4}{5}-\dfrac{8}{7}[/tex]
Taking LCM, we get
[tex]ab-ac=\dfrac{-28-40}{35}[/tex]
[tex]ab-ac=\dfrac{-68}{35}[/tex]
Now,
[tex]LHS=RHS[/tex]
Hence proved.
Help please!! Plots of land between two roads are laid out according to the boundaries shown. The boundaries between the two roads are parallel. What is the length of Plot 3 along Cheshire Road?
Answers
Answer: Choice D
53 and 1/3 yards
=======================================================
Work Shown:
40/48 = x/64
5/6 = x/64
5*64 = 6*x
320 = 6x
6x = 320
x = 320/6
x = 53.33333...
x = 53 + 0.3333...
x = 53 + 1/3
x = 53 and 1/3, answer is choice D
------------
Explanation:
Basically because the quadrilaterals are similar, this means the sides are proportional to one another. This allows us to set up the equation at the very top. In step 3, I cross multiplied. Then later on, I divided both sides by 6.
Keep in mind that the similar figures are because of the parallel lines. If the lines weren't parallel, then the figures may not be similar.
Answer:
46 [tex]\frac{2}{3}[/tex] (For those with the Shelby Road Plot 3 Measurement that says 56 yards.)
Step-by-step explanation:
[tex]\frac{40}{48} = \frac{x}{56} \\\\48x = 2240\\\\x = 46.6667 \\or 46\frac{2}{3}[/tex]
guys, please help its graph-related. please i will dieeee
Answers
(a) Dilation is the process of extending the line segment AB to the longer one A'B'. The scale factor has to be larger than 1, and also it has to be positive.
(b) To get the dilation factor, you should first compute the length of AB, then compare it to the length of A'B'.
A is the point (-4, 2), and B is the point (2, -4). So the length of AB is
√((-4 - 2)² + (2 - (-4))²) = √((-6)² + 6²) = √72
A' is the point (-8, 4) and B' is (4, -8). The coordinates of A' and B' are twice the coordinates of A and B, so the distance is
√((2(-4) - 2(2))² + (2(2) - 2(-4))²) = √(2²×72) = 2√72
Then the dilation factor is
(2√72) / √72 = 2
As for dying, don't worry about it. It happens to everyone.
(b) If n(U)= 300, n(M) = 150, n(T) = 144 and n( MT)= 33. Find the value of n(MUT). (ii) Present the above information in a Venn diagram.
Answers
Answer:
Step-by-step explanation:
n(M ∪ T) = n(M) + n(T) - n(M∩T)
= 150 + 144 - 33
= 294 - 33
= 261
If 4 over 7 ton of concrete covers 7 over 8 of a bridge, how many tons of concrete are required to cover the entire bridge?
Answers
Answer:
Your answer would be 32/49.
Step-by-step explanation:
4/7 tons = 7/8 x
4/7 / 7/8
32/49
The tons of concrete are required to cover the entire bridge is 32/49 tons.
What are fractions?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 4/7.
How many tons is needed to cover the whole bridge?To determine this value, divide 4/7 by 7/8
4/7 ÷ 7/8
4/7 x 8/7 = 32/49 tons
To learn more about the division of fractions, please check: https://brainly.com/question/25779356
PLEASE HELP WILL GIVE BRAINSLIST
Answers
Answer: 3. 55° 2. 225° 1. 125°
Step-by-step explanation: don't want brainliest
You are an avid coin collector. You decide to start keeping better track of your coin collection:after 15 days you count and find out you have 155 coins. After 22 days,you have 218 coins. Write an equation in point-slope form
Answers
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Answer:
y - 155 = 9(x -15)
Step-by-step explanation:
The given points are ...
(days, coins) = (15, 155) and (22, 218)
The slope is given by the slope formula:
m = (y2 -y1)/(x2 -x1) = (218 -155)/(22 -15) = 63/7 = 9
The point-slope form is for a line with slope m through point (h, k) is ...
y -k = m(x -h)
Here, we have m=9 and (h, k) = (15, 155), so the equation can be written ...
y - 155 = 9(x -15)
The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers.
[ x + y = 90 ; x = 14 + 3y ]
Answers
Answer:
fourteen times six equals eighty-four, eighty-four plus six equals 90
Please help I don’t understand how to solve this !
Answers
Answer:
x = 30
Step-by-step explanation:
x + 2x + 3x = 180
6x = 180
6 6
x = 30
When do we use the AC Test?
Answers
Porfa es para un examen xD
Answers
Answer: -13
Step-by-step explanation:
M(3) → x = 3M(2) → x = 2[tex]\frac{M(3)+M(2)}{2} =\frac{[-2(3)^{2}] +[-2(2)^{2}]}{2}=\frac{(-2)(9)+(-2)(4)}{2}=\frac{-18-8}{2}=\frac{-26}{2}=-13[/tex]
For what values of x does 25^x = 5^x^2^-3?
Answers
The correct option is Second Option
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