Answer:
none of them
Step-by-step explanation:
Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
Using polar coordinates, volume of the given solid is, 32√3π.
What is volume of solid?
An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units
We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.
So, the volume is
[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]
[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]
[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]
[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]
[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]
[tex]32\sqrt{3}\pi[/tex]
Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].
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3. Adam is 20 years younger than Brian. In two years Brian will be twice as old as
Adam is now. How old
are they now? Solve the problem using the elimination method.
Answer:
Here,
Let the age of Adam be x
and ,Brian be y
so,x=y+20.........eqn 1
and ,2(y+2)=x
or,2y+4=x......eqn 2
Now ,
subtracting eqn1 and eqn 2
so, x=y+20
x=2y+4
- - -
______________
0 = -y+16
so,y=16 and x=y+20 =16+20=36 .
so Adam is 36 years old and brian is 16.
lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. Work out how much money Elliot received. Elliot received £
If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.
How to find the amount received?Given data;
Sharing ratio 8:5
Amount Elliot got = 21
In order to determine the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.
Equation
21 × 8 ÷ (8-5)
Hence,
£21 × 8 ÷ (8-5)
£168 ÷ 3
= £56
Therefore Elliot received £56.
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If using the method of completing the square to solve the quadratic equation
x² - 13x +31 = 0, which number would have to be added to "complete the
square"?
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 13x + 31 = 0
(x - 13/2)² + (293/4) = 0
The number added to complete the square is 293/4.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
x² - 13x + 31 = 0
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 2 x (13/2)x + (13/2)² - (13/2)² + 31 = 0
(x - 13/2)² + 169/4 + 31 = 0
(x - 13/2)² + (293/4) = 0
Thus
The number added to complete the square is 293/4.
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Find the values of x, y, and z. The diagram is not to scale.
Answer:
x= 68 z= 180 y=38
Step-by-step explanation:
Please helppppppppppp
Answer:
1
2
[
x
2
2
−
x
3
3
]
2
0
=
1
2
[
(
4
2
−
8
3
)
−
(
0
)
]
=
1
2
(
−
2
3
)
=
−
1
3
Step-by-step explanation:
write an expression using division that could be used to find the width of the rectangle
The expression used to find the width using division is:
W = A/L
Which expression can be used to find the width?We know that for a rectangle of width W and length L, we know that the area is given by the product between these two dimensions, then:
A = L*W
We want a expression using division that can be used to find the width, so, suppose we know the values of the area and the length, the we can divide both sides by L to get:
A/L = W
This expression gives the width.
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What is the range of the given function ?
The range of the function is y ≤ 3.
What is the range of the function?The set of a function's potential output values is known as its range.
Given, the graph of the function.
The range of a function is the set of values of y the function can take.
The maximum y value of the function is 3, and the graph is going down both sides infinitely.
Therefore, the range of the function is y ≤ 3.
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Calculate the standard score (z-score) of the given sample mean. Round your answer to two decimal places.
μ=31 and σ=9; n=64; x¯=30
The standard score (z-score) of the given sample mean is equal to 7.11
What is a standard score?A standard score is also referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
Mathematically, the standard score of a given sample mean can be calculated by using this formula:
[tex]Z=\frac{\bar{x}\;-\;\mu}{ \frac{\delta}{n} }[/tex]
Where:
Where:
x represents the sample score.u represents the mean point.z represents the standard score.σ represents the standard deviation.n represents the number of samples.Substituting the given parameters into the formula, we have;
Standard score, z = (30 - 31)/(9/64)
Standard score, z = -1/0.140625
Standard score, z = 7.11
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What is 8% off of 12$?
Answer:
11.04 U.S. dollarsStep-by-step explanation:
because it is the answer I looked it up (;-;)damian bought a new game station for $774 using the stores zero intrest finace plan. He will pay$43 a month for 18 months. Which equation csn he use ti fund out how much money he still owes
The equation Damian can use to found out how much money he still owes is -
y = - 43x + 774
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
Damian bought a new game station for $774 using the stores zero interest finance plan. He will pay $43 a month for 18 months.
We can represent the equation he can use to found out how much money he still owes using a straight line as follows -
y = 774 - 43x
y = - 43x + 774 [x] is the number of month
Therefore, the equation Damian can use to found out how much money he still owes is -
y = - 43x + 774
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Can anyone help me in this question? pls.........
Answer: A
Step-by-step explanation :
HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )
In the first five math quizzes, Patty had an average score of 8. She got a 7 and a 5 on the next two quizzes. After the eighth quiz, her
average stood at 7.5. What was her score on the eighth quiz?
*
Answer: 8
Step-by-step explanation:
(Sum of first 5 quizzes) / 5 quizzes = 8
Sum of 1st 5 quizzes = 8 x 5 = 40
let x = score on the 8th quiz
(40 + 7 + 5 + x) / 8 = 7.5
52 + x = (7.5)(8) = 60
x = 60 - 52 = 8
what fraction of the numbers from 1 to 20 contain the digit 7
If each standard room cdn fill 2 guests what is the maximum number of guests that all standard rooms can accommodate
The maximum number of guests that can fill all the standard rooms is twice the number of the standard rooms
How to find the number of guests that can fill the standard roomsInformation from the question
each standard room can fill 2 guests
the maximum number of guests that all standard rooms can accommodate = ?
The problem is solved by multiplication
each standard room (1) = 2 guests
all standard rooms = ?
cross multiplying
? * 1 = 2 * all standard rooms
? = all standard rooms times two
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In the acute triangle ABC with angle ACB = 60°, M is the midpoint of side AB. Points D and E are the height points on sides BC and AC, respectively. Show: The triangle MDE is equilateral
An equilateral triangle in geometry is a triangle with three equal-length sides. An equilateral triangle has congruent sides, which means that each side is the same length. The triangle MDE is equilateral only because it is midpoint of ACB
Explain about the Acute triangle?If the square of the longest side is smaller than the sum of the squares of the two smaller sides, the triangle is said to have an acute angle according to Pythagoras's theorem. Given a triangle with sides "a," "b," and "c," with side "a" being the longest, the triangle is steeply angled if "a2" exceeds "b2" plus "c2."
By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you may determine whether the triangle is acute, right, or obtuse. The triangle is sharp because this total is higher.
Isosceles, equilateral, or scalene acute triangles are all possible. An acute triangle's longest side is located across from its biggest angle.
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Elena collects data to investigate the relationship between the number of bananas she buys at the store, , and the total cost of the bananas, . Which value for the correlation coefficient is most likely to match a line of best fit of the form for this situation?
The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:
0.9.
What is a correlation coefficient?The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.
If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.
In the context of this problem, the variables are listed as follows:
Number of bananas bought.Total price of the bananas.The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:
0.9.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Jeffrey earns a constant hourly rate of $12.25 at the tire shop. Which of these best represents the relationship between the number of hours Joseph worked, h, and his total amount earned, t?
Answer:
The correct equation is t = 12.25h.
PLEASE HELP! ALGEBRA 1 HW I WILL GIVE BRAINLYEST FOR ANSWER!!
In the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.
What do we mean by equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the values of C are:
Equation: 12.5x + 5y = CCalculate as follows:
(A) When x = -2 and y = 15.
12.5(-2) + 5(15) = CC = 50(B) When x = 0 and y = 10.
12.5(0) + 5(10) = CC = 50(C) When x = 2 and y = 5.
12.5(2) + 5(5) = CC = 50(D) When x = 4 and y = 0.
12.5(4) + 5(0) = CC = 50Therefore, in the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.
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Sheila is making accessories for the soccer team. She uses 784.96 inches of fabric on headbands for 28 players and 4 coaches. She also uses 238.28 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answer: 3.28 inches
Step-by-step explanation:
Fabric used for players and coaches is 776.32 inches.
Number of players is 29 and coaches is 3
So fabric used for each player and coach for the headbands is
776.32/29+3 = 24.26 inches
So, for the players 24.26 of fabric will be used for the headbands.
Total fabric used for the wristbands is 247.66 inches
Fabric used for the wristband is
247.66/29 = 8.54 inches
So, total amount of fabric used by Shelia for the wristband and headband is 24.26 + 8.54 = 32.8 inches.
Write an equation for line L in point-slope form and slope-intercept form?
L is perpendicular to y=5x
Write an equation for the line L in point - slope form
The linear equation in the slope-intercept is:
y = (-1/5)*x - 26/5
And it can be written as:
y = (-1/5)*(x + 1) - 5
How to find the equation for line L?
We can write the equation for line L as:
y = a*x +b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular if the product between the slopes is equal to -1.
So if we want our line to be perpendicular to y= 5x, then we must have:
a*5 = -1
a = -1/5
So our line is something like:
y = (-1/5)*x + b
And the line passes through (-1, -5), replacing these values:
-5 = (-1/5)*-1 + b
-5 = 1/5 + b
-5 - 1/5 = b
-26/5 = b
The linear equation is:
y = (-1/5)*x - 26/5
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An airplane travels 3582 kilometers against the wind in 6 hours and 4482 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
Answer: Let us assume speed of jet in still air =x
speed of wind =y
Jet flying against the wind
Relative speed of the jet = speed of jet in still air -speed of the wind=x-y
distance covered =3426
time =6 hours
distance = speed * time
3426=(x-y)*6
x-y =3426/6
x-y=571——(1)
Jet flying with the wind
Relative speed of the jet = speed of jet in still air +speed of the wind=x+y
distance covered =4026
time =6 hours
distance = speed * time
4026=(x+y)*6
x+y =4026/6
x+y=671———-(2)
solving 1 and 2 we get
x+y=671
x-y=571
x=621
y=50
speed of jet in the still air =x= 621 miles per hour
Step-by-step explanation:
What is the relationship between Figure A and Figure B?
-Figure A was translated left 2 units and up 4 units
-Figure A was reflected over the y-axis
-Figure A was translated right 4 units and up 2 units
-Figure A was dilated by a scale factor of 2
Answer:
Figure A was translated right 4 units and up 2 units
Ted invests in an annuity which earns 6.2% annual interest and he contributes $250 per month for 30 years. If Ted wants to perform some calculations to determine his future value, what formula would Ted use?
The future value of the annuity investment is expressed in option A
Future ValueThe future value formula is used to calculate the future value (FV) of an investment with given inputs of compounding periods (N), interest/yield rate (I/Y), starting amount, and periodic deposit/annuity payment per period (PMT).
The formula can be expressed as
FV = [MP(1 + r/n)^nt - 1] / [r/n]
FV = future valuemp = monthly paymentr = rate n = number of times compoundedWe can substitute the values into the equation;
FV = 250[(1 + 0.062/12)^12 * 30] / 0.062 /12
The answer to this question is option A
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y5 • y14 =
A. 2y19
B. y60
C. y19
D. 2y60
ALGEBRA
In how many ways can a person order one ice cream cone with 3 different flavors of ice cream if there are 11 flavors to choose from and it matters to the person how the 3 flavors are stacked on the one cone? That is, which flavor is on top, middle, and bottom.
Answer:
I think the answer is 33?
1. A sign in front of a roller coaster says "You must be 40 inches tall to ride." What percentage of this
height is:
a) 34 inches?
b) 54 inches?
The required percentage of height of 34 and 54 inches are 85% and 135%.
Given that,
The percentage of the height of 34 inches and 54 inches against the height of 40 inches is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
a,
percentage = 34/40 × 100%
Percentage = 85%
b,
percentage = 54/40 × 100%
Percentage = 135%
Thus, the required percentages of height of 34 and 54 inches are 85% and 135%.
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I understand it but it won't give me the marks for explaining. What should I try?
Answer:
B is never true
Step-by-step explanation:
you can't get a negative number when you have a even power
expand and simplify 3(2x+1)+(x+4)
Select the correct rational numbers.
-4 2/3 ,-3 2/3, -1 2/3 2/3
