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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Two integers are separated by 24 units on a number line. The sum of the integers is -12 and the quotient is -3. What are the two integers?
Answer:
6 and - 18
Step-by-step explanation:
let the 2 integers be a and b , then
a + b = - 12 → (1)
[tex]\frac{a}{b}[/tex] = - 3 → (2)
multiply both sides by b ( b ≠ 0 )
a = - 3b
substitute a = - 3b into (1)
- 3b + b = - 12
- 2b = - 12 ( divide both sides by - 2 )
b = 6
substitute b = 6 into (1) and solve for a
a + 6 = - 12 ( subtract 6 from both sides )
a = - 18
the two integers are - 18 and 6
Pls help urgent someone hurry please
Proved that the triangle ABW ≅ triangle DCW
In the given question,
The length of WA = The length of WD
The measure of angle 5 = The measure of angle 7
Here we have to prove that one angle and two sides of the triangle ABW is equal to the one angle and two sides of the triangle DCW
Consider the triangle ADW,
In the triangle ADW the length of the WA is equal to the length of WD.
Therefore the measure of angle A is equal to the measure of angle D.
So in triangle ABW and the triangle DCW, one side and two angles are equal.
Therefore the triangle ABW and triangle DCW are congruent
Hence, proved that the triangle ABW ≅ triangle DCW
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HELP!!WILL MARK BRAINILIEST!!
Which graph shows a proportional relationship between x and y?
Graph C appears to show a proportional relationship between x and y. Because it is a straight line across the origin.
What is a proportional relationship?
Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them.A line graph is a particular sort of graph in which the connecting segments of straight lines represent the data points. A straight line is made up of many points connected at each end.
A straight line with a beginning point of represents a proportionate relationship on a graph (0, 0). By computing a second point and then connecting the two with a straight line, the graph is produced.
As a result, graph C seems to indicate that x and y are proportionate. due to the fact that it crosses the origin directly.
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Solve the Inequality and graph the solution set.
-8-8(2x-4)>-5(4x-5)-21
Answer:
x > -5
Make a number line. Put a circle on the number line at -5 and then darken an arrow on the number line going to the right of -5
Step-by-step explanation:
-8-8(2x-4) > -5(4x -5) -21 Distribute the -8 and -5
-8 - 16x + 32 > -20x +25 -21 Combine like terms
-16x + 24 > -20x +4 Add 20x to both sides
4x + 24 > 4 Subtract 24 from both sides
4x > -20 Divide both sides by 4
x > -5
1. Write an addition problem that has a sum of -4 a. The two addends have the same sign. b. The two addends have different signs.
Answer:
a. -1 + (-3)
b. -9 + 5
Step-by-step explanation:
the sum of two numbers = -4
a.
two addends have the same sign
Since the sum is negative, then both addends must be negative.
Answer: -1 + (-3) =
b.
two addends have different signs
One addend is positive, and one addend is negative. Since the sum is negative, then the addend with the greater absolute value must be negative.
Answer: -9 + 5 =
18. MULTIPLE CHOICE
(Lesson 2-6)
(A) X=-4
B) X= 4
Ox=8
(D) X = 20
Solve
3
x + 4
=
2
X-4
Answer:
Step-by-step explanation:
solving 3x+4=2x-4
now 3x-2x=-4-4
⇒ x=-8
(c) x=8 here you have given it as O thank you
write an equation in slope-intercept form the table. help fast please
x: -4, 0, 4, 8, 12
y: 5, 6, 7, 8, 9
The linear equation in the table is written as:
y = (1/4)*x + 6
How to write the linear equation?The linear equation in slope-intercept form is written as:
y = m*x+ b
Where m is the slope and b is the y-intercept.
We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table:
(-4, 5) and (0, 6), so the slope is:
m = (6 - 5)/(0 + 4) = 1/4
And because of the point (0, 6) we know that the y-intercept is 6, then the line is:
y = (1/4)*x + 6
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A notebook computer has a mass of 2.25 kilograms . about how many pounds does the notebook weigh
Answer:
5 pounds
Step-by-step explanation:
1 kg = 2.205 lbs.
2.25×2.205
⇒4.96125
A pool can be filled by one pipe in 3 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill
the pool?
Answer:
i think it 8h
Step-by-step explanation:
Write an inequality that represents the graph
The line represents that x is anywhere from negative infinity to 1:
x < 1
Answer: x<1
Step-by-step explanation:
X is less than one on the graph because everything on the darker line is the solution.
Ex:
-1<1
A scientist claims that 9% of viruses are airborne.
If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 533 viruses would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of airborne viruses in a sample of 533 viruses would differ is 0.0062.
How to calculate the probability?From the information, the scientist claims that 9% of viruses are airborne and the proportion of airborne viruses in a sample is 533 viruses.
The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.
The mean is 0.09 and the standard deviation is 0.012.
The probability will be:
= 1 - P[Z < (0.12 - 0.09/0.013)]
= 1 - P(Z < 2.5)
= 1 - 0.99379
= 0.0062
This shows the concept of solving probability regarding z values.
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Please help please and thank you..
The value of x for the triangle by the mid point theorem is obtained as 5.
What is defined as the mid-point theorem?The line segment of a triangle connecting the midpoint in two the triangle's sides is thought to be parallel to that third side and also half the length of the third side, according to the midpoint theorem. A location that is at, close, or equally far both from ends of a line segment is referred to as the midpoint. To put it another way, the midpoint is indeed the place in a fact where the beginning and the conclusion meet.For the given diagram in the question.
As, the sides of the triangle is divided in equal parts.
By the mid -point theorem-
(1/2)24 = x + 7
12 = x + 7
x = 12 - 7
x = 5
Thus, the value of x for the triangle by the mid point theorem is obtained as 5.
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(42x³ + 16x² + 46x +42) ÷ (7x + 5)
응
Find the circumference and the area of a circle with diameter 7 cm.
The circumference of the circle is 21.98cm and the area of the circle is 38.465 square cm.
Circumference of the circle:
The Circumference (also known as) perimeter of circle = 2πR
where,
R is the radius of the circle
π is the mathematical constant with an approximate value is 3.14.
Area of circle:
The formula to find the area of the circle is;
A = πr²
Where r represents the radius of the circle.
Given,
The diameter of the circle is 7 cm.
Here we need to find the circumference and the area of a circle.
Here we have the value of diameter, in order to find the circumference we have to find the value of radius that can be derived by dividing the diameter by 2.
So, the radius is
=> 7/2 = 3.5
Now the circumference of the circle is calculated as,
C = 2 x π x 3.5
When the value of π = 3.14
Therefore, the circumference of the given circle is,
=> C = 2 x 3.14 x 3.5
=> C = 21.98
Now, the area of the circle is,
=> A = π x (3.5)²
=> A = 3.14 x 12.25
=> 38.465
Therefore, the area of the circle is 38.465 square cm.
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(MARKING BRAINLIEST) Maggie and Katie go out to dinner there a bill comes to $64.50 they are required to pay 8.5% sales tax what is the total amount Maggie and Katie have to pay ?
Answer:
$69.98
Step-by-step explanation:
8.5% of 64.50 is around 5.48 or to be exact, 5.4825 which there are no more dollar denominations beyond the hundredth place so it would be 5.48. 64.50+5.48 is $69.98.
Answer:
$69.98
Step-by-step explanation:
It is percent increase.
So, 100% + 8.5% = 108.5% which is 1.085.
64.50 × 1.085 = 69.9825
we need to round to 2 decimal places
$69.98
Una torre de 50 pies está a la orilla de un río. El ángulo de elevación entre la orilla opuesta y la punta de la torre es de 37°. ¿Qué anchura tiene el río?
Usando una relación trigonometrica veremos que la anchura del rio es 66.4 pies.
¿Como encontrar la anchura del rio?
Podemos ver la situación como si trabajaramos con un triangulo rectangulo, donde la torre de 50 pies es un cateto y la anchura del rio es el otro cateto. (la imagen de este triangulo se puede ver en la imagen al final)
Usando la relacion:
tan(a) = (cateto opuesto)/(cateto adjacente)
Podemos escribir:
tan(37°) = 50ft/x
Resolviendo para x, la anchura del rio:
x = 50ft/tan(37°) =66.4 ft
El rio tiene un ancho de 66.4 pies.
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A rectangle has a width (3x-2) and a length of (5x). The rectangle has the same perimeter as a square with a perimeter of 44 units.
Find the value of x.
Check the picture below.
??? brianlest?? help please
math
Answer:
try to show it step by step
help me 10 pnts thanks so much
The expression 3.2^2 - 1 and 10 - 0.33 * 2 should be joined by less than to form an inequality
What is inequality?Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe given expression is solved as follows
3.2^2 - 1
= 10.24 - 1
= 9.24
10 - 0.33 * 2
= 10 - 0.66
= 9.34
The two expressions can be joined as below
9.24 < 9.34
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help pleas now...............math
The value of q after solving the expression, q/3+2/3 = 8q/3-5/3, is 1.
According to the question,
We have the following expression:
q/3+2/3 = 8q/3-5/3
Now, taking 3 as the denominator on both the sides:
(q+2)/3 = (8q-5)/3
Now, 3 in the denominator on the left hand side can be divided by 3 in the denominator on the right hand side:
q+2 = 8q-5
Now, changing the sides of this expression:
8q-5 = q+2
Moving q from the right hand side to the left hand side:
8q-q-5 = 2
7q -5 = 2
Moving 5 from the left hand side to the right hand side:
7q = 2+5
7q = 7
q = 7/7
q = 1
Hence, the value of q after solving the given expression is 1.
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2 1/7:15a=5/14:0.8. solve
The value of a from the equation is a = 0.32
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be 2 1/7 : 15a = 5/14 : 0.8
Now , on simplifying the equation , we get
15/7 : 15a = 5/14 : 0.8
Multiply by 14 on both sides of the equation , we get
( 15 x 2 ) : 15a = 5 : 0.8
30 : 15a = 5 : 0.8
So , on simplifying the equation , we get
30 / 15a = 5 / 0.8
Divide by 5 on both sides , we get
6 / 15a = 1 / 0.8
Multiply by 0.8 on both sides of the equation , we get
15a = 6 x 0.8
15a = 4.8
Divide by 15 on both sides , we get
a = 4.8 / 15
a = 0.32
Therefore , the value of a = 0.32 or a = 8 / 25
Hence , the value of a in the equation is a = 0.32
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Define rational number in your own words.
Answer:A rational number is a number thats a quotient or fraction
Step-by-step explanation:
4\6 would be a rational number 8 over 4 as well.
Find the values of x and y.
The required angles of x and y are x = 65° and y = 25°
Given is a triangle which is right angled
Thus the sum of the right angled triangle is 180 degrees
So we will write
y° + x + 90 = 180 [ angle sum property of the triangle ]
90 + x + y = 180
let the above equation be considered as equation 1
Since two sides are equal
thus the other angle will also be x°
Also the angle adjacent to 40° can be found out by linear angle property
thus according to this :
x + x + ( 90 - 40 ) = 180 °
2x + 50 = 180
thus subtracting 50 on both sides we get
2x = 130
x = 65°
Thus by equation 1
we can rewrite it as
y + x + 90 = 180
65 + 90 + y = 180
155 + y = 180
this implies y = 180 - 155
y = 25°
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Question 6
A road drops 795 feet for every 265 feet forward, determine the slope of the road. The
slope can be positive or negative.
The slope of the road is 159/53
What is a slope?
How steeply a line slopes from left to right is known as its slope. By dividing a line's rise, or vertical change, by run, or horizontal change, one can calculate a line's slope, the slope of a line is always constant (it never varies).
To calculate the slope of a line using the formula
m = rise / run = (y₂ - y₁)/(x₂ - x₁)
where, m = slope
(x₁, y₁) = coordinates of the first point in the line
(x₂, y₂) = coordinates of the second point in the line
Here, we have
rise = 795
run = 265
by using the slope formula,
m = rise/run
m = 795/265
m = 159/53
Hence, the slope of the road is 159/53.
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Pixel A is located 80 km from the Jacksonville radar. How many seconds did it take for the radar pulse to travel to the target at Pixel A and return to the radar? (It will be a very small answer!)
C= 3 × 10^8 m s−1
R= 80,000
R= CT/2
[tex]C=3\times 10^8~\frac{m}{s}\hspace{5em}R=80000\implies R=8\times 10^4 \\\\[-0.35em] ~\dotfill\\\\ R=\cfrac{CT}{2}\implies 2R=CT\implies \cfrac{2R}{C}=T\implies \cfrac{2(8\times 10^4)}{3\times 10^8}=T \\\\\\ \cfrac{16\times 10^4}{3\times 10^8}=T \implies \cfrac{16}{3}\times\cfrac{10^4}{10^8}=T\implies \cfrac{16}{3}\times\cfrac{1}{10^8\cdot 10^{-4}}=T \\\\\\ \cfrac{16}{3}\times\cfrac{1}{10^{8-4}}=T \implies \cfrac{16}{3\times 10^4}=T\implies \cfrac{16}{30000}=T\implies \cfrac{1}{1875}=T[/tex]
For each equation, determine whether it represents a direct variation, an inverse variation, or neither.
Find the constant of variation when one exists and write it in simplest form.
The equation 4y = -x is a direct variation and k = - 1 / 4.
The equation 3x = 2y - 7 is neither a direct variation nor a inverse variation.
How to solve direct and inverse equation?Direct variation describes a simple relationship between two variables . We say y varies directly to x when it is represented as follows:
y = kx
where
k = constant of proportionalityTherefore,
4y = - x
divide both sides of the equation by 4
4y / 4 = -x / 4
[tex]y =- \frac{x}{4}[/tex]
Therefore, the equation is direct variation and the value of k is - 1 / 4.
For two quantities with inverse variation, as one quantity increases, the other quantity decreases. Inverse variation is represented as follows:
y = k / x
Therefore, 3x = 2y - 7 is neither an inverse nor a direct variation.
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The average cost per night of a hotel room in New York City is $273 (Smart Money, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.
Show all work for each solution
a. With 95% confidence, what is the margin of error?
b. What is the 95% confidence interval estimate of the population mean?
c. Two years ago the average cost of a hotel room in New York City was $229. Discuss the change in cost over the two-year period.
With 95% confidence, the margin of error is 19.523, population mean is (253.477, 292.523) and the change in cost over the two-year period is 19.21%.
In the given question,
The average cost per night of a hotel room in New York City(y) = $273
Number of rooms in hotel(n) = 45.
The sample standard deviation(s) = $65
(a.) Now finding the margin of error, with 95%(0.95) confidence.
The formula of margin of error is
ME= [tex]z_{\alpha /2}\times \frac{s}{\sqrt n}[/tex]
Now find the value of [tex]z_{\alpha /2}[/tex].
[tex]\alpha[/tex] = 1-0.95
[tex]\alpha[/tex] = 0.05
[tex]\alpha[/tex]/2 = 0.05/2
[tex]\alpha[/tex]/2 = 0.025
Now the value of [tex]z_{\alpha /2}[/tex]
[tex]z_{\alpha /2}=z_{0.025}[/tex]
From the standard table of z is 2.015.
Now putting the value in formula
ME= 2.015 × 65/√45
ME= 2.015 × 65/6.708
ME= 2.015 × 9.689
ME= 19.523
Hence, with 95% confidence, the margin of error is 19.523.
(b) Now finding .the 95% confidence interval estimate of the population mean.
Population Mean = y ± ME
Population Mean = 273 ± 19.523
Population Mean = {(273-19.523), (273+19.523)}
Population Mean = (253.477, 292.523)
(c) Now two years ago the average cost of a hotel room in New York City was $229 then the change in cost over the two-year period is
The change in cost = difference between the cost/old cost
The change in cost = (273-229)/229 *100
The change in cost = 44/229 *100
The change in cost = 0.1921 *100
The change in cost = 19.21%
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The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
B) if it takes the car 36 minutes to drive down the road, what will it's average speed
Answer:
a) 24 minutes
b) 20 mph
Step-by-step explanation:
Speed - distance -time:time= 12 min
[tex]\sf = \dfrac{12}{60} \ hour[/tex]
speed = 60 mph
[tex]\sf \boxed{distance =speed * time}[/tex]
[tex]\sf = 60 * \dfrac{12}{60}\\\\ = 12 \ m[/tex]
a) Speed = 30 mph
[tex]\sf \boxed{time = \dfrac{distance}{speed}}[/tex]
[tex]\sf = \dfrac{12}{30}\\\\ = \dfrac{2}{5} \ hour\\\\ = \dfrac{2}{5}*60\\\\= 2 * 12\\\\= 24 \ minutes[/tex]
It will take 24 minutes.
c) time = 36 minutes
[tex]\sf = \dfrac{36}{60} \hour[/tex]
[tex]\sf \boxed{speed= \dfrac{distance}{time}}[/tex]
[tex]\sf = \dfrac{12}{ \dfrac{36}{60}}\\\\\\ = 12* \dfrac{60}{36}\\\\= 20 \ mph[/tex]
Average speed = 20 mph
394.6/ 9 but use compatible numbers to estimate the quotient
The quotient estimated value of 394.6/9 is 43.84
What is quotient?A quotient is the number which is generated when we perform division operations on two numbers. Basically, it is the result of the division method. There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient and remainder. For example, 15/3= 5 .The number that is being divided ( 15) is called the dividend, and the number that it is being divided by (3) is called the divisor. The result of the division(5) is the quotient.
Therefore the quotient of 394.6/9= 43.84
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A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 193 pounds with a margin of error of 9 pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?
Considering the confidence interval, the non-reasonable value for the true mean weight of the residents of the town is:
A value that is less than 184 or more than 202.
How to obtain the confidence interval?The confidence interval for a population mean is given by the point estimate of this mean, which is the sample mean, plus/minus the margin of error.
For the context of this problem, these parameters are given as follows:
Point estimate: 193 pounds.Margin of error: 9 pounds.Hence the lower bound of the interval is:
193 pounds - 9 pounds = 174 pounds.
The upper bound of the interval is:
193 pounds + 9 pounds = 202 pounds.
All the values that are in the interval are reasonable values for the population mean, hence, in the context of this problem, the not reasonable values are given as follows:
A value that is less than 184 or more than 202.
(as they would be outside the confidence interval).
Missing InformationThe options are not given, hence the answer was given in general terms.
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