A company produces plates with area A=πr^2, where r is the radius of the plate. Find the inverse by solving for r without switching the variables.
The inverse is r=____
Explain your reasoning.
Answers
Final answer:
The inverse of the formula A = πr^2 is found by dividing the area A by π and then taking the square root of the resulting quotient, which gives r = √(A/π). The accuracy of this inverse is limited by the number of significant figures in the original measurement of the radius.
Explanation:
To find the inverse of the formula A = πr^2 for the area of a circle, we want to solve for the radius r in terms of A. We follow these steps:
Starting with A = πr^2, divide both sides of the equation by π to isolate r^2: A/π = r^2.
Take the square root of both sides of the equation to solve for r: r = √(A/π).
The inverse is therefore r = √(A/π).
When using a calculator, it is important to remember that the number of significant figures in a given measurement limits the accuracy of the calculations. As shown in the example, if the radius has two significant figures, the calculated area has to be limited to two significant figures as well, thus A=4.5 m².
Related Questions
helpppppppppppppppppppppppppp
Answers
The fourth function is just a constant (with exponent 0), so it is an even function.
1. f(x) = (x-1)^2 = x^2 - 2x + 1
f(-x) = (-x-1)^2 = x^2 + 2x + 1
These two don't match, not an even function
2. f(x) = 8x
f(-x) = -8x
These two don't match, not an even function
3. f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
These two don't match, not an even function
4. f(x) = 7
f(-x) = 7
Match, is an even function
The length of a rectangle is three more than twice the width. determine the dimensions that will give a total area of 27m^2
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.. A = W*L
.. 27 = x*(3 +2x)
.. 2x^2 +3x -27 = 0
.. (2x +9)(x -3) = 0
.. x = {-4.5, 3} . . . . . . . . . . width, only the positive answer is of interest
.. 3 +2x = 3 +2*3 = 9 . . . . .this is the length
The rectangle is 3 m by 9 m.
A radius is an angle that connects any point on the circle to the center of that circle. A. True B. False
Answers
Answer:
IT REALLY IS FALSE FOREHEADS
Step-by-step explanation:
Three consecutive integers whose sum is 138
Answers
Hope this helps!
X → first integer
X + 1 → second integer
X + 3 → third integer
X + X + 1 + X + 2 = 138
3x + 3 = 138
-3 -3
3x = 135
÷3 ÷3
X = 45
X + 1 = 46
X + 2 = 47
Jen picked 3/4 of a gallon of strawberries in half an hour. If she keeps picking strawberries at the same rate, how many gallons will she have picked in 2 hours.
Answers
3/4 = 0.75 as a decimal
We know that Jen picks 0.75 of a gallon of strawberries in half an hour, and now we want to find out how many gallons she'll pick in 2 hours.
Half an hour = 0.5 2 ÷ 0.5 = 4 There are four half hours in 2 hours.
0.75 × 4 = 3
ANSWER:
Jen will have picked 3 gallons of strawberries in 2 hours.
Classify each polynomial (monomial, binomial, trinomial) based on number of terms it contains.
-2x^2-x+3.5
10xyz^3
-x^2y^2+2y
8x^2+0.25
x^3y^4+2x^2y-3z
Answers
Answer:
it is 10xyz^3 for monomial. 8x^2+0.25 and -x^2y^2+2y for binomial. And -2x^2-x+3.5 and x^3y^4+2x^2y-3z for trinomial.
Step-by-step explanation:
[tex]10xyz^3[/tex] for monomial. [tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex] for binomial. And [tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex] for trinomial.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We need to find each polynomial (monomial, binomial, trinomial) based on number of terms it contains.
Therefore,
If there is one term, the polynomial will be called monomial thus;
[tex]10xyz^3[/tex]
If there are two terms, the polynomial will be called binomial thus;
[tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex]
If there are three terms, the polynomial will be called trinomial thus;
[tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex]
Learn more about polynomials here:
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The length of a rectangular park is 20 feet longer than the width of the park. If the length of the park is 36 feet, what is the width of the park? 4 feet 16 feet 42 feet 56 feet
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Four consecutive integer numbers add to 2. What are the numbers?
Answers
Hope this helps
Four consecutive integer numbers add to 2. What are the numbers?
Let the smallest integer=x
The three consecutive integers will be x+1,x+2, x+3
Sum of four consecutive integers=2
So, x+x+1+x+2+x+3=2
Adding like terms, we get
4x+6=2
Subtract 6 from both sides
4x+6-6=2-6
4x+0=-4
4x=-4
To solve for x, let us divide by 4 on both sides
4/4x=-4/4
x=-1
So, the four consecutive integers are =x=-1
x+1=-1+1=0
x+2=-1+2=1
x+3=-1+3=2
So, the four consecutive integers are:= -1,0,1,2
Why is circle 1 similar to circle 2?
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
.
A) Circle 1 is a dilation of circle 2 with a scale factor of 2.
.
B) Circle 1 is a dilation of circle 2 with a scale factor of 7.
.
C) Circle 1 is a translation of circle 2.
.
D) Circle 1 and circle 2 have the same center.
Answers
1/2 = r1/r2 = 14/7 = 2 --> dilation scale factor
We have a golden rule about similarity of figures. It is "All circle are always similar to each other".
In other words, Every circle is dilated version of another circle. To find the value of dilation, we can find the ratio of its redii.
The ratio of radii of two circles is called the scale factor of dilation between them.
Given are two circles with following information :-
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
Finding the ratio of their radii :-
[tex] \frac{Circle\; 1\; radius}{Circle\; 2\; radius} =\frac{14}{7} = 2 [/tex]
So, scale factor is 2. It means circle 1 is a dilation of circle 2 with a scale factor of 2.
Hence, option A is correct i.e. Circle 1 is a dilation of circle 2 with a scale factor of 2.
The diameter of the base of a cylindrical can is 4 in. The height of the can is 6.5 in. Find the can’s surface area to the nearest tenth.
Answers
diameter of the base of a cylindrical can= 4 in----------> r=2 in
h=6.5 in
[surface area]=2*[pi*r²]+[2*pi*r*h]
then
[surface area]=2*[pi*2²]+[2*pi*2*6.5]=[ 25.13 ]+[ 81.68 ]=106.81 in²
the answer is 106.8 in²
Answer:
106.8 in2
Step-by-step explanation:
Seventy-five bottles of water are randomly tested from the large inventory in a warehouse. Which term refers to the large inventory of water bottles in the warehouse
Answers
ich sequence of transformations would result in a figure that is similar, but not congruent, to the original figure? Select all that apply. a dilation with a scale factor of 0.6 followed by a translation of 2 units up a reflection across the y-axis followed by a rotation about the origin of 10 a translation 2 units up followed by a translation of 2 units to the left a rotation about the origin of 50° followed by a dilation with a scale factor of 8
Answers
The 1st and 4th selections apply.
Find the area of the following ellipse Use = 3.14 and round to nearest tenth. a = 7 in.; b = 9 in.
Answers
Round to the nearest tenth
197.82~ 197.2 in^2
Answer:
197.82
Step-by-step explanation:
A student earned grades of C, A, B, and A in four different courses. Those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. The grading system assigns quality points to letter grades as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Compute the grade point average (GPA) and round the result to two decimal places.
Answers
To compute the GPA, multiply each grade by its corresponding credit hours, sum up the grade points, and divide by the total number of credit hours. In this case, the GPA is 3.40.
Explanation:To compute the grade point average (GPA), we need to multiply each grade by its corresponding number of credit hours to get the grade points. Then, we sum up the grade points and divide by the total number of credit hours. Here are the calculations:
Course 1: C grade (2 grade points) x 4 credit hours = 8 grade pointsCourse 2: A grade (4 grade points) x 5 credit hours = 20 grade pointsCourse 3: B grade (3 grade points) x 1 credit hour = 3 grade pointsCourse 4: A grade (4 grade points) x 5 credit hours = 20 grade pointsTotal grade points = 8 + 20 + 3 + 20 = 51 grade points
Total credit hours = 4 + 5 + 1 + 5 = 15 credit hours
GPA = Total grade points / Total credit hours = 51 / 15 = 3.40
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hhhhhhhellllllllp.....................................
Answers
28/3 = 9.3333
The pen will be 9.3333 by 9.3333 meters
Classify the following expression by degree and term: (2 points)
x2y − 7xy + xyz + x
Answers
xyz - 5xy + x
Remember to always arrange terms in your polynomial in descending order according to the degree.
Now for degree, just get the sum of the exponents to determine the highest degree. The first term in the new equation has 3 variables, x,y, and z. Each of them, even when the power is not expressed are each raised to the power of 1. There are three variables so it will be:
1+1+1 = 3
The first term is classified as 3rd degree, which is the highest. So now you can conclude that this expression is a 3rd degree trinomial.
The given expression is a third-degree polynomial and consists of four terms: x^2y, -7xy, xyz, and x. Each term has a degree based on the sum of the exponents of the variables within it.
The expression in question is x2y − 7xy + xyz + x. To classify this expression by degree and by term, we need to look at the exponents of the variables in each term. The term 'degree' of a term in a polynomial is the sum of the exponents of the variables in that term.
x2y: The degree is 3 (2 from x2 and 1 from y).−7xy: The degree is 2 (1 from x and 1 from y).xyz: The degree is also 3 (1 from x, 1 from y, and 1 from z).x: The degree is 1, as there is only one occurrence of x.So the expression is a polynomial of third degree with four terms.
When cyclist squeezes her brake lever, she can stop with an acceleration of -3.0 m/s^2 how far will her bike travel while coming to a complete stop if her initial speed was 11 m/s
Answers
v² = u² + 2as
where
v = final speed. v = 0 because the cyclist comes to a complete stop.
u = initial speed. u = 11 m/s, given
a = acceleration. a = -3.0 m/s², given
s = distance traveled, m.
Therefore
0 = 11² + 2(-3.0)*s
0 = 121 - 6s
That is,
6s = 121
s = 121/6 = 20.167 m
Answer: 20.2 m (nearest tenth)
Final answer:
The cyclist will travel approximately 20.17 meters before coming to a complete stop when decelerating with an acceleration of [tex]-3.0 m/s^2[/tex] from an initial speed of 11 m/s.
Explanation:
To calculate the distance the cyclist's bike will travel while coming to a complete stop with an initial speed of 11 m/s and an acceleration of [tex]-3.0 m/s^2[/tex], we can use one of the equations of motion. Specifically, we need to use the equation [tex]v^2 = u2 + 2as[/tex], where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
In this case, the final velocity v = 0 m/s (because the bike comes to a stop), the initial velocity u = 11 m/s, and the acceleration a = [tex]-3 m/s^2[/tex] (the negative sign indicates that it is a deceleration).
Plugging these values into the equation, we get:
0 = 112 + 2(-3)s
0 = 121 - 6s
6s = 121
s = 121/6
s = 20.17 meters
Thus, the cyclist will travel approximately 20.17 meters before coming to a complete stop.
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
x y
2 3
4 5
6 7
8 9
A. Initial value: 1, rate of change: 2 (Not the answer)
B. Initial value: 1, rate of change: 1
C. Initial value: 2, rate of change: 2 (Not the answer)
D. Initial value: 3, rate of change: 2
Answers
B. Initial value: 1, rate of change: 1
D is completely off. To get the initial value on a table you have to find the place where the input is zero.
So, you would take (2,3) and decrease both slots by 2 until x reaches zero. Now, we have (0,1). 1 is now our Initial Value.
To find the rate of change, you simply see how much the values increase/decrease. For example, let's take (6,7) and (8,9). As I said before, the input and output value increase by 2. Now, you put the change in 'y' over the change in 'x' and you have 2/2. After simplification, you are left with 1 as a whole number.
-Hope that wasn't too confusing, lol. I got a hundred on my test so I can assure you B. is correct. Good luck on your quiz :)
Answer:
Initial value: 1, rate of change: 1
Step-by-step explanation:
Took the FLVS test
The radius of the circular lens of a magnifying glass is 4 centimeters.
What is the area, in square centimeters of the glass?
Answers
Answer: 50.24 square centimeters.
Step-by-step explanation:
Given: The radius of the circular lens of a magnifying glass = 4 centimeters
The area of a circle is given by :-
[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.
Then the area of the circular lens of a magnifying glass is given by :-
[tex]\text{Area}=\pi (4)^2=(3.14)(16)=50.24\text{ square centimeters }[/tex]
Hence, the area of the circular lens of a magnifying glass = 50.24 square centimeters.
What is a Banknote? Does a banknote have to come from the government?
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A rational expression that will be undefined at x=1?
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[tex]r(x)= \dfrac{p(x)}{q(x)} [/tex]
will be undefined for the zeros of the expression [tex]q(x)[/tex]. For an expression with a zero equal to 1, the simplest way is to use [tex](x-1)[/tex] as a factor in [tex]q(x)[/tex]. In can be your only one, or you can mix in other factors.
But, so long as the denominator of [tex]r(x)[/tex] is equal to zero, as it is when [tex]q(x)=x-1[/tex], the expression will be undefined at that point x, because it would involve division by zero.
You could use as your sample:
[tex] \dfrac{x-7}{x-1} [/tex]
You can try to get fancy and square some factors or add in some radicals or trigonometric functions or anything else, so long as the 1 makes the denominator equal to zero!
In what range do the closing costs on a home loan typically fall?
a. 1% to 3%
b. 3% to 5%
c. 5% to 7%
d. 7% to 10%
Answers
Answer:
The answer is b.
Step-by-step explanation:
Answer:
b. 3% to 5% is the right choice.
Step-by-step explanation:
When a person buys a house, he will pay anywhere between 2 to 5 percent of the actual home price or the purchase price in the closing fees.
For example - if a home costs $200,000, a person can pay between $4000 and $10000 in closing costs.
So, option B : 3% to 5% is the correct answer.
Luiza delivers newspapers in her neighborhood. If you plot the points (−1, 1), (4, 1), (4, −2) and (−1, −2), you will create a representation of the route she takes, in miles. How many miles does her route cover?
Answers
We have then that the resulting figure is a rectangle.
We must find the perimeter of the rectangle that is given by:
P = 2L + 2W
Where,
L: long
W: width
Restoring the values:
P = 2 * (5) + 2 * (3)
P = 16
Answer:
her route cover 16 miles.
Answer: 16 i just did this
Step-by-step explanation:
Kristen owns a bakery called Kristen’s cakes and such and is considering lowering the price of her cakes Kristen pulls her customers and determines that she can sell 100 cakes each week when she charges $25 each she also discovers that for every one dollar decrease in the price of the cake she will sell five more cakes the graph below represents Christians projected weekly revenue for each decrease in the price at what price she Christian sell her cakes in order to meet her maximum potential revenue
Answers
explain why the amount of propane in a grill’s tank and the time spent grilling could represent an inverse variation
Answers
The obvious answer is because propane is a gas at room temperature, while 2-propanol is a liquid at room temperature.
That happens because the intermolecular forces that exist between 2-propanol, or isopropyl alcohol, molecules are stronger than those that exist between propane molecules.
The amount of propane in a grill's tank and the time spent grilling represent an inverse variation. As the amount of propane in the tank decreases, the time spent grilling increases.
Explanation:In the context of a propane grill, the amount of propane in the grill's tank and the time spent grilling represent an inverse variation. In an inverse variation, as one variable increases, the other variable decreases, and vice versa. In this case, as the amount of propane in the tank decreases (more grilling time), the time spent grilling increases. This is because the more propane that is used up, the less time you have left to grill before running out of gas.
Suppose a triangle has two sides of the length 2and 3 and that the angle between these two sides is 60 what is the length of the third side of the triangle
Answers
.. c^2 = a^2 +b^2 -2ab*cos(C)
.. c^2 = 2^2 +3^2 -2*2*3*cos(60°)
.. c^2 = 7
.. c = √7 ≈ 2.6458
The third side of the triangle is √7, about 2.6458.
Answer: √7
Step-by-step explanation:
took the test
Rank the nine career characteristics in order of their importance to you with the first being the most important
Answers
2. Farmers
3. Army Forces/ Police
4. Doctors
5. Education Administrators
6.Engineers
7. Lawyers
8.Construction Workers
9. Shopkeepers and other workers
That took a lot of thought, and I doubt I may have covered the most important careers of our society. I hope this helps and I'm extremely sorry if I left out a career and I hope nobody gets offended in any way.
Answer:
dont listen to the other dude
Step-by-step explanation:
Which of the following is a solution of y - x > -3?
(6, 2)
(2, 6)
(2, -1)
Answers
y - x > -3
(6, 2) → x = 6, y = 2
substitute
2 - 6 = - 4 < -3 NOT
(2, 6) → x = 2, y = 6
substitute
6 - 2 = 4 > -3 CORRECT
(2, -1) → x = 2, y = -1
substitute
-1 - 2 = -3 NOT
Answer: (2, 6)
What is the midpoint of the segment whose endpoints are (-6,5) and (4,-7)?
Answers
(-6+4)/2=x
(-2)/2=x
-1=x
(5+-7)/2=y
(-2)/2=y
-1=y
To start, the formula to find the midpoint coordinate pair of two given coordinates is as follows:
([tex] \frac{x1+x2}{2} [/tex], [tex] \frac{y1+y2}{2} [/tex])
Knowing this, plug in your given values (the two x values are -6 and 4; the two y values are 5 and -7) and simplify:
([tex] \frac{-6+4}{2} [/tex], [tex] \frac{5+-7}{2} [/tex])
=([tex] \frac{-2}{2} [/tex], [tex] \frac{-2}{2} [/tex])
=(-1,-1)
Therefore, the midpoint of the coordinates (-6,5) and (4,-7) would be (-1,-1).
Hope this helps and have a marvelous day! :)
.help me solve please and thank you✨