Three circles are inscribed in a rectangle of width w and height h as shown. Two of the circles are congruent and are each tangent to two adjacent sides of the rectangle and to each other. The other circle is larger and is tangent to three sides of the rectangle and to the two smaller circles. What the ratio of h to w? Express your answer as a decimal to the nearest hundredth.
Answers
==========================================
Explanation:
The two smaller circles have a height of h, so one circle has a height of h/2 = 0.5h
The radius of each smaller circle is (0.5h)/2 = 0.25h
Draw an xy axis. Place the bottom left corner of the rectangle at the origin (0,0)
The center of the lower smaller circle is at location (0.25h, 0.25h). Call this point A.
Let B be the center of the larger circle. It has coordinates (x,y). We don't know x, but we know that y = 0.5h since the center must be at the halfway point in terms of the height of this rectangle. So the larger circle has a radius of 0.5h
Draw a line segment connecting A and B. The length of this segment, call it d, is d = 0.5h + 0.25h = 0.75h. Note how I added the two radius values mentioned earlier.
-------------
Summarizing everything so far, we have
A = (0.25h, 0.25h)
B = (x, 0.5h)
d = 0.75h
The distance formula is then used
d = distance from A to B
d = length of segment AB
d = sqrt( (x1-x2)^2 + (y1-y2)^2 )
0.75h = sqrt( (0.25h - x)^2 + (0.25h - 0.5h)^2 )
(0.75h)^2 = (0.25h - x)^2 + (-0.25h)^2
0.5625h^2 = 0.0625h^2 - 0.5hx + x^2 + 0.0625h^2
x^2 - 0.5hx + 0.4375h^2 = 0
From here you use the quadratic formula to get x = 0.9571067811865h approximately (the other solution is ignored as it's negative). See the attached image below if you're curious what the quadratic formula steps would look like.
This x value is the x coordinate of point B, which is the center of the larger circle. This spans the horizontal distance from the left edge of the rectangle to the center of the larger circle. The remaining horizontal distance is h/2 as it is the radius of the larger circle.
Therefore,
w = 0.9571067811865h + 0.5h
w = 1.4571067811865h
-------------
We have turned w into a roughly equivalent expression that has an h in it, allowing us to find the ratio of h to w
h/w = h/(1.4571067811865h) = 1/1.4571067811865 = 0.68629150101527
When rounding to two decimal places, we get roughly 0.69
Related Questions
Fill in the table below so that the table matches the
graph.
х
-2
-1
0
1
2
y
??
Answers
Answer: x y
0 1
-2 3
- 1 1
1 3
2 5
Step-by-step explanation:
please help me on this
Answers
Answer:
i believe x=10
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
The segment from the vertex to the base is a perpendicular bisector.
Thus the base is divided into 2 equal parts, that is
3x - 8 = 2x + 2 ( subtract 2x from both sides )
x - 8 = 2 ( add 8 to both sides )
x = 10
#6) Beth saved a total of $30 per month for her first car. Beth saved
money for 20 months and opened her account with $100. What is the
domain and range of the situation representing the amount of money
Beth saved in respect to time she saved? Write your answer in
interval notation.
D:
R:
Answers
Answer:
Domain = 0≤m≤20 for mEZ+
Range = $100≤A≤$700 for all values of m
Step-by-step explanation:
Initial amount in the account = $100
Amount saved by beth monthly = $30
Amount in the bank after X month = $100+$30X where X is the number of months beth intend to save up to.
The amount in her bank in her first month = $100+$30(1)
= $100+$30
= $130
Amount saved in the second month will be when X = 2
= $100+$30(2)
= $100+$60
= $160
The amount in the bank will keep increasing by $30 monthly until the 20month.
The amount he will have in her bank in the 20th month will be at when X = 20
= $100+30X
= $100+30(20)
= $100+$600
= $700
This means that her money will be $130 in the first month and will keep increasing until it reaches $700 in the 20th month.
The DOMAIN will be the interval of the time she used in saving. Since she saved for 20months, the domain will be expressed as 0≤m≤20 for mEZ+ where m is the number of month she uses to save.
The Range will represent the amount she saved within the specified time and will be expressed as $100≤A≤$700 for all values of m.
Where $100 is the amount in the account initially and $700 is the amount in the account after 20 months.
Your Teacher is wondering if the absolute value of a number can ever be negative. Is she correct? Why or Why not? Use specific examples and sound mathematical reasoning to support your answer
Answers
(for example if you walk backwards, you’re still walking forwards in a given direction so that wouldn’t be negative distance traveled.)
how can i get some awnser
Answers
Step-by-step explanation:
You need to ask a question about the problem/s you need help with
Fran’s store spent $64,000 on expenses last year. Rent of the store was 35% of those expenses .How much did Fran spend on rent.
Answers
Answer:
$22400
Step-by-step explanation:
multiply 64000 with 0.35 (35%)
Which of the follwing equations has a quotient with a remainder?
Select the three that apply. A. 946/32
B. 1157/11
C.3524/44
D.37,392/82
B,C,D
A,B,C
A,C,D
A,B,D
Answers
Answer: Choice 2) A, B, C
====================================
Explanation:
Use a calculator to find that,
946/32 = 29.56251157/11 = 105.1818 approximately3524/44 = 80.0909 approximately37392/82 = 456The first three results have a decimal portion as the answer. So there is a remainder here. The remainder is the leftover bit that couldn't make another full value. Only choice D results in a whole number that isn't a decimal value, so this does not have a remainder.
As a smaller example, let's say we had 20 cookies and 3 people. If we want to divide the cookies evenly, then each person gets 20/3 = 6 full cookies and there would be 2 cookies left over (6*3 = 18 are eaten so 20-18 = 2 is left over). Notice that 20/3 = 6.67 approximately. The non-whole number decimal value indicates we have a remainder. If we had 21 cookies, then each person gets 21/3 = 7 full cookies with nothing left over, so there's no remainder here.
true or false? Induction is a kind of thinking you use to form general ideas and rules based on mathematical formulas?
Answers
your answer is false
Paul is planning a 303 mile road trip driving his truck that gets about 23 mpg. When he starts out, one gallon of gas costs $3.02. Using front-end estimation, choose which one of the following is the best estimate of the total cost of gas for this trip.
Answers
Answer:
45
Step-by-step explanation:
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
Answers
Answer:
The interest accrued is $258.48.
Step-by-step explanation:
Given that:
Initial balance in the savings account = $359
Interest rate = 8%
Time for which no withdrawals or deposits were done = 9 years
To find:
Simple Interest accrued = ?
Solution:
First of all, let us have a look at the formula for simple interest.
[tex]SI = \dfrac{PRT}{100}[/tex]
Where P is the Principal Amount.
R is the annual rate of interest
T is the time in years.
Here, we are given:
P = $359
R = 8%
T = 9 years
Let us put all the values in the formula:
[tex]SI = \dfrac{359 \times 8 \times 9}{100}\\\Rightarrow SI = \dfrac{359 \times 72}{100}\\\Rightarrow SI = \dfrac{25848}{100}\\\Rightarrow \bold{SI = \$258.48}[/tex]
So, the interest accrued is $258.48.
In a recent year a baseball team paid seven times as much to their ace pitcher as they paid to their shortstop. If they paid $ 24 million for the two salaries, what did they pay each player?
Answers
Answer:
Shortstop =$3,000,000;
ace pitcher = $21,000,000
Step-by-step explanation:
Let amount earned by shortstop = s
Then, amount earned by ace pitcher = 7 times amount earned by shortstop = (7 × s) = 7s
Total amount Paid = $24,000,000
Amount earned by each player :
s + 7s = 24,000,000
8s = $24,000,000
s = 24,000,000 / 8
s = 3,000,000
Hence,
Salary earned by shortstop = $3,000,000
Salary earned by ace pitcher = (7 * 3,000,000) = $21,000,000
Which proportion could be used to solve
the following problem?
A recipe for sesame chicken calls for
cup of chopped carrots. If the recipe
2
is for 4 servings, how many cups of
carrots are needed for 9 servings?
Answers
Answer:
Cups of carrot needed for 9 servings = 4.5 cups
Step-by-step explanation:
A recipe for sesame chicken calls for cup of chopped carrots
recipe 2 is for 4 servings
That is
2 cups of carrot = 4 servings
2 : 4
= 1 : 2
1 cup of carrot = 2 servings
how many cups of
carrots are needed for 9 servings?
Let x= number of carrot needed for 9 servings
1 : 2 = x : 9
1 /2 = x/ 9
Cross product
1*9 = 2*x
9=2x
Divide both sides by 2
9/2 = x
x= 4.5 Or 4 1/2
Which fraction is equivalent to 20%?
Answers
Answer:
1/5
Step-by-step explanation:
1= 100%
1/5= 100%/5
1/5= 20%
Fraction equivalent to 20% is [tex]\frac{1}{5}[/tex]
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
What is Fraction?A numerical quantity that is not a whole number.
We know,
A percentage is a number or ratio expressed as a fraction of 100.
Therefore,
20% = [tex]\frac{20}{100}[/tex]
Then,
[tex]\frac{20}{100}=\frac{1}{5}[/tex]
Hence, the fraction equivalent to 20% is [tex]\frac{1}{5}[/tex]
Learn more about Percentage and Fraction here
https://brainly.com/question/12715980
#SPJ2
Simplify by combining like terms. Type the terms
in alphabetical order.
-59-2+29-8=
Answers
Answer:
Step-by-step explanation:
-59 - 2 + 29 - 8 = -61 + 29 - 8
Here -59 & -2 have same sign, so add both
= -61 - 8 + 29
= - 69 + 29
-69 & 29 have different sign. so subtract and the answer will have the sign of the bigger number
= - 40
Help!!!!!!!!!!!!!!!!
Answers
Answer:
B
Step-by-step explanation:
To get x by itself, you have to divide each side by the number that x is attached with.
For the first one, divide each side by 3 so that x is by itself and 21/3 is 7 to get x<7
Do the same with the other side but with 5 to get x>11
Solve : - 43 - 4x = 3(1 - 9x)
Answers
Answer:
x = 2
Step-by-step explanation:
-43 - 4x = 3(1 - 9x)
Distribute the 3:
-43 - 4x = 3 * 1 - 3 * 9x
-43 - 4x = 3 - 27x
Add 27x to both sides:
-43 - 4x + 27x = 3 - 27x + 27x
-43 + 23x = 3
Add 43 to both sides:
-43 + 43 + 23x = 3 + 43
23x = 46
Divide both sides by 23:
23x / 23 = 46 / 23
x = 2
Answer:
The answer is
x = 2- 43 - 4x = 3(1 - 9x)
Expand the terms
That's
- 43 - 4x = 3 - 27x
Group like terms
Send the constants to the right side of the equation and those with variables to the left side
That's
- 4x + 27x = 43 + 3
Simplify
23x = 46
Divide both sides by 23
[tex] \frac{23x}{23} = \frac{46}{23} [/tex]
We have the final answer as
x = 2Hope this helps you
Number 51 is decreased to 26 what is the percentage by the numbers decrease
Answers
Answer:
about 49
Step-by-step explanation:
I basically estimated my way to the answer, you need to do a lot of calculations for this problem, but as long as you understand the concept, its fine by me to usr a calculator to get the percentage
Answer:49.0
Step-by-step explanation: First you subtract 26 from 51 and then divide that by the original number(51) and multiply that by 100
find the equation of the line passing through the point (-4,1) and the perpendicular to the line y=1/3x+4
Answers
Answer:
The answer is
[tex]y = - 3x - 11[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
[tex]y = \frac{1}{3} x + 4[/tex]Comparing it with the general equation above
Slope / m = 1/3
Since the lines are perpendicular to each other the slope of the other line is the negative inverse of the original line
That's
Slope of perpendicular line = - 3
Equation of the line using point (-4 , 1) and slope - 3 is
[tex]y - 1 = - 3(x + 4) \\ y - 1 = - 3x - 12 \\ y = - 3x - 12 + 1[/tex]We have the final answer as
y = - 3x - 11Hope this helps you
How do I isolate the y variable?
[tex]x = \frac{2y + 4}{3} [/tex]
Answers
Answer:
y = [tex]\frac{3x}{2}[/tex] - 4
Step-by-step explanation:
first multiply by 3 on both sides
then subtract 4 on both sides
finally you have to divide by 2 on both sides to get
y = [tex]\frac{3x}{2}[/tex] - 4
Simplify each expression 6x + 4y + 5x
Answers
combine like terms together (add 6x and 5x)
Explanation:
The like terms are 6x and 5x. They add to 11x since 6+5 = 11, and then we tack x onto each to get 6x+5x = 11x.
You can think 6x representing the idea we have 6 boxes. Then adding on 5x means we have 5 more boxes to get 6+5 = 11 boxes total.
10) Gabe put up a fence around his rectangular vegetable garden this weekend.
The garden has a perimeter of 38 ft and an area of 48 ft? What is the length and
the width of the garden?
Answers
Answer:
The length is 16 ft, and the width is 3 ft.
Step-by-step explanation:
Let L = length & let W = width.
The perimeter of a rectangle is
P = 2(L + W)
The area of a rectangle is
A = LW
We know the perimeter and the area, so we substitute those values int he equations above and we switch sides in both equations.
Perimeter: 2(L + W) = 38
Divide both sides by 2:
L + W = 19
Area: LW = 48
We have a system of two equations in two unknowns:
L + W = 19
LW = 48
Solve the first equation for L and substitute it into the second equation.
L = 19 - W
(19 - W)W = 48
19W - W^2 - 48 = 0
Multiply both sides by -1, and rearrange the order of the terms.
W^2 - 19W + 48 = 0
(W - 16)(W - 3) = 0
W - 16 = 0 or W - 3 = 0
W = 16 or W = 3
Use W = 3 to find L
L = 19 - W
L = 19 - 3
L = 16
Answer: The length is 16 ft, and the width is 3 ft.
Elaine is 8 years younger than her brother Tyler. The sum of their ages is 34. Define a variable and then write and solve an equation to find Elaine’s and Tyler’s ages.
Answers
Answer: Elaine=13 years old Tyler=21 years old
Step-by-step explanation:
Let x = Elaine's age, so her brother Tyler's age = x+8
Elaine+Tyler=34
x+(x+8)=34
2x+8=34
2x=26
x=13
Elaine=13 years old
Tyler=21 years old
twice a number less than 5
Answers
Answer:
2n≤5
Step-by-step explanation:
Answer:
2n < 5
Step-by-step explanation:
2 times a number has to be less than 5.
So assuming the number is n,
2n < 5
Please pick me as brainliest.
Given g ( x ) = − 3 x − 4 g(x)=−3x−4, find g ( 5 ) g(5)
Answers
Answer:
g(5)=-19
Step-by-step explanation:
Plug in 5 for the x's and get g(x)=-3(5)-4 and then -15-4 which is -19 so g(x)=-19
Answer:
g(5) = -19Step-by-step explanation:
[tex]g( x ) = -3 x -4\\\\g(5) = \:?[/tex]
Substitute 5 for x in the equation
[tex]-3(5)-4\\-15-4\\= -19[/tex]
Need help with math!!!
Answers
-2y+16=6+3y
16-6=3y+2y
10=5y
5=y
y=4
hope it helps
Answer:
-7y-3=2(y+4)
-(11)/(9)
Step-by-step explanation:
In what ways are the steps for the long division of polynomials algorithm similar to the steps for the multiplying polynomials algorithm? In what ways are they different?
Answers
Answer:
Undermentioned explanation, similarity & dissimilarity between long division & multiplication of polynomials
Step-by-step explanation:
Long Division of Polynomial steps :
Complete missing terms in divisor with zero coefficients, sort terms in decreasing exponential order
Divide leading term, multiply divisor x quotient, subtract partial product & carry down remainder ............ (continue same)
Multiplication of Polynomial steps :
Multiply the 1st, 2nd, 3rd term(s) in the first polynomial with 1st, 2nd, 3rd consecutive term(s) in the second polynomial........... (go on)
Similarity (ies) : Both involve term by term treatment, multiplying monomial & polynomial
Dissimilarity (ies) : Division includes subtracting of exponential power. However, multiplication includes adding of exponential power
Please help
Let a and b be positive integers. 23a×23b=?
Answers
Answer:
A) 23^(a+b)
Step-by-step explanation:
if you multiply a number with diferrent exponents, the exponents will always add.
The bases are the same, so we add the exponents
The answer is [tex]23^{a+b}[/tex] which is choice A============================================
Here's an example of why we add the exponents
Lets say we want to multiply 7^2 with 7^3
7^2 = 7*7
7^3 = 7*7*7
We have two copies of "7" being multiplied with 7^2, then we have an additional three copies of "7" with 7^3. Overall there are 2+3 = 5 copies of "7" that we multiply out.
So,
7^2*7^3 = (7^2) * (7^3)
7^2*7^3 = (7*7) * (7*7*7)
7^2*7^3 = 7*7*7*7*7
7^2*7^3 = 7^5
This example is fairly small in that we don't have that many copies of the base being multiplied. For larger examples, its best to use the formula mentioned
a^b*a^c = a^(b+c)
Find the smallest number which must be added to the following numbers so as to make them a perfect square 4931
Answers
Answer:
110.
Step-by-step explanation
4900 = 70^2
71^2 = 5041
5041- 4931 = 110
Answer is 110
Consider the table for the exponential function, LaTeX: p\left(x\right)=2^xp ( x ) = 2 x, shown below. Calculate the Average Rate of Change between the interval [2, 6].
Answers
Answer:
15
Step-by-step explanation:
To find the average rate if change of the exponential function between the interval [2, 6], use the formula, [tex] m = \frac{p(b) - p(a)}{b - a} [/tex]
Where,
[tex] a = 2, p(2) = 4 [/tex]
[tex] b = 6, p(6) = 64 [/tex]
Plug in the above values into the formula:
[tex] m = \frac{64 - 4}{6 - 2} [/tex]
[tex] m = \frac{60}{4} [/tex]
[tex]m = 15[/tex]
Average rate of change is 15
correct
Ken's temperature prediction for February
is -3°C. By May, Ken predicts that the average
temperature will increase by 11°C.
Use the number line interactive tool to determine the
predicted temperature in May. What is Ken's
temperature prediction for May?
Answers
Answer:
Ken's prediction for May is 8 degrees centigrade : [tex]8\,C^o[/tex]
Step-by-step explanation:
Locate the starting point at the value -3 on the number line, and count (add) 11 units to the right of that point, ending at the point 8 on the number line.
Answer:8c
Step-by-step explanation: