It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track? ...?

Answers

Answer 1
 Length of outer track = sum of length of 10 pieces = circumference of the outer circle 


if R is the Radius of outer circle then... 

Circumference of the outer track = 2pi*R 


Similarly the circumference of the inner track (with radius r) = 2pi*r 


length of each outer piece is 3.4 inch more than length of inner piece 

So total outer length is 10*3.4 =34 inches more than the inner length. 


=> Outer Circumference - Inner Circumference = 34 inches 

=> 2pi*R - 2pi*r = 34 

=> 2pi(R -r) = 34 

=> R-r = 34/2pi = 5.41 inches 

=> R-r = Width of the track = 5.41 inches
Answer 2
Final answer:

To find the width of the track, add up the lengths of all the inside and outside arcs and subtract the total length of the inside arcs from the total length of the outside arcs.

Explanation:

To find the width of the track, we first need to determine the difference between the inside and outside arcs of each piece. Let's assume the outside arc has a length of A inches. According to the question, the inside arc is 3.4 inches shorter than the outside arc. Therefore, the inside arc has a length of A - 3.4 inches.



Since there are ten identical pieces forming the circular track, we can add up the lengths of all the inside arcs and all the outside arcs to find the total distance covered by the track. The width of the track is then the difference between the total length of the outside arcs and the total length of the inside arcs.



Let's express the width of the track as a function of A. The total length of the outside arcs is 10A inches, and the total length of the inside arcs is 10(A - 3.4) inches. Therefore, the width of the track is:



Width = 10A - 10(A - 3.4) inches.

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Related Questions

What does the common difference or common ratio​ mean??

Answers

The common ratio is the difference between two numbers in a geometric sequence. 

in mathematics, the common difference or we can call it the rate of change is the amount that we are constantly changing by either adding or subtracting to get to our next term. In other words, it’s consecutive terms increasing or decreasing.

Which function represents the graph y=3(1/2)^x ?

Function a


Function b


Function c


Function d

Answers

The answer Function B

Answer:

Option B.

Step-by-step explanation:

Consider the below figure attached with this question.

The given function is

[tex]y=3(\frac{1}{2})^x[/tex]            .... (1)

We need to find the graph of given function.

The general form of an exponential function is

[tex]y=ab^x[/tex]               .... (2)

where, a is initial value and b is growth or decay factor.

If 0<b<1, then it is a decreasing function.

If b>1, then it is an increasing function.

On comparing (1) and (2) we get

[tex]a=3, b=\frac{1}{2}[/tex]

a=3, it means y-intercept of the function is 3.

[tex]b=\frac{1}{2}[/tex], it means it is a decreasing function.

The table of values is

x          y

-2       12

-1        6

0        3

1       1.5

2       0.75

Plot these ordered pairs on a coordinate plane and connect then by a hand curve. Graph B represents the given function.

Therefore, the correct option is B.

Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. Which statement describes the number and nature of all roots for this function?

f(x) has two real roots and one imaginary root.
f(x) has three real roots.
f(x) has five real roots.
f(x) has three real roots and two imaginary roots.

Answers

f(x) has three real roots and two imaginary roots.
The second imaginary root is the conjugate of the first. The third real root can be obtained by multiplying the two imaginary ones together.

Answer: The correct option is f(x) has three real roots and two imaginary roots.

Explanation:

It is given that the roots of fifth degree polynomial function are -2, 2 and 4+i.

Since he degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.

According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).

Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).

From the the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.

Therefore, the correct option is f(x) has three real roots and two imaginary roots.

Find the average of the function over the given interval and all values of x in the interval for which the function equals its average value. (Round your answer to three decimal places.)
f(x) = 8 cos(x),
(0, π/6)

...?

Answers

Integrate and then divide by the length of the path
i.e. find

[tex]\frac{6}{\pi}\int_0^{\frac{\pi}{6}} 8 \cos(x)dx[/tex]

[tex]\frac{48}{\pi}\int_0^{\frac{\pi}{6}} \cos(x)dx \\ \\ \frac{48}{\pi}\sin{x}|_0^ \frac{\pi}{6} \\ \\ \frac{48}{\pi}(\sin{\frac{\pi}{6}}-\sin{0}) \\ \\ \frac{48}{\pi}( \frac{1}{2}-0) \\ \\ \frac{48}{\pi}\times \frac{1}{2} \\ \\ \frac{24}{\pi}[/tex]

6, 1, -4, -9,...
---
Is this sequence arithmetic or geometric? What's the common difference or common ratio? What is the recursive formula?

Answers

Texaschic nailed it when saying that it's arithmetic

The recursive way to write this is to say

[tex]a_1 = 6[/tex]
[tex]a_n = a_{n-1} - 5[/tex]

which tells us "start at 6 and each time subtract off 5"

The [tex]a_n[/tex] portion is the nth term while [tex]a_{n-1}[/tex] is the term just before the nth term

A population of bacteria is introduced into a culture. the number of bacteria P can be modeled by P=500(1+4t/(50+t^2 )) where t is time in hours. Find the rate of change in population when t=2 ...?

Answers

P(t)=500(1+4t/(50+t^2 ))

P'(t) = 500 [(50+t^2).4 - 4t.2t]/(50+t^2)^2

  by the quotient rule

 500 (-4t^2 + 200)/(t^2 + 50)^2

Hence

 P'(2) = 500 . (-16 + 200)/54^2 ~= 31.6

5 inches equals how many centimeters

Answers

It would equal to 12.7 cm because an inch equals 2.54 cm.

How to solve: 52 is 65% of what number?

Answers

Let, that number = x
It would be: x * 0.65 = 52
x = 52 / 0.65
x = 80

So, that number and your answer is 80

Hope this helps!

The number 52 is 65% of the number 80.

What is Percentage?

Chance formula is used to find the quantum or share of commodity in terms of 100. In its simplest form, percent means per hundred. To express a number between zero and one, chance formula is used. It's defined as a number represented as a bit of 100. It's denoted by the symbol, and is majorly used to compare and find out rates.

We have to find 65% of what number is 52.

let the number be x.

So, 65% of x =52

65/100 x = 52

0.65 x = 52

x= 52/ 0.65

x= 80.

Thus, 65% of 80 is 52.

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what is the multiple zero and multiplicity of x^3+2x^2+x

Answers

=x(x^2+2x+1)
=x(x+1)^2
Single root at x=0
Double root at x=-1

Answer:

Step-by-step explanation:

It is 2x by the third power because i dont know lol

Help?

Which of the following equations represents a parabola that opens up and has a vertex with a positive x-value?
A. y=-x^2+8x-15
B. y=2x^2-16x+38
C. y=2x^2+16x+24
D. y=-4x^2-14x-12

Answers

I think B is the answer
opens up means in y=ax^2+bx+c form, a is positive
not A or D
vertex witha positive x value

for y=ax^2+bx+c
the x value of the vertex is -b/2a

test b and c
B. 2x^2-16x+38
-b/2a=-(-16)/2=16/2=8, that is positive

C. 2x^2+16x+24
-b/2a=-16/2=-8, negative


B is the answer

How many solutions are there to the equation below?
17x- 8 = 3x + 16
A. 1
B. 0
C. infinitely many

Answers

The answer is A.
There is 1 solution to the equation

Answer:

only one solution

Step-by-step explanation:

The given equation is

17x- 8 = 3x + 16

Add 8 to both sides

17x = 3x + 24

Subtract 3x to both sides

14x = 24

Divide both sides by 14

x = 24/14

x = 12/7

Since, we got only one value of x.

Therefore, the equation has only one solution.

A is correct option.

56 is what percentage of 112

Answers

The answer I got is 62.72

Evaluate -6^ 2 - 28 ÷ 4 + (-9).

52
-52
20
-20

Answers

I hope this helps you




-36-7-9


-52

Which of the following is the definition of a rational number? a number that can be written as a nonterminating or nonrepeating decimal a number that is divisible by only 1 and itself a number that can be written as a ratio of two integers a number that has a multiplicative inverse

Answers

Final answer:

A rational number is a number that can be written as a ratio of two integers, with the denominator not equal to zero.

Explanation:

The definition of a rational number is a number that can be written as a ratio of two integers, where the numerator and the denominator are both integers and the denominator is not zero. For example, fractions such as 2/3, where both 2 and 3 are integers, represent rational numbers. This is different from irrational numbers like √2 or transcendental numbers like π, which cannot be expressed as a ratio of two integers.

Furthermore, while all integers are themselves rational numbers (since any integer 'a' can be written as 'a/1'), not all rational numbers are integers, particularly when the numerator is not a multiple of the denominator.

Anthony's birthday, his mother is making cupcakes for his 12 friends at his daycare. the recipe calls for 3 cups of flour. this recipe makes 2 1/2 dozen cupcakes. anthony's mother has only 1 cup of flour. is there enough flour for each of his friends to get a cupcake? k

Answers

You would need to set up a proportion to solve. 
3/30=1/x
Cross multiply: 3x=30, so x=10
It would not be enough flour for each friend to get a cupcake.

Deandre has put his coins into 3 stacks. each stack has the same number of coins. there are 12 coins total. how many coins are in each stack?

Answers

basically 12/3=what?
12=4*3
so
12/3=
(4*3)/3=
(4*3)/(3*1)=
(4*3)/(1*3)=
(4/1)*(3/3)=
(4/1)*(1)=
4*1=
4

answer is 4 coins per stack

Which is bigger 4.953 or 4.951?

Answers

4.953 is bigger compared to 4.951 because 3 is bigger than 1.

Hope this helps!

4.953 is larger than 4.951 because when comparing the digits from left to right, the thousandths place is different, where 3 is greater than 1.

To determine which number is larger, we compare them digit by digit starting from the left:

Both numbers have the same digit in the units place: 4.

Both numbers have the same digit in the tenths place: 9.

Both numbers have the same digit in the hundredths place: 5.

In the thousandths place, 4.953 has a 3, and 4.951 has a 1.

Since 3 is greater than 1, 4.953 is larger than 4.951.

What is the sum of the first ten non-zero multiples of twenty

Answers

1,2,4,5,10,20

42 is the answer to your question

The sum of the first ten non-zero multiples of twenty is 1100. This is calculated using the arithmetic series sum formula where n=10, the first term is 20 and the last term is 200.

The sum of the first ten non-zero multiples of twenty can be calculated using the formula for the sum of an arithmetic series. The first ten non-zero multiples of twenty are 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200.

To calculate their sum, you detect a common difference which is the number 20 itself and use the sum formula for an arithmetic series where Sn = n/2 * (a1 + an), where Sn is the sum of n terms, a1 is the first term, and an is the last term.

In this case, n=10, a1=20, and an=200. So, the sum Sn = 10/2 * (20 + 200) = 5 * 220 = 1100. Therefore, the sum of the first ten non-zero multiples of twenty is 1100.

Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 6 inches.

Answers

5.2 square inches

All angles are 60 degrees.
2/3h=r
2/3h=6
h=9
 
You have a right triangle therefore you can calculate the base as (9tan30)=sqrtof3 over 3
 
Area of triangle 1/2 bh = 1/2(sqrt3 over 3)

(9) As this is just 1 triangle you then need to multiply it by 2

bh = sqrt of 3 over 3 * 9

What is the derivative of cos(pi*t/4) ?

Answers

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-\pi}{4} \sin \bigg( \frac{\pi t}{4} \bigg)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \cos \bigg( \frac{\pi t}{4} \bigg)[/tex]

Step 2: Differentiate

Trigonometric Differentiation [Derivative Rule - Chain Rule]:                   [tex]\displaystyle y' = -\sin \bigg( \frac{\pi t}{4} \bigg) \cdot \frac{d}{dt} \bigg[ \frac{\pi t}{4} \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]:                                   [tex]\displaystyle y' = -\sin \bigg( \frac{\pi t}{4} \bigg) \cdot \frac{\pi}{4} \frac{d}{dt}[t][/tex]Basic Power Rule:                                                                                         [tex]\displaystyle y' = \frac{-\pi}{4}\sin \bigg( \frac{\pi t}{4} \bigg)[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Write this function in vertex form, and Identify its vertex x^2-4x-17

Answers

x^2-4x-17 is the same as 1x^2 + (-4)x + (-17)

It is in the form y = ax^2 + bx + c where

a = 1
b = -4
c = -17

To find the value of h, we use this formula
h = -b/(2a)
h = -(-4)/(2*(1))
h = 4/2
h = 2

Plug this back into the original function to find k
k = x^2-4x-17
k = (2)^2-4(2)-17
k = 4-8-17
k = -4-17
k = -21

So we know that a = 1, h = 2 and k = -21 making
y = a(x-h)^2 + k
turn into
y = 1(x-2)^2 - 21
which is now in vertex form. The vertex is (h,k) = (2,-21)

rewrite each expression more simply 5x+4x

Answers

So all you do is add the 5 and the 4 and add the x. 9x

Explain how the order of operations determines how you simplify a numeric expression. Be sure to explain the rules for addition, subtraction, multiplication, division, and the use of grouping symbols. Use examples to illustrate your points.

Answers

First we solve math inside brackets. They have the highest order.
example: 2+3*(5+4) 
first we solve 5+4 and than multiply it by 3 and finally add 2

after brackets multiplication and division have highest order. We solve them before we solve summing and subtraction.

3+4*5   first we do 4*5
1-5+6/3*5   here it doesnt matter if we first divide 6 by 3 and than multiply by 5 or we multiply 6 and 5 and than divide by 3. They have same order and result will be the same.

Finaly subtraction and addition is done.

How do i find an angle that is complementary to theta?

...?

Answers

z=90−θ
90 degrees minus theta is the complimentary angle.


If two lines intersect and form 4 right angles, then ___________.
A.the lines are parallel
B.the lines are perpendicular
C.the angles are complementary
D.the lines are not coplanar

Answers

Final answer:

Two lines that intersect and form four right angles are perpendicular to each other. This is because they cross at a single point creating four 90 degree angles. Therefore, the lines are not parallel, the angles are not complementary, and their coplanar status is irrelevant.

Explanation:

If two lines intersect and form four right angles, it means that the lines are perpendicular to each other. In geometry, when two lines are perpendicular, they intersect at one point forming four right angles. A right angle is an angle of 90 degrees, which is the total division of a straight angle. Therefore, the two lines are not parallel because parallel lines do not intersect. The angles would not be complementary because complementary angles are two angles that add up to 90 degrees. Lastly, the lines being coplanar or not has no bearing on the angles they form when they intersect.

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Final answer:

Two lines intersecting to form four right angles are perpendicular, which is reflected in B. the lines are perpendicular. Parallel lines don't intersect, complementary angles are about their sum, and not coplanar doesn't relate to angles formed by intersection.

Explanation:

When two lines intersect and form 4 right angles, they possess a special relationship known as perpendicularity. These perpendicular lines meet to form 90-degree angles, also referred to as right angles. This fact is grounded in basic geometric principles.

The correct answer to the question is B. the lines are perpendicular. Choosing any of the other options would not accurately describe the relationship between the lines. Parallel lines do not intersect, complementary angles sum up to 90 degrees but do not describe the relationship between lines, and being not coplanar implies the lines do not lie in the same plane which is irrelevant to the intersection forming right angles.

It is important to recognize that according to Theorem 1, two straight lines cannot intersect in more than one point and Theorem 2 states that vertical angles, which are the angles opposite each other when two lines intersect, are equal. All this supports the fact that if the lines intersect in such a way to form 4 right angles, they are indeed perpendicular.

A grocery store display has 60 oranges and 18 apples.

What is the ratio of oranges to apples?

Enter your answer in simplest fractional form in the box.

?

Answers

Hello, I hope this will help you out!

The ratio of oranges to apples is 10/3! Hope that helped!

Answer:

Given condition: A grocery store display has 60 oranges and 18 apples.

Then,

Number of oranges = 60 and

Number of apples = 18.

Then, we use ratios to make comparisons between two things.

When we express a ratios in words we use the word ''to'' then we say that the ratio of something to something else.

Ratio of oranges to apples = [tex]\frac{Number of oranges}{Number of apples}[/tex]

then,

Ratio of oranges to apples =[tex]\frac{60}{18}[/tex]

Divide numerator and denominator by 6, we get

Ratio of oranges to apples =[tex]\frac{10}{3}[/tex] which is in the simplest fractional form.


The solution to -16 + x = -30 is -14.

True
False

Answers

Answer:

True

Step-by-step explanation:

[tex]x = - 30 + 16 \\ \\ or \: \: x = - 14[/tex]

What number is halfway between 8.270 and 8.280?

Answers

8.275, hope this helps

fourteen boxes of candle were sold for 91.00.each box contains 5 candles. what is the cost of 1 candle

Answers

The cost of one candle can be found by dividing the total cost ($91.00) by the total number of candles sold (70), resulting in $1.30 per candle.

To find the cost of 1 candle, first calculate the total cost of all the candles sold. Fourteen boxes were sold for $91.00 in total. Since each box contains 5 candles, you can find the total number of candles by multiplying 14 boxes by 5 candles per box.

14 boxes × 5 candles per box = 70 candles total.

Now, to find the cost of one candle, divide the total cost by the total number of candles.
$91.00 / 70 candles = $1.30 per candle

Therefore, the cost of one candle is $1.30.

(6 points)
2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(a) 6x + 4x - 6 = 24 + 9x
(b) 25 - 4x = 15 - 3x + 10 - x
(c) 4x + 8 = 2x + 7 + 2x - 20
Answer:

Answers

Use the acronym DCOAM [Distribute, Combine like terms, one side the variable, Add or subtract, Multipy or divide]

A has only one solution , x= 30

B is an identity because if you combine like terms and add, you get
25-4x=25-4x

C has no solutions

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