Answer:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
Step-by-step explanation:
The distance around the track (400 m) has two parts: one is the circumference of the circle and the other is twice the length of the rectangle.
Let L represent the length of the rectangle, and R the radius of one of the circular ends. Then the length of the track (the distance around it) is:
Total = circumference of the circle + twice the length of the rectangle, or
= 2πR + 2L = 400 (meters)
This equation is a 'constraint.' It simplifies to πR + L = 400. This equation can be solved for R if we wish to find L first, or for L if we wish to find R first. Solving for L, we get L = 400 - πR.
We wish to maximize the area of the rectangular region. That area is represented by A = L·W, which is equivalent here to A = L·2R = 2RL. We are to maximize this area by finding the correct R and L values.
We have already solved the constraint equation for L: L = 400 - πR. We can substitute this 400 - πR for L in
the area formula given above: A = L·2R = 2RL = 2R)(400 - πR). This product has the form of a quadratic: A = 800R - 2πR². Because the coefficient of R² is negative, the graph of this parabola opens down. We need to find the vertex of this parabola to obtain the value of R that maximizes the area of the rectangle:
-b ± √(b² - 4ac)
Using the quadratic formula, we get R = ------------------------
2a
-800 ± √(6400 - 4(0)) -1600
or, in this particular case, R = ------------------------------------- = ---------------
2(-2π)
-800
or R = ----------- = 200/π
-4π
and so L = 400 - πR (see work done above)
These are the dimensions that result in max area of the rectangle:
width of rectangle = 2R = (200/π) = 400/π meters
length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters
pls help me!!!!!!!!!!!!!!!!
Answer:
4 for the first one, 1 for the second one
Step-by-step explanation:
A bakery sells 1/2 dozen cookies for $6.48. At this rate, how much would it cost for 3 dozen cookies?
what is 351.86 in terms of pi?
Answer:
It can either be 17593pi/9000 rad or if youre looking for a decimal answer is it 1.95pi and rad=6.14
Step-by-step explanation:
The price of a gallon of milk increased from $5.50 to $7.50. Describe the price increase as a percent.
Step-by-step explanation:
7.50= (1 + x/100 ) × 5.50
7.50/ 5.50 = 1+x/100
x/100 = 0.36
x= 36.36%
2x - 5y = 6 and -2x + 7y = 14
*Using elimination*
You are given the first four terms of an arithmetic sequence. Under what
conditions might a recursive formula be preferred over the explicit formula?
Under what conditions might an explicit formula be preferred over the
recursive formula?
What are the odds of not rolling a three on a standard six-sided die?
Answer:
5/6
Step-by-step explanation:
Hope this is helpful
Answer:
5/6
Step-by-step explanation:
60% of students at a local high school participate in club activities. Rewrite this percent as a fraction
Answer:
The correct answer is 3/5
Step-by-step explanation:
I know its correct :)
The original price of a dress is 95.00. A discount of 10% is offered for cash payment. How much does one save by paying cash for the dress?
Answer:
10% of 95 is 9.5
So 95 - 9.5 = 85.5
A table is on sale for 32% off. The sale price is $459.
What is the regular price?
the regular price is "x", which of course is the 100%, but we also know that $459 is 32% off that, hmmmmm well 100% - 32% = 68%, so $459 is really 68% of "x", because $459 is whatever "x" is minus 32%.
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 459&68 \end{array}\implies \cfrac{x}{459}=\cfrac{100}{68}\implies \cfrac{x}{459}=\cfrac{25}{17} \\\\\\ 17x = 11475\implies x = \cfrac{11475}{17}\implies x = 675[/tex]
help me with this i dont understand
Answer:
4
Step-by-step explanation:
Answer:
3Step-by-step explanation:
The scale factor is the ratio of the corresponding sides.
Take the base of both quadrilaterals.
Large quadrilateral:
6 - (-6) = 12Small quadrilateral:
2 - (-2) = 4Scale factor:
k = 12/4 = 3Sue ran 7 miles more than Jill last week. Sue ran 11 miles. Which equation will tell you how many miles Jill ran?
A)
x + 7 = 11
B)
X-7 = 11
9
C)
x + 7 = -11
D)
X - 7 = -1
Answer:
The number of miles Jill ran is the number of miles Sue ran (11) minus the number of miles Sue ran more than Jill (7).
So far, x=11-7.
Reorder the equation. Add 7 to both sides.
x + 7 = 11.
So, the correct equation is A.
:)
A) x + 7 = 11
Jill runs x amount of miles and Sue runs x miles plus 7 miles.
Please take a look at the picture
Answer:
x=-22.42
Step-by-step explanation:
-18.43=3.99+x
Move the variable to the left-hand side and move the constant to the right. Change their signs.
-x=3.99+18.43
Add.
-x=22.42
Change the signs on both sides of the equation.
x=-22.42
Hope this helps :)
find the area of a circle when the radius is 10cm. Take the value of pi as 3.14
Answer:
314.16 cm squared
Step-by-step explanation:
Christine made $143 for 11 hours of work.
At the same rate, how many hours would she have to work to make $221?
Answer:
17
Step-by-step explanation:
Evaluate 12.3v+11.9w when v=7 and w=8.
please
Answer:
181.3
Step-by-step explanation:
I hope this helps!
two numbers are in the ratio 7:9. The smaller number is 42. what is the number?
42 = 7*6
so,
7:9 = 7*6 : 9*6 = 42:54
Please help and only answer if correct!
Answer: So last time it was 1/4 and 4 so it's no different it just going down by one so it's 1/3 and 3 if it's not I give up.
Step-by-step explanation:
A motorboat is capable of traveling at a speed of 14 miles per hour in still water. On a particular day, it took 15 minutes longer to travel a distance of 12 miles
upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that day?
By solving a system of equations we will find that the rate of current in the stream is S = 2 mi/h.
When the motorboat travels downstream, the total velocity will be the velocity of the motorboat in still water plus the velocity of the stream, while if the motorboat travels upstream, we have the velocity of the stream subtracted.
So upstream the speed is:
(14 mi/h - S)
Downstream the speed is:
(14 mi/h + S)
Where S is the rate of current in the stream.
We know that downstream it takes 15 minutes more to travel 12 miles, then we can write the system of equations:
(14 mi/h + S)*T = 12 mi
(14 mi/h - S)*(T - 15 min) = 12 mi
To solve this, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:
T = (12 mi)/(14 mi/h + S)
Replacing that in the other equation we will get:
(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi
Now we can solve this for S. Now we can multiply both sides by (14 mi/h + S).
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)
Also notice that the speeds are in hours, so we can rewrite:
- 15 min = -0.25 h
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)
168 mi^2/h - 12mi*S + 49mi^2/h + 0.25h*S^2 = 168mi^2/h + 12mi*S
- 12mi*S + 49mi^2/h - 0.25h*S^2 = 12mi*S
-24mi*S - 0.25h*S^2 + 49mi^2/h = 0
This is a quadratic equation, the solutions are:
[tex]S = \frac{24mi \pm \sqrt{(-24mi)^2 - 4*(49mi^2/h)*(-0.25h)} }{2*-0.25h} \\\\S = \frac{24mi \pm 25 mi }{-0.5h}[/tex]
We only take the positive solution, so we get:
S = (24 mi - 25 mi)/(-0.5 mi) = 2 mi/h
The rate of current in the stream is 2 mi/h.
If you want to learn more, you can read:
https://brainly.com/question/24345308
3. Sarah has a goal to save $81.84 for a new gan
If she has 12 weeks to save the money, how much does she need
to save each week?
Answer:
Hi!
12x = 81.84
x = 6.82
6.82 dollars every week
I went to many other places, I saw their answers and turns out the only answer I searched up was wrong!
Answer:
I understand how that feels
Step-by-step explanation:
Determine the value of x. Question 4 options: A) 10 B) 5 C) 10 D) 5
Find an expression that gives you a quotient
of 16
Answer: Does 32/2 work it equals 16
Step-by-step explanation:
The number expression would be 32/2 which gives 16 after applying the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
The quotient is 16
Let us assume 32 and 2 are the numbers that can be use in the number expression
The number expression is:
= 32/2
= 16
Thus, the number expression would be 32/2 which gives 16 after applying the arithmetic operation.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ2
solve please: 1/4x-5+1.2x
Answer:
29x/20 - 5
Step-by-step explanation:
1/4x - 5 + 1.2x
=> 0.25x - 5 + 1.2x
=> 1.45x - 5
=> 29x/20 - 5
Therefore, this is the simplified form: 29x/20 - 5
Find the equation of the line where m = 1 and b = 8.
y = 8 - x
y = 8
y = 8x + 1
y = x + 8
Answer:
Y=x+8
Step-by-step explanation:
pls help me I will try to give brainleist bc i don't know how
Answer:
2195
Step-by-step explanation:
filler filler filler lol
Answer: 2,195
Step-by-step explanation:
439x5
9x5=45
3x5+4=19
4x5+1=21
2195
find the amount accumulated in an account after $9000 is invested for 8 years at a 4% coumpounded monthly
Step-by-step explanation:
9000(1+0.04/12)^(8*12)
9000(1.0033333)^96
9000(1.3763)
A=12,387.56
Help me plz I really need help
Answer:
it won't let me message back.
Step-by-step explanation:
A car is being compacted into a rectangular solid. The volume is decreasing at a rate of 2 m3/sec. The length and width of the compactor are square, but the height is not the same length as the length and width. If the length and width walls move toward each other at a rate of 0.25 m/ sec, find the rate at which the height is changing when the length and width are 2 m and the height is 1.5 m.
Using implicit differentiation, it is found that the height is changing at a rate of -0.875 m/sec.
The volume of a rectangular solid of length l, width w and height h is given by:
[tex]V = lwh[/tex]
Applying implicit differentiation, the rate of change of the volume is given by:
[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]
In this problem:
Volume is decreasing at a rate of 2 m3/sec, hence [tex]\frac{dV}{dt} = -2[/tex]The length and width walls move toward each other at a rate of 0.25 m/ sec, hence [tex]\frac{dl}{dt} = \frac{dw}{dt} = 0.25[/tex]Length and width are 2 m and the height is 1.5 m, hence [tex]l = w = 2, h = 1.5[/tex]Then:
[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]
[tex]-2 = 2(1.5)(0.25) + 2(1.5)(0.25) + 2(2)\frac{dh}{dt}[/tex]
[tex]4\frac{dh}{dt} = -3.5[/tex]
[tex]\frac{dh}{dt} = -\frac{3.5}{4}[/tex]
[tex]\frac{dh}{dt} = -0.875[/tex]
The height is changing at a rate of -0.875 m/sec.
A similar problem is given at https://brainly.com/question/9543179
Simplify the following expression.
(42x + 59y) + (-14x + 35y)
A.
28x + 94y
B.
56x + 94y
C.
56x + 24y
D.
28x + 24y
Answer:
A. 28x + 94y
Step-by-step explanation:
First, line up the like terms as if you were adding vertically, and combine them.
(42x + 59y)
+ (-14x + 35y)
(28x + 94y)
Hope this helps :)