Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 4
Answers
Answer:
The length and width that maximize the area are:
W = 2*√8
L = 2*√8
Step-by-step explanation:
We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.
Remember that the area of a rectangle of length L and width W, is:
A = L*W
You can see the image below to see how i will define the length and the width:
L = 2*x'
W = 2*y'
Where we have the relation:
4 = √(x'^2 + y'^2)
16 = x'^2 + y'^2
Now we can isolate one of the variables, for example, x'
16 - y'^2 = x^'2
√(16 - y'^2) = x'
Then we can write:
W = 2*y'
L = 2*√(16 - y'^2)
Then the area equation is:
A = 2*y'*2*√(16 - y'^2)
A = 4*y'*√(16 - y'^2)
If A > 1, like in our case, maximizing A is the same as maximizing A^2
Then if que square both sides:
A^2 = (4*y'*√(16 - y'^2))^2
= 16*(y'^2)*(16 - y'^2)
= 16*(y'^2)*16 - 16*y'^4
= 256*(y'^2) - 16*y'^4
Now we can define:
u = y'^2
then the equation that we want to maximize is:
f(u) = 256*u - 16*u^2
to find the maximum, we need to evaluate in the zero of the derivative:
f'(u) = 256 - 2*16*u = 0
u = -256/(-2*16) = 8
Then we have:
u = y'^2 = 8
solving for y'
y' = √8
And we know that:
x' = √(16 - y'^2) = √(16 - (√8)^2) = √8
And the dimensions was:
W = 2*y' = 2*√8
L = 2*y' = 2*√8
These are the dimensions that maximize the area.
Related Questions
Which inequality matches the graph?
X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on graph has positive slope and runs through negative 3, negative 8 and 1, negative 2 and 9, 10. Above line is shaded.
−2x + 3y > 7
2x + 3y < 7
−3x + 2y > 7
3x − 2y < 7
Answers
Given:
The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).
Above line is shaded.
To find:
The inequality for the given graph.
Solution:
Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]
[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]
[tex]y+2=\dfrac{12}{8}(x-1)[/tex]
[tex]y+2=\dfrac{3}{2}(x-1)[/tex]
Multiply both sides by 2.
[tex]2(y+2)=3(x-1)[/tex]
[tex]2y+4=3x-3[/tex]
[tex]2y-3x=-3-4[/tex]
[tex]-3x+2y=-7[/tex]
Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.
[tex]-3x+2y>-7[/tex]
This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.
[tex](-3x+2y)(-1)<-7(-1)[/tex]
[tex]3x-2y<7[/tex]
Therefore, the correct option is D.
look at the image for the question and answers
Answers
Answer:
C
Step-by-step explanation:
Answer:
2 units
Step-by-step explanation:
Using the given formula
P = 2(l + w)
= 2([tex]\frac{2}{3}[/tex] + [tex]\frac{1}{3}[/tex] )
= 2(1)
= 2 units
Find the missing side of the right triangle if two sides are 6, and 10
Answers
Hope this helps!!
(If you have any questions, feel free to ask in the comments, If you found my answer helpful, please consider marking my answer brainliest, thanks!!)
What is the value of x?
[tex] \frac{4}{5} x - \frac{1}{10} = \frac{3}{10} [/tex]
Answers
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{5}[/tex] x - [tex]\frac{1}{10}[/tex] = [tex]\frac{3}{10}[/tex]
Multiply through by 10 ( the LCM of 5 and 10 ) to clear the fractions
8x - 1 = 3 ( add 1 to both sides )
8x = 4 ( divide both sides by 8 )
x = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
HELP I AM TIMED. Determine whether the equation is an identity or not an identity.
Answers
Answer:
It is not an identityStep-by-step explanation:
There are 10 common trig identities which I am aware of.
Some are in the image attached
The first image is known as b
Basic Identities
The second are known as Trigonometric / Pythagorean Identities .
The third : Co-function identities
and many more.
I'm only allowed to post five images so that's all I have.
Help pls I’ll mark you brainliest
Answers
Answer:
Step-by-step explanation:
If the 2 lines are parallel
then x = 70 cos ( alternate interior angle)
but if not sorry man I just in grade 9 its my best effort
Really sorry. <3
:(
The value of -9 is __ than the value of -12 because -9 is to the __of -12 on the number line.
Less
Or
Greater
Answers
Answer:
Step-by-step explanation:
-9 is greater than the value of -12 because -9 is to the right of -12 on the number line.
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $20 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month
Answers
The question is incomplete. The complete question is :
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $15 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month. Job B-1 used 82 direct labor hours and $3650 worth of direct material used. Job B-2 used 130 direct labor hours and $2,900 worth of direct material. What is the total cost of job B-2? Round to closest whole dollar (no cents).
Solution :
Particulars Job B-2
Direct material used $ 2,900
Add : Direct labor cost (130 hours x $15) $ 1,950
Add : overhead cost (130 hours x $ 42) $ 5,460
Total Cost of Job B-2 $ 10,310
Therefore, the total cost of the Job B-2 is $ 10,310.
Find the equation of the line through point (2,2) and parallel to y=x+4. Use a forward slash (i.e.”/“) for fractions (e.g. 1/2 for
Answers
Answer:
The equation of the line is, y = x
Step-by-step explanation:
The constraints of the required linear equation are;
The point through which the line passes = (2, 2)
The line to which the required line is parallel = y = x + 4
Two lines are parallel if they have the same slope, therefore, we have;
The slope of the line, y = x + 4 is m = 1
Therefore, the slope of the required line = 1
The equation of the required lime in point and slope form becomes;
y - 2 = 1 × (x - 2)
∴ y = x - 2 + 2 = x
The equation of the required line is therefore, y = x
Which value of w ww makes 14 = 11 + w 8 ⋅ 6 14=11+ 8 w ⋅614, equals, 11, plus, start fraction, w, divided by, 8, end fraction, dot, 6 a tru
Answers
Answer:
w=4
Step-by-step explanation:
Bethany is making trail mix with 3 cups of raisins for every 2 cups of peanuts. Which table represents this proportional relationship?
A 2-column table with 3 rows. Column 1 is labeled Peanuts (x) with entries 3, 12, 16. Column 2 is labeled Raisins (y) with entries 2, 8, 12.
A 2-column table with 3 rows. Column 1 is labeled Peanuts (x) with entries 2, 3, 6. Column 2 is labeled Raisins (y) with entries 8, 12, 24.
A 2-column table with 3 rows. Column 1 is labeled Peanuts (x) with entries 3, 8, 12. Column 2 is labeled Raisins (y) with entries 2, 16, 24.
A 2-column table with 3 rows. Column 1 is labeled Peanuts (x) with entries 2, 8, 12. Column 2 is labeled Raisins (y) with entries 3, 12, 18.
Answers
Answer:
Table 4 is the answer. Step-by-step explanation: Bethany is making trail mix with 3 cups of raisins for every 2 cups of peanuts. So, the ratio of peanuts to raisins is 2 : 3.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
GOT IT RIGHT edge 2021
pplied for a job as a cashier at a hardware store. As part of her employment screening, she was asked to take an exam that had general mathematical aptitude questions in it. This type of selection test is referred to as a
Answers
Answer:
cognitive ability
Step-by-step explanation:
Factorize
a⁴-3a²b²+b⁴
Answers
(a⁴-3a²b²+b⁴)/(a²-ab-b²)
Let me know if there is something wrong to my answer ^_^
Answer:
hope it will helpfulll to youuu
Inventor A had 630 inventions, 600% more than the number of inventions inventor B had. How many inventions did B have?
Answers
Answer:
105 inventions
Step-by-step explanation:
Find how many inventions Inventor B had by dividing 630 by 6:
630/6
= 105
So, Inventor B had 105 inventions
Please help me here. I've tried this one over and over and I'm unable to get the answer that was given. How do I find the area of this triangle?
Answers
Answer:
jjdjdjdj and technology and technology and technology and technology and technology
Solve an equation to find the missing angle
Answers
11.
[tex]6x = 30 \\ x = \frac{30}{6} \\ x = 5[/tex]
Missing angle:
[tex]6x \\ = 6 \times 5 \\ = 30[/tex]
_________________________________________
12.
[tex](4 + 5x) + (x + 2) = 180 \\ 6x + 6 = 180 \\ 6x = 180 - 6 \\ 6x = 174 \\ x = \frac{174}{6} \\ x = 29[/tex]
Missing angle 1:
[tex](4 + 5x) \\ = 4 + (5 \times 29) \\ = 4 + 145 \\ = 149[/tex]
Missing angle 2:
[tex]x + 2 \\ = 29 + 2 \\ = 31[/tex]
_________________________________________
13.
[tex]5x + (3x + 12) = 180 \\ 8x + 12 = 180 \\ 8x = 180 - 12 \\ 8x = 168 \\ x = \frac{168}{8} \\ x = 21[/tex]
Missing angle 1:
[tex]5x \\ = 5 \times 21 \\ = 105[/tex]
Missing angle 2:
[tex](3x + 12) \\ = (3 \times 21) + 12 \\ = 63 + 12 \\ = 75[/tex]
_________________________________________
14.
[tex]32 + (6x + 4) = 90 \\ 36 + 6x = 90 \\ 6x = 90 - 36 \\ 6x = 54 \\ x = \frac{54}{6} \\ x = 9[/tex]
Missing angle:
[tex](6x + 4) \\ = (6 \times 9) + 4 \\ = 54 + 4 \\ = 58[/tex]
_________________________________________
15.
[tex](2x + 1) + (x + 2) = 90 \\ 3x + 3 = 90 \\ 3x = 90 - 3 \\ 3x = 87 \\ x = \frac{87}{3} \\ x = 29[/tex]
Missing angle 1:
[tex](2x + 1 ) \\ = ( 2 \times 29) + 1 \\ = 58 + 1 \\ = 59[/tex]
Missing angle 2:
[tex]x + 2 \\ = 29 + 2 \\ = 31[/tex]
_________________________________________
16.
[tex](3x + 1) + (4 + 2x) = 90 \\ 5x + 5 = 90 \\ 5x = 90 - 5 \\ 5x = 85 \\ x = \frac{85}{5} \\ x = 17[/tex]
Missing angle 1:
[tex](3x + 1) \\ = (3 \times 17) + 1 \\ = 51 + 1 \\ = 52[/tex]
Missing angle 2:
[tex](4 + 2x) \\ = 4 + (2 \times 17) \\ = 4 + 34 \\ = 38[/tex]
What is the recursive formula for this geometric sequence?
-3, -21, -147, -1029, ..
Answers
Answer:
b . is the answer
Step-by-step explanation:
ha ahhgahga
Pls help ASAP
Compare and contrast how to graph: x=2 and y= -4
Answers
Answer:
plotting x = 2
see the x- axis look for the point x = 2(on right side of the origin ). Mark that point and draw a straight line parallel to the y- axis.
This is the graph of x = 2
plotting y = -4
see the y- axis and then look for the point y= -4 (that must be 4 units below the origin). Mark that point and draw a straight line parallel to the x- axis.
This is the graph of y = -4
we see that, the graph x = 2 is parallel to the y-axis whereas the graph y = -4 is parallel to the x- axis.
Apply the distributive property to create an equivalent expression.
\dfrac15(15+10k) =
5
1
(15+10k)=start fraction, 1, divided by, 5, end fraction, left parenthesis, 15, plus, 10, k, right parenthesis, equals
Answers
Answer:
3 + 2k
Step-by-step explanation:
Given:
1/5(15 + 10k)
= (1/5 * 15) + (1/5 * 10k)
= (1 * 15)/5 + (1 * 10k)/5
= 15/5 + 10k/5
= 3 + 2k
Therefore,
1/5(15 + 10k) = 3 + 2k
The equivalent expression is 3 + 2k
Hey is there any chance anyone could help me with this question ASAP?? Tysm :)
Answers
Answer:
6
Step-by-step explanation:
A = π. r²
36π = π. r²
eliminate π, we get:
36=r²
r=√36
r = 6
Answer:
r = 6
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
Given A = 36π , then
πr² = 36π ( divide both sides by π )
r² = 36 ( take the square root of both sides )
r = [tex]\sqrt{36}[/tex] = 6
Please help me with this one
Answers
Answer:
2×5×7+2×5×2+2×7×2
70+20+28
108cm^2
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]l = 5 \: cm \\ w = 2 \: cm \\ h = 7 \: cm[/tex]
The formula to find SA => 2lh + 2lw + 2hw
[tex]SA => 2lh + 2lw + 2hw \\ = 2 \times 5 \times 7 + 2 \times 5 \times 2 + 2 \times 7 \times 2 \\ = 70 + 20 + 28 \\ = 118 \: \: cm {}^{2} [/tex]
=> The surface area of the rectangular prism is 118 cm².
Find the value of "x" Wrong answer will be reported and explain please
Answers
Answer:
x = 20
Step-by-step explanation:
The consecutive angles in a parallelogram are supplementary, sum to 180°
5x + 4x = 180
9x = 180 ( divide both sides by 9 )
x = 20
Answer:
The value of x is 40⁰.
Step-by-step explanation:
5x + 4x = 360⁰
DUE TO THE SUM OF QUADRATIC ANGLE.
The incubation time for Rhode Island Red chicks is normally distributed with mean of 22 days and standard deviation of approximately 3 days. Of 1000 eggs are being incubated, how many chicks do we expect will hatch in 19 to 28 days
Answers
Answer:
We should expect 818 chicks to hatch in 19 to 28 days
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 22 days and standard deviation of approximately 3 days.
This means that [tex]\mu = 22, \sigma = 3[/tex]
Proportion between 19 and 28 days:
p-value of Z when X = 28 subtracted by the p-value of Z when X = 19.
X = 28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 22}{3}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.977.
X = 19
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22}{3}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.159.
0.977 - 0.159 = 0.818
Out of 1000:
0.818*1000 = 818
We should expect 818 chicks to hatch in 19 to 28 days
What is the product of 3/5 and 25. Is the product more or less than 14? Explain your answer in complete sentences.
(3/5 is a fraction Not Disvison )
Answers
Answer:
15, The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15
Step 1: Set up equation
[tex]\frac{25}{1}*\frac{3}{5}[/tex]
Step 2: Cross reduce
you can cross reduce 25 and 5 because they are both share a common divisor
[tex]\frac{5}{1} *\frac{3}{1}[/tex]
Step 3: Multiply numerator and denominator together
[tex]\frac{15}{1}[/tex]
Final Answer:
15
The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15
Where do i move the graph (new points)?
Answers
Answer:
l
Step-by-step explanation:
can someone please help me solve this? thank you!:)
Answers
First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.
P = L + 2W
A = L * W
Now that we have our equations, we need to plug in what we know, which is the 40m of rope.
40 = L + 2W
A = L * W
Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.
L = 40 - 2W
Now, we can substitute the value for L into L in the area equation and get a quadratic equation.
A = W(40 - 2W)
A = -2W^2 - 40W
The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.
V = -b/2a
V = 40/2(2) = 40/4 = 10
Derivative:
-4w - 40 = 0
-4w = 40
w = |-10| = 10
To find the other dimension, use the perimeter equation.
40 = L + 2(10)
40 = L + 20
L = 20m
Therefore, the dimensions of the area are 10m by 20m.
Hope this helps!
Answer:
Width: 10 m
Length: 20 m
Step-by-step explanation:
Hi there!
Let w be equal to the width of the enclosure.
Let l be equal to the length of the enclosure.
1) Construct equations
[tex]A=lw[/tex] ⇒ A represents the area of the enclosure.
[tex]40=2w+l[/tex] ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.
2) Isolate one of the variables in the second equation
[tex]40=2w+l[/tex]
Let's isolate l. Subtract 2w from both sides.
[tex]40-2w=2w+l-2w\\40-2w=l[/tex]
3) Plug the second equation into the first
[tex]A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w[/tex]
Great! Now that we have a quadratic equation, we can do the following:
Solve for its zeros/w-intercepts.Take the average of the zeros to find the w-variable of the vertex. (The area (A) in relation to the width of the swimming area (w) is what we've established in this equation, and the area (A) is greatest at the vertex. Finding the value of w of the vertex will tell us what the width needs to be for the area to be at a maximum.)Plug this w value into one of the equations to solve for l4) Solve for w
[tex]A=-2w^2+40w[/tex]
Factor out -2w
[tex]A=-2w(w-20)[/tex]
For A to equal 0, w=0 or w=20.
The average of 0 and 20 is 10, so the width that will max the area is 10 m.
5) Solve for l
[tex]40=2w+l[/tex]
Plug in 10 as w
[tex]40=2(10)+l\\40=20+l\\l=20[/tex]
Therefore, the length of 20 m will max the area.
I hope this helps!
Which of the following inequalities matches the graph?
Answers
Answer:
second one
Step-by-step explanation:
just read where the purple line finishes on the x axis, in this case it’s 5 so it’s greater than 5 or equal to it.
A number cube has faces numbered 1 to 6.
What is true about rolling the number cube one time?
Answers
Answer:
All numbers have an equal chance of being landed on.
Use the equation of the water level of the river represented by the equation y = −4x + 170, where x represents the number of years and y represents the total feet. What points are located on the line? Check all that apply. (170, 0) (0, 170) (12, 126) (50, 30) (5, 150) (60, –70)
Answers
Answer:
(0, 170) (5, 150) (60, -170)
Step-by-step explanation:
Plug each x value into the equation. The point is located on the line if the y values match.
Ex. -4 (170) + 170 = -510 this point is not on the line
-4 (0) + 170 = 170 this point is on the line because it is a "true" statement
Answer:
(0, 170) (5, 150) (60, -170)
Step-by-step explanation:
what is the average number of students who like cookies, chips, and crackers?
Cookies=10
Chips=3
Crackers=2
Answers
Answer:
m = 15/3 = 5 is the mean
Step-by-step explanation:
Answer:
5 Students But divide by 15/3 to 5
Step-by-step explanation:
What does Average mean?
1. a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number.
So, to find the answer just ADD 10 + 2 + 3 = ?
10 + 2 = 12 So put that to the side for now.
Now, 10 + 2 = 12 + 3 = 15
So the total number of students who like cookies, chips, and crackers are 15.
Now do 15/3 to get 5.
