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
The radius of a circle is 3 cm. Find its area in terms of pi
Answers
Answer:
A = 9 pi cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
r=3
A = pi (3)^2
A = 9 pi cm^2
Area of circle = πr²
Area = π3²
Area = 9π
There area in terms of pie is 9πcm²
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Write the area A of an equilateral triangle as a function of the length s of its sides.
STEP 1: Find the base of the equilateral triangle in terms of s.
STEP 2: The height of an equilateral triangle can be found via the Pythagorean theorem. Use this information to find h in terms of s.
Answers
Write the area A of an equilateral triangle as a function of the length s of its sides. Draw the triangle; label each side "2s". Draw the altitute; it will bisect the base into s and s. ... Therefore, the area is equal to the measure of the bisected side times the measure of the altitude, quantity divided by 2.
HOPE SO IT HELPS YOU
Answer:
Step-by-step explanation:
Part A
Each side including the base is s.
Part B
Use 1/2 the base to find the height. The height meets the base at 90 degrees which gives you the right to use c^2 = b^2 + a^2
The hypotenuse is s
The base is 1/2s
h^2 = s^2 - (1/2s)^2
h^2 = s^2 - 1/4 s^2
h^2 = 3s^2/4
h = sqrt(3)/2 *s
Area = 1/2 * s * sqrt(3)/2 s
Area = 1/4 * s^2 * sqrt(3)
Use the graph that shows the solution to f(x) = g(x).
f(x) = 1+2x/x
g(x) = 2+x
What is the solution to f(x) = g(x)?
Select each correct answer:
X = -2
X = -1
X = 1
X = 2
Answers
Answer:
B and C
Step-by-step explanation:
The equation intersects each other at x=-1 and x=1
Diana and Dulce were selling tickets for their upcoming
softball game. Dulce sold 20% more than Diana. If they
sold 55 tickets total, how many tickets did each of them
sell?
Answers
Answer:
Diana sold 25 tickets and Dulce sold 30 tickets
Step-by-step explanation:
Let us assume that Diana sold x number of tickets, dulce sold 20% more x or 1.2x. ATQ, x+1.2x=55. x=25. So Diana sold 25 tickets and Dulce sold 30 tickets
Jol 28, 3:44:44 AM
Solve the equation for all values of x.
(x2 – 16)(x2 + 49) = 0
Answer:
Submit Answer
Answers
Answer:
x = 4, -4, 7i, -7i
Step-by-step explanation:
(x^2 – 16)(x^2 + 49) = 0
x^2 – 16 = 0 or x^2 + 49 = 0
x^2 = 16 or x^2 = -49
x = ± 4 or x^2 = ±7√-1 =±7i
find the missing side
Answers
Answer:
[tex]\boxed{x=13.89\:km}[/tex]
Step-by-step explanation:
Pythagorean theorem
[tex]x^2=(12^2)+(7^2)[/tex]
[tex]x^2=144+49[/tex]
[tex]x^2=193[/tex]
[tex]x=\sqrt{193}[/tex]
[tex]\boxed{x=13.89\:km}[/tex]
What is the missing reason in the proof? Given: ∠ABC is a right angle, ∠D B C is a straight angle Prove: ∠ABC ≅ ∠A B D A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle. definition of angle bisector segment addition property definition of congruent angles transitive property
Answers
Answer:
Definition of Congruent angles.
Step-by-step explanation:
Given
See attachment
Required
Complete the proof at step 8
At step 8, we have:
[tex]\angle ABC \cong \angle ABD[/tex]
When the sign [tex]\cong[/tex] is used, it means congruence
In other words;
ABC and ABD are congruent
Hence, the missing statement at step 8 is: Definition of Congruent angles.
Answer:
ABC and ABD are congruent
Step-by-step explanation:
Which models best illustrates the inequality and its graph?
t< 55
a.) t is at least 55
b.) t is less than 55
c.) t is 55 or more
d.) t is at most 55
Answers
Answer:
B
Step-by-step explanation:
Open circle means the number is not included.
Hope this helps <3
Can sone One help me please, Thanks a lot
Answers
Answer:m
Step-by-step explanation:m
4x+3=x+9
What is the number?
X=?
Answers
Answer:x=3
Step-by-step explanation:
4x+3=x+9
4x-x=(-3)+9
3x=6
x=6:3
x=2
HELP!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1. 22+b
2. 7x
3. 6+t
4. Z(4+6)
5. -10+4a
6. N(8+-2)
7. X^2/2
4/5(m^2)
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
1.) b + 21
2.) x × 7 or 7x
3.) t + 6
4.) 4 + 6z
5.) -10+4a
6.) 8 +(-2n)
7.) (1/2)×n³
8.) (4/5)×m²
Must click thanks and mark brainliest
How much would $500 invested at 9% interest compounded annually be
worth after 4 years? Round your answer to the nearest cent.
Answers
Answer:
I think 705.79 if I did it right
Step-by-step explanation:
500(1+.09/1)^4 = 705.79
Let ε = {5,6,7,8,9}, A = {x | x >7} and B = {5,6} Find
1. P(A’)
2. P(A) U P(B)
3. P(A) ∩ P(B)
4. P(A ∩ B)
Answers
Answer:
A={x| x>7} = 8,9
B= {5,6}
1,
2,{5,6,8,9}
3,{}
4{}
I do not understand this question can someone help me with good explanation will give Brainliest
Answers
Answer:
60 (E)
Step-by-step explanation:
He plants seeds -> plants grow to 12 times the original weight of the seeds -> he sells 50 tonnes from the harvest -> remainder is used as the next batch of seeds
He harvested 120 tonnes this year which means the original weight of the seeds planted was 120÷12 = 10 tonnes. This means that last years harvest would be the 10 tonnes used as seeds plus the 50 tonnes that would have been sold immediately, 10+50 = 60 tonnes
PLEASE HELPP!!!!
Find the area.
A.530in²
B. 779in²
C.390in²
D.1060in²
Answers
Answer:
530in²
Step-by-step explanation:
Area of triangle(a)=1/2bh=1/2*40*26.5=530
The following relation is a function (10,12),(5,3),(15,10),(5,6),(1,0) true false
Answers
Answer:
True
Step-by-step explanation:
A baby can crawl ¾ foot in ¼ minute. How far does the baby get per minute?
Answers
Answer:
3 ft per minute
Step-by-step explanation:
Take the distance and divide by the time
3/4 ft ÷ 1/4 minute
Copy dot flip
3/4 * 4/1
Rewriting
3/1 * 4/4
3/1 *1
3 ft per minute
Kristian and Stephanie share money in the ratio 3 :2 Kristian receives $72 How much will Stephanie receive
Answers
Answer:
48
Step-by-step explanation:
Kristian : Stephanie
3 2
Kristian receives 72
72/3 = 24
Multiply each side by 24
Kristian : Stephanie
3*24 2*24
72 48
3x – (7x + 2) > 5x + 4
Answers
Answer:
x < -2/3Step-by-step explanation:
3x – (7x + 2) > 5x + 4= 3x -7x - 2 > 5x + 4= -4x - 2 > 5x + 4= -4x -5x > 4 + 2 = -9x > 6= x < -2/3[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Q: Marci wants to prove that the diagonals of
a rectangle are congruent. Which of these
procedures would be best for Marci to use
to write a correct proof?
a) She should use the fact that the
diagonals of a square are perpendicular
and then use the triangle-angle-sum
theorem.
b) She should use the fact that the
opposite sides of a parallelogram are
congruent and then use the
Pythagorean theorem.
c) She should use the fact that the
opposite angles of a parallelogram are
congruent and then use triangle
similarity relationships.
d) She should use the fact that the
diagonals of a parallelogram bisect the
angles of the parallelogram and then
use triangle congruence relationships.
Answers
Answer: Option B
She should use the fact that the
opposite sides of a parallelogram are
congruent and then use the
Pythagorean theorem.
We cannot use the diagonals of square property because this is a rectangle, opposite angles will also not work, and we cannot use the diagonal property because thats what we have to prove.
Must click thanks and mark brainliest
What is the range of function represented by the graph below?
Answers
Answer:
y ≥ 0
Step-by-step explanation:
The range of the function is the output values.
The y value goes from 0 to infinity
y ≥ 0
Find the length of the third side. If necessary, round to the nearest tenth.
16
12
Answer:
Submit Answer
PLS HELP ASAP
Answers
Answer:
I think 16.
Step-by-step explanation:
because 12 is impossible and last answer is 16.
Answer:
the third side will be √500
Step-by-step explanation:
[tex]\sf{}[/tex]
using PGT
(16)²+(12)²=H²
=> 256+144 = H²
=> 500 = H ²
=> √500 = H
Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 2 with
these dice. Be sure to reduce.
[?]
Answers
Answer:
1/36
Step-by-step explanation:
it is the exact same as if both your dice had the numbers {1,2,3,4,5,6}
you said the SUM of the dice that is indicates the answer of the addition of two (or for that matter more) numbers,... the only numbers that would sum 2 is 1+1,... and because you only have two ones (one per die) the answer is the same as if they where die with normal numbers,...
The probability of rolling a sum of 2 with these dice is 1/36.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
Pair of dice have= {1,2,2,3,3,4}
Now,
The probability of rolling a sum of 2 with two dice is the same as the probability of rolling snake eyes, since the only way to get a sum of 2 is if both dice show a 11. The probability of rolling a 1 on a single die is 1/6, so the probability of rolling a 1 on both dice is (1/6) × (1/6) = 1/3612.
However, in this case, the dice are not standard six-sided dice, but have different numbers on their faces. The first die has {1,2,2,3,3,4} and the second die has {1,3,4,5,6,8}. The probability of rolling a 1 on the first die is still 1/6, but the probability of rolling a 1 on the second die is also 1/6. Therefore, the probability of rolling a sum of 2 with these dice is still (1/6) × (1/6) = 1/36.
This probability cannot be reduced any further, since 1 and 36 have no common factors other than 1.
Therefore, the probability will be 1/36.
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ7
Lydia runs an experiment to determine if a coin
Answers
I really need help anyone know which option is correct.?
Answers
Answer:
B, [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
This problem is essentially asking one to envision a line passing through the set of points on the coordinate plane, then to find the constant of proportionality of that line. The constant of proportionally, also known as the rate of change, or the slope, is a number that can be used to describe the range that happens between points on a line. The following formula can be used to find the slope of a line passing through a set of points.
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where the points ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line.
As one can see, on the given coordinate plane, the points ([tex]2,-1[/tex]), and ([tex]4,-2[/tex]) are on the coordinate plane. Substitute these points into the formula to find the slope of the line, then simplify to evaluate the equation and find the slope,
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
([tex]2,-1[/tex]), ([tex]4,-2[/tex])
[tex]=\frac{-2-(-1)}{(4)-(2)}[/tex]
[tex]=\frac{-2+1}{4-2}\\\\=\frac{-1}{2}\\\\=-\frac{1}{2}[/tex]
Which of the following are good ideas to use when gathering your resources?
Check all that apply.
O A. Form an equation:
B. Draw a diagram.
C. List potential formulas.
D. Guess at the solution and see if you are close.
E. Organize into a table.
F. Write down the facts.
Answers
Answer:
Organize into a table for good gatherings.
5. Which expression is a simplified form of (3x2 + 2x - 4) + (-7x2 + 6x - 2)?
a 10x2 + 8x - 6
b. -4x2 + 8x - 2
C.-4x2 + 8x + 2
d. -4x2 + 8x - 6
Answers
Answer:
d. -4x² + 8x - 6
Step-by-step explanation:
(3x² + 2x - 4) + (-7x² + 6x - 2)
3x² + 2x - 4 - 7x² + 6x - 2
3x² - 7x² + 2x + 6x - 4 - 2
-4x² + 8x - 6
whats the volume the triangular prism?
Answers
Answer:
the volume is 1000 cm^3
Step-by-step explanation:
first we need to find where is the base, and height, for this case, the trian is the base, not the rectangle, so it maybe eas if you draw a upright angle os the shape, with the triangle facing down.
As show you need to have bare and height for the volume of the prism, which we already know the height is 25 (h=25) so now we need to find the base.
for the base, since it’s a triangle, which has the area formal of 1/2(bh), so now just plot the number in, 1/2x10x8= 40 cm^2
now using the volume of prism formal; V = bh = 40 x 25 = 1000 cm^3
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 8 N acts on a certain object, the acceleration of the object is 4 m/s?. If the acceleration of the object becomes 3 m/s?, what is the force?
Answers
Here Mass is constant
F1=8Na_1=4m/s^2a_2=3m/s^2F_2=?Using Newtons s law
[tex]\\ \sf \longmapsto F=ma[/tex]
[tex]\\ \sf \longmapsto \dfrac{F}{a}=m[/tex]
[tex]\\ \sf \longmapsto \dfrac{F_1}{a_1}=\dfrac{F_2}{a_2}[/tex]
[tex]\\ \sf \longmapsto \dfrac{8}{4}=\dfrac{F_2}{3}[/tex]
[tex]\\ \sf \longmapsto F_2=\dfrac{24}{4}[/tex]
[tex]\\ \sf \longmapsto F_2=6N[/tex]
Answer:
F = 6N
Step-by-step explanation:
Equation
F = ka
F - force
k - constant of proportionality
a - acceleration
Step 1 - find k
8N=k*4m/s^2
k=2
Step 2 - find F
F=2*3m/s^s
F=6
What is the slope of the line through (3,2) and (-3,4)
Answers
Answer:
-1/3
Step-by-step explanation:
slope = m = rise/run = (difference in y)/(difference in x)
m = (4 - 2/(-3 - 3)
m = 2/(-6)
m = -1/3
