9.56 m of the wire should be used for the square, to maximize the total area of the wire
Let x be the side length of the square.
So, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
Let y represent the side length of the equilateral triangle.
So, the perimeter of the triangle is:
[tex]\mathbf{P_t=3y}[/tex]
The length of the wire is given as:
[tex]\mathbf{P=22}[/tex]
This implies that:
[tex]\mathbf{P_s + P_t=22}[/tex]
Substitute values for Ps and Pt
[tex]\mathbf{4x + 3y=22}[/tex]
Make y the subject
[tex]\mathbf{y=\frac{22 -4x}3}[/tex]
For an equilateral triangle of side length y, the height (h) of the triangle is:
[tex]\mathbf{h =\frac y2\sqrt 3}[/tex]
The area of the triangle is then calculated as:
[tex]\mathbf{A_t = \frac 12 yh}[/tex]
This gives
[tex]\mathbf{A_t = \frac 12 y\times \frac y2\sqrt 3}[/tex]
[tex]\mathbf{A_t = \frac{y^2}{4}\sqrt 3}[/tex]
The area of the square is:
[tex]\mathbf{A_s = x^2}[/tex]
So, the total area is:
[tex]\mathbf{A = A_s + A_t}[/tex]
[tex]\mathbf{A = x^2 + \frac{y^2}{4}\sqrt 3}[/tex]
Substitute [tex]\mathbf{y=\frac{22 -4x}3}[/tex]
[tex]\mathbf{A = x^2 + (\frac{22 - 4x}{3})^2 \times \frac{\sqrt 3}{4}}[/tex]
Differentiate
[tex]\mathbf{A' = 2x + \frac{\sqrt 3}{4} \times \frac 19 \times 2(22 - 4x) \times (-4)}[/tex]
[tex]\mathbf{A' = 2x - \sqrt 3 \times \frac 19 \times 2(22 - 4x) }[/tex]
[tex]\mathbf{A' = 2x - \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Set to 0
[tex]\mathbf{2x - \frac{2\sqrt 3}9 (22 - 4x) = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Divide through by 2
[tex]\mathbf{x = \frac{\sqrt 3}9 (22 - 4x) }[/tex]
Multiply through by 9
[tex]\mathbf{9x = \sqrt 3 (22 - 4x) }[/tex]
Open bracket
[tex]\mathbf{9x = 22\sqrt 3 - 4x\sqrt 3 }[/tex]
Collect like terms
[tex]\mathbf{9x +4x\sqrt 3= 22\sqrt 3 }[/tex]
Factor out x
[tex]\mathbf{x(9 +4\sqrt 3)= 22\sqrt 3 }[/tex]
Solve for x
[tex]\mathbf{x= \frac{22\sqrt 3}{9 +4\sqrt 3} }[/tex]
Simplify
[tex]\mathbf{x= \frac{38.11}{9 +6.93} }[/tex]
[tex]\mathbf{x= \frac{38.11}{15.93} }[/tex]
[tex]\mathbf{x= 2.39 }[/tex]
Recall that, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
So, we have:
[tex]\mathbf{P_s=4 \times 2.39}[/tex]
[tex]\mathbf{P_s=9.56}[/tex]
Hence, 9.56 m of the wire should be used for the square
Read more about maximizing lengths at:
https://brainly.com/question/3433355
Solve for the variable shown
Y=
Answer:
y≈94.31
Step-by-step explanation:
Hi there!
We're given a right triangle (notice the 90 degree angle), the measure of one of the legs (one of the sides that make up the right angle) as 46, the other one as y, and one of the angles as 26°
We want to solve for y
We can use a trigonometric ratio to do that.
First, let's recall the three most-well known ratios:
Sine is [tex]\frac{opposite}{hypotenuse}[/tex]
Cosine is [tex]\frac{adjacent}{hypotenuse}[/tex]
Tangent is [tex]\frac{opposite}{adjacent}[/tex]
Since we are given one of the angles, let's find out which sides are the opposite, adjacent, and hypotenuse, in reference to the given angle (the 26° angle)
In reference to that angle, the side opposite to that angle (also the side known as "opposite) is the side marked as 46, the adjacent side is y, and the hypotenuse is the unmarked side
Since we know the opposite and adjacent, let's use the ratio for tangent
Since we based our labels off of the 26 degree angle, the tangent ratio is the tangent OF 26, or tan(26)
tan(26)=[tex]\frac{46}{y}[/tex]
Now we need to solve the equation
Start by multiplying both sides by y
tan(26)*y=46
Divide both sides by tan(26)
y=[tex]\frac{46}{tan(26)}[/tex]
Plug [tex]\frac{46}{tan(26)}[/tex] into your calculator, and remember to have the calculator on degree mode
[tex]\frac{46}{tan(26)}[/tex]≈94.31
Remember that [tex]\frac{46}{tan(26)}[/tex] is equal to y, which means that y is about 94.31
Hope this helps!
Which equation represents this sentence?
3 times the difference of 6 and a number is equal to 15
3x−6=15
3(6−x)=15
6−3x=15
3(x−6)=15
Answer:
B. 3(6-x)=15
Step-by-step explanation:
3 times means to multiply 3
difference means to subtract, so the difference between 6 and a number would be 6-x (x representing the unknown number)
Hope this helps!
Answer:
B.
Step-by-step explanation:
Find the slope:
Find the slope:
Answer:
Ok let me explain what is WRONG!
Step-by-step explanation:
1. IT IS LITTERLY BLURRED
2. I CAN NOT READ ANY OF THE NUMBERS
3.And three THE FREAKING SLOPE IS RIGHT THERE!?
Help me pls brainlist
Answer:
The y-intercept is (0, 35)
The y-coordinate of the y-intercept represents the height at which the line intersects the y-axis.
The slope is 5/2.
Step-by-step explanation:
Which of the following equations
have a slope of 2
A) y + 3 = 2(x + 1)
B) y = -3x + 2
C) y-11 = -1(x + 2)
D) -6x+2y=12
Answer:
A) y + 3 = 2(x + 1)
Step-by-step explanation:
This is because in this equation (y-y=m(x+x)) m is the slope and the 2 is in the M's place making it the slope.
what expression is equivalent to 184 + w + 237 + x
9 ) Jason bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Jason start with ?
Answer:
He started with 53 cards
Step-by-step explanation:
He has 31 now
If 31 is half of what he had, then we need to double it
31 x 2 = 62
If he had bought 9, then we need to do the opposite
62 - 9 = 53
Two fractions between 2 and 2 1/2
How do I solve this?
Answer:
X = 10
Step-by-step explanation:
<1 = 2x + 10
<2 = x + 20
<3 = 180 - 6x (linear angles = 180 degrees)
<1 + <2 + <3 = 180 degrees
2x + 10 + x + 20 + 180 - 6x = 180
-3x + 210 = 180
-3x = 180 - 210
x = -30/-3
x = 10
Answer:
Step-by-step explanation:
what you do id try to find the math book on quizelit or some websire and find the answer
What's the answer to this question
Answer:
x = -7
Step-by-step explanation:
Write out the equation: 3x - 2 = -x - 30
Isolate the x
3x - 2 = -x - 30
+2 +x
4x = -28
Divide to simplify the x
x = -7
17 = -13 - 8x
can i get it step by step
Answer:
x = 30/-8 = -15/4 = -3.75 = -3 3/4
Step-by-step explanation:
17 = -13 - 8x
add 13 to each side
30 = -8x
divide each side by -8
30/-8 = x
30/-8 = -15/4 = -3.75 = -3 3/4
5. Mr. Quick bought a new computer system. The regular price was $1580, but he got a 15% discount. How much did he pay?
Answer:
He paid $1343
Step-by-step explanation:
[tex]\frac{x}{1580} =\frac{15}{100}[/tex]
Cross multiply
[tex]x100=23700[/tex]
Divide 100 from both sides
[tex]x=237[/tex]
1580 - 237 = 1343
Hope this is helpful
Answer:
He paid $1343
Step-by-step explanation:
Thanks for the pts
✌️❤️✌️
Can someone help me for 9, 10, 11, 12, and 13 please
Answer:
you have nice handwriting
Step-by-step explanation:
no answer
Write an equation of the line through the points (-3, 3) and (7, 5) in slope-intercept form. What is the y-intercept?
The sum of 8n²- 3n + 10 and 3n² - 6n-7 is ?
Step-by-step explanation:
= (8n² - 3n + 10) + (-3n² - 6n - 7)
= (8 - 3)n² + (-3 - 6)n + (10 - 7)
= 5n² - 9n + 3
Option → #1
IN A CLASS OF 60 STUDENTS, 25 PLAYS BASKETBALL, 2O PLAY VOLLEYBALL, AND 10 STUDENTS PLAY BOTH OF THEM. HOW MANY STUDENTS PLAY NEITHER BASKETBALL NOR VOLLEYBALL ?
Answer:
5
Step-by-step explanation:
60-25=35
35-20=15
15-10=5
5 people dont play either of them
Answer:
25
Step-by-step explanation:
To solve this, we can add the number of basketball players and the number of volleyball players:
25 + 20 = 45
But we know that there are ten players who are counted twice because they play both. So we subtract 10:
45 - 10 = 35
And that is the total number of students who play either basketball or volleyball. Now to figure out those that play neither sport we subtract the number of students by the number of players:
60 - 35 = 25
That’s the number of students who don’t play one of those sports.
[tex]y^2dy=(x+2)dx[/tex]
Integrate both sides:
y² dy = (x + 2) dx
∫ y² dy = ∫ (x + 2) dx
1/3 y³ = 1/2 x² + 2x + C
Bentley was playing with 3 old dog toys and 6 new dog toys. If Bentley has 18 old dog toys how many new dog toys does he have?
Answer: 36 new dog toys
Step-by-step explanation: With the given information, we can see that Bentley has a total of 18 old dog toys. IF Bentley is playing with a proportional relationship of toys, then all we have to do is multiply 6 by 6. Since 3 times 6 is 18, we have to do 6 times 6 which is 36.
use the following formula to solve the following quadratic equation 2x^+7a=15
Answer:
Hope this helps pls mark me Branliest
Step-by-step explanation:
that's my answer
Find the value of 6a + 4(3), if a = 2
Help
Credits: Hello! I'm from the Philippines! Mabuhay!!
Hey there!
6a + 4(3)
= 6(2) + 4(3)
= 12 + 12
= 12
Therefore, your answer is: 12
Good luck on your assignment and enjoy your day’
~Amphitrite1040:)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag correct position in the answer box. Release your mouse button when the item is place. If you change your m the item to the trashcan. Click the trashcan to clear all your answers. Indicate the equation of the line through (2, -4) and having slope of 3/5. IG V + + | C 123456 718190x y2 NEXT QUESTION O ASK FOR HELP
Answer:
Y=3/5 X -4 just trust me on this one. eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
A cone with a radius 4 m and a
height of 12 m.
What is the volume
Answer:
201.06 cu in
Step-by-step explanation:
Answer:
64π
Step-by-step explanation:
πr^2*h/3 is the formula for volume of a cone.
So 16pi * 12/3
Then 16pi *4
so 64 pi is the volume
There are 200 students in Year 11
75 of the students are girls.
Write down the fraction of the students that are girls.
Answer:
3/8
Step-by-step explanation:
36 to 37.50 percent increase
Answer:
4.16667% increase
Step-by-step explanation:
37.50 - 36 = 1.5
1.5 / 36 = 0.0416666666666
0.0416666666666 x 100
find the sum of 3x² + 5x - 1 and x² - 2x -7
Calculate the simple interest rate. (Round your answer to one decimal place.)
P = $3600, I = $330, t = 1 year
Answer:R = 9.1667%/year
Step-by-step explanation:
Solving our equation
r = 330 / (3600 × 1) = 0.09166667
r = 0.09166667
converting r decimal to a percentage
R = 0.09166667 × 100 = 9.1667%/year
The interest rate required to
accumulate simple interest of $330.00
from a principal of $3,600.00
over 1 years is 9.1667% per year.
MARK ME AS BRAINILIEST8. Heather purchased an iPad mini on sale 20%
off for $263.20. What was the original price of
the iPad mini?
A. $315.84
B. $329
C. $210.56
D. $400
Answer:
Answer is A.
Step-by-step explanation:
0.2 x 263.20 = 52.64
52.64 + 263.20 = 315.84
Find the volume of the following square pyramid.
Answer:
34610.83
Step-by-step explanation:
the height is 41.533 (found using the right triangle)
please help me asapppp! excel computer
Answer:
dddddddddddddddddddddddddd
Step-by-step explanation:
Please help! I cant get this wrong ahh. Brainliest to correct
Answer:
About 80,000
Step-by-step explanation:
take the % multiply by the years to get your answer
