The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.
Let's denote:
- [tex]\( x \)[/tex] as the length of one side of the square (in feet).
- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.
1. Area of the Square [tex](\( A_s \))[/tex]:
The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].
2. Area of the Circle [tex](\( A_c \))[/tex]:
The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:
[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]
Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]
The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].
Substituting the value of [tex]\( r \)[/tex], we get:
[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]
[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]
The perimeter of a rectangle is 42 m. the length of the rectangle is 3 m more than twice the width. find the dimensions of the rectangle.
42/2 = 21
21 = w +2w+3
21 = 3w +3
18 =3w
w = 18/3 = 6
width is 6
length = 6x2=12+3 = 15
6+6+15+15 = 42
width = 6 m
length = 15 m
The perimeter of a triangle is 510 ft and the sides are in the ratio of 11:16:24. Find the area of the triangle. Need help, is there a specific formula for this?
Final answer:
To find the area of a triangle with sides in a given ratio, first find the value of x by setting up and solving an equation using the perimeter. Then, multiply each side by x to find the base and height of the triangle. Finally, substitute the base and height into the formula for the area of a triangle.
Explanation:
To find the area of a triangle, we can use the formula: Area = 1/2 × base × height. In this case, we don't know the base and height directly, but we do know that the sides of the triangle are in the ratio of 11:16:24. Let's assume the sides are 11x, 16x, and 24x. The perimeter of the triangle is 510 ft, which means 11x + 16x + 24x = 510. Simplifying this equation, we get 51x = 510. Therefore, x = 10. Now we can find the base and height of the triangle by multiplying the corresponding sides by 10. The base is 11x * 10 = 110 ft and the height is 16x * 10 = 160 ft.
Now we can substitute these values into the formula to calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 110 ft × 160 ft = 8800 square feet.
Practice writing linear equations in different forms. Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB? y – 4 = 3x y – 2 = 3(x – 6) y + 4 = x y + 6 = x - 2
the answer is c . y + 4 = x
which of the following fractions will convert to repeating decimals?
a. 1/3
b. 1/6
c. 1/4
d. 3/8
e. 1/5
PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?
3y − x = −6
4y − x = 44
3y + x = −6
4y + x = 44
3y − 3x = −6
4y − 4x = 44
3y + 3x = −6
4y + 4x = 44
Answer: Hello!
we have that:
one third x − 2 = one fourth x + 11
this means:
(1/3)x - 2 = (1/4)x + 11
if this are equal numbers, we can write it as:
(1/3)x - 2 = y = (1/4)x + 11
now we have the system of equations:
(1/3)x - 2 = y
(1/4)x + 11 = y
if we "simplify" the rational therm in each equation, we get:
3*(1/3)x - 3*2 = 3y
x - 6 = 3y
and
4*(1/4)x + 4*11 = 4y
x + 44 = 4y
Then our system of equations is:
x - 6 = 3y
x + 44 = 4y
Now we can subtract x in each side of both equations:
-6 = 3y - x
44 = 4y - x
Then the right option is the first one.
3y - x = -6
4y - x = 44
Which of the following is an identity? A. sin2x sec2x + 1 = tan2x csc2x B. sin2x - cos2x = 1 C. (cscx + cotx)2 = 1 D. csc2x + cot2x = 1
Edit: no one answered but I figured out that the right answer is A
Answer: A is the correct answer.
Step-by-step explanation:
Just did the question, followed OP's advice since no one answered. Good luck.
what would be the measure of angle DGF, if segment DG is a bisector of angle G
30 degrees.60 degrees.90 degrees.None of the choices are correct.
In a 45-45-90 triangle, the length if the hypotenuse is 11. Find the length of one of the legs
Answer:
[tex] \frac{11\sqrt{2}}{2}[/tex]
Step-by-step explanation:
In a 45-45-90 triangle, the length if the hypotenuse is 11
WE use the common ratio of 45-45-90 degree triangle
common ration is x: x: x sqrt(2)
x sqrt(2) is the length of the hypotenuse
[tex]x\sqrt{2} = 11[/tex]
Divide by sqrt(2) on both sides
[tex]x= \frac{11}{\sqrt{2}}[/tex]
To rationalize the denominator, multiply by sqrt(2) at the top and bottom
sqrt(2) * sqrt(2) = 2
[tex]x= \frac{11\sqrt{2}}{2}[/tex]
A card is chosen at random from a standard deck of 52 playing cards. What is the probability that the chosen card is a jack or a queen?
The sum of three interior angles of a convex Pentagon is 420°.if the remaining angles are equal how much does each angle measure?
Each one of the remaining angles measures 60°.
How much does each angle measure?
We know that the sum of the interior angles of a closed figure of n sides is given by:
(n - 2)*180°.
A pentagon has 5 sides, so we use n = 5 and we get:
(5 - 2)*180° = 540°
Now we know that 3 angles add up to 420°.
Then the other two angles must add up to:
540° - 420° = 120°
And those two angles are equal, then each one measures:
120°/2 = 60°.
If you want to learn more about angles, you can read:
https://brainly.com/question/17972372
Zeus Industries bought a computer for $2011. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 5 years?
A polygon with 12 sides is called a/an
In geometry, a dodecagon or 12-gon is any twelve-sided polygon.
hope this helps!
Find the measure of an angle whose supplement is 9 times the measure of its complement
The equation is 180 - x = 9 (90 - x).Then the measure of the angle will be 78.75 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Let 'x' be the angle. Then the equation is given as,
180 - x = 9 (90 - x)
180 - x = 810 - 9x
8x = 630
x = 78.75 degrees
The measure of the angle will be 78.75 degrees.
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ5
200 gallon tank fills at 3 gallons/minute and loses 2 gallons/minute how long does it take to fill up
it fills at 3 gallons per minute, but loses 2 gallons per minute
3-2 =1, so it fills at 1 gallon per minute
200 gallons at 1 gallon per minute = 200 minutes,
200/60 = 3 hours and 20 minutes
Carissa is budgeting for her next semester at college. She spent $50 on gas this month. Economists are predicting gas prices to rise 8% per month for the next 6 months. How much should she budget for gas if classes start next month and are 4 months long?
The answer is D.243.33
(I looked up the question and couldnt find it so i thought i'd post it for anyone who needed it)
Find the value of x in the equation √ x + 5 = √ x + 45.
Find the number of permutations of the first 8 letters of the alphabet taking 4 letters at a time.
lady runs 20 miles in 4 hours. write an equation representing the direct relationship between distance and time
A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volume the same?
Please HELP
1-) Solve the equation using the Properties of Equality.
11 − c = −17
2-)Solve the equation using the Properties of Equality.
1/2y + 1/5=1/2
Emily is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 14 km/h. After nine hours, the velocity of the cyclist is 4 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 10 hours? (5 points)
10-2v=-5-50
+5 +5
10-3v=-50
+3 +3
10=47
Ac=3x+6 and CD=2x+14 what is the value of x
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
We have been given that [tex]AC=3x+6[/tex] and [tex]CD=2x+14[/tex].
To solve for x, we are assuming that C is the midpoint of segment AD and we will equate both expressions as:
[tex]3x+6=2x+14[/tex]
[tex]3x-2x+6=2x-2x+14[/tex]
[tex]x+6=14[/tex]
[tex]x+6-6=14-6[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.
Use the information in the figure. If m∠F = 76°, find m∠E
Answer:
m∠E=52°.
Step-by-step explanation:
The given triangle has two sides equal. In isosceles triangle two sides are equal and base angles are equal.m∠E=m∠D.
Let m∠D=m∠E= x
The sum of angles in any triangle is 180°.
Or,
x+x+76= 180
Addling like terms :
2x+76=180
Subtracting 76 both sides,
2x=104.
Dividing by 2:
x=52.
m∠E= 52°.
Find the midpoint of the segment below
0.43 is 10 times as mush as what
The number that is 10 times less than 0.43 is 0.043, found by dividing 0.43 by 10.
To find the number that 0.43 is 10 times as much as, we need to divide 0.43 by 10. This is the same as multiplying by 10 raised to the power of -1, which is a division by 10.The operation looks like this:
0.43*10^{-1} = 0.043.
Therefore, 0.43 is 10 times as much as 0.043
HELP
If f(x)=-6x+12, then f^-1(x)=?
To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How much lemonade did you make?
What is the solution set of the following equation? 3x2 - 6x = 0
A chocolate bar measures 40 mm wide, 80 mm long, and 5 and 1 over 2 mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper
Answer:
Will’s Wrapping Company needs 7,720 mm of paper to wrap the chocolate bar.