The minimum perimeter is 23.24m and dimensions of the fenced area is 15.5m x 3.8m.
Let us assume the length of the fenced area to be L and breadth of the fenced area to be W. As we know, only three sides are to be fenced,
So, the perimeter P of the fenced would be,
P = L + 2W
Also, it is given that, area of the fence is 60m²,
So, the are should be,
60m² = LW
60m²/L = W
Now, to minimize the perimeter,
P = L + 2W
P = L + 120/L
Differentiating both sides with respect to "L",
d(p)/dL = 1 - 240/L²
To find the value of "L", putting dp/dL equal to 0,
d(P)/dL = 0
1 - 240/L² = 0
L = √240m
Now, from the first derivative test, we know that, the perimeter will be maximum or minimum if value of L>√240 or L<√240 respectively,
For minimum, L should be,
L = √240m
L = 15.5m
Now we know from area,
area = LW
60 = 15.5 x W
W = 60/15.5
W = 3.8m
Hence, the minimum perimeter will be,
L + 2W = 23.24m
The dimensions are,
L = 15.5m
W = 3.8m
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Consider a cube with an inscribed sphere. The function can be used to find the radius, r, of a sphere given the volume, v. The function can be used to find the side length of the cube, s, depending on the radius of the sphere. The function can be used to find the surface area, a, of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?
The composed function for the surface area of the cube for any given volume of an inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The function used to find the radius r of a sphere given volume V,
r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex]
The function used to find the length of the side s of the cube depending on the radius r of the sphere, s(r) = 2r
The function used to find the surface area A of the cube depending on the side of the cube s, A(s) = 6s²
We need to find the composed function for the surface area A of the cube for any given volume V of an inscribed sphere. i.e., A(V)
We have, A(s) = 6s²
Substituting function for s to A(s)
⇒ A(s(r)) = 6(2r)² = 24r²
Substituting function for r into A(s(r)),
⇒ A(s(r(V))) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
So the function for the surface area of the cube depending on the volume of the inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The question is incomplete. Find the complete question below:
Consider a cube with an inscribed sphere. The function r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex] can be used to find the radius, r, of a sphere given the volume, V . The function s(r) = 2r can be used to find the side length of the cube, s , depending on the radius of the sphere. The function A(s) = 6s² can be used to find the surface area, A , of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?
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Answer:
Answer is D
Step-by-step explanation:
Do number 8 please thank you
Answer:
a) true
b) false
c) false
Step-by-step explanation:
Here are these 4 sets in order of including more numbers to including fewer numbers.
R = all real numbers
Z = all integers
W = all whole numbers
N = all natural numbers
a) true
b) false
c) false
Write an equation in point-slope form
I NEED HELP ASAP
[tex]\huge\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]
Given a point and a slope, we want to write an equation in point-slope form.
The point-slope form is defined as:
[tex]y-y_1=m(x-x_1)[/tex]
In this equation, [tex](x_1, y_1)[/tex] is a known point on the line and [tex]m[/tex] is the line's slope.
Substitute in the values:
[tex]y-(-2)=-\dfrac{4}{3}(x-3)[/tex]
Finally, simplify. Subtracting a negative number is the same as adding a positive number:
[tex]\large\boxed{y+2=-\dfrac{4}{3}(x-3)}[/tex]
The parking garage charges $3 per hour to park for two hours or less.
The garage charges $3 for each additional hour of parking, up to and
including 5 hours. If a car uses the parking garage for more than 5
hours, there is a flat fee of $20.
Fill in the missing domain values for the following situation.
3x
(Value 1) ≤ x ≤2
f(x) = 6 4(x - 2) (Value 2) < r ≤ 5
20
x> (Value 3)
Value 1 =
Value 2 =
Value 3
The function will become:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
We are given that:
The parking garage charges $ 3 per hour if the car is parked there for less than 2 hours.
So, we get that:
Parking fees = 3 x for 0 ≤ x ≤ 2
Now, we get that, if the car is parked for more than 2 hours and less than 5 hours, then the parking fee is
6 + 4 ( x - 2) for 2 < x ≤ 5
Now, we are given that it charges a fixed fee of $ 20 if car is parked for more than 5 hours. So, the parking fee will be
20 for x > 5
So, the function becomes:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
Therefore, we get that, the function will become:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
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Sophie borrowed some money from her friend in order to help buy a new video game system. Sophie agreed to pay back her friend $2 per week and originally borrowed $10. Make a table of values and then write an equation for L,L, in terms of t,t, representing the amount Sophie owes her friend after tt weeks.
what is the equation and the 1 2 3 4
The equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is; L = 2t + 10
How to write an equation in Slope Intercept Form?
The general formula for equation of a line in Slope Intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the given question, the table of values is;
Number of weeks Amount of money owed
0 10
1 8
2 6
3 4
Now, since Sophie agreed to pay back her friend $2 per week and originally borrowed $10, it means that;
Slope = 2
y-intercept = 10
Thus, the equation for L, in terms of t, representing the amount Sophie owes her friend after t weeks is;
L = 2t + 10
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note: enter your answer and show all the steps that you use to solve this problem in the space provided. simplify the expression 8 2 9 ( 12 ÷ 3 ⋅ 2 ) − 7 . 82 912÷3·2-7. explain each of your steps.
129 is the value of expression .
What is PEMDAS?
The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.We use , P/E/M/D/A/S (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract)
8^2 + 9(12/3*2) - 7
= 64 + 9(8) -7
= 64 + 72 - 7
= 129
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find the equivalent fractionsss with large denominatorsss
Answer:
12
Step-by-step explanation:
[tex] \frac{3}{8} = \frac{?}{32} [/tex]
8*4=32
3*4=12
what type of solution is y=5x+4+5x-2
The type of solution to the given simultaneous equations is no solution
What is the solution to the simultaneous equations?When it comes to linear simultaneous equations as given in the question, there are different types such as; one solution, no solution or infinitely many solution.
We are given the simultaneous equations;
y = 5x + 4 ---(1)
y = 5x - 2 ----(2)
Using elimination method, subtract eq 1 from eq 2 to get;
0 = -2 - 4
0 = -6
0 cannot be equal to -6 and as such there is no value of x that makes the simultaneous equations true. Thus, the type of solution to the given simultaneous equations is no solution
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The coordinates of the point
of the way from A to B are____
The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).
How to find the coordinates of a point within a line segment
In this problem we find a line segment whose endpoints are known: A(x, y) = (- 3, - 6), B(x, y) = (10, 4), and of which we need to find a point C such that it is 3 / 10 of the way from point A to point B, whose exact location can be found by means of the line segment formula:
C(x, y) = A(x, y) + (3 / 10) · [B(x, y) - A(x, y)]
C(x, y) = (- 3, - 6) + (3 / 10) · [(10, 4) - (- 3, - 6)]
C(x, y) = (- 3, - 6) + (3 / 10) · (13, 10)
C(x, y) = (- 3, - 6) + (3.9, 3)
C(x, y) = (0.9, - 3)
The coordinates of the point that is 3 / 10 of the way from point A to point B is C(x, y) = (0.9, - 3).
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in exercises 13–17, the position d of a bicyclist (measured in kilometers) is a linear function of time t (measured in minutes). at time t
The position of the bicyclist at t=8 minutes is 3.2 km
Speed is the rate of change of position of an object in any direction.
position the way in which something or someone is placed or arranged.
when time t = 6 position d = 5
when time t = 5 position d = 2
when time t = 8 position d = x
therefore we can say
8 / x = 5 / 2
x = 8 * 2 /5
= 3.2 km.
Hence the position of the bicyclist at t=8 minutes is 3.2 km.
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complete question:
The position "d" of a bicyclist (measured in kilometers) is a linear function of time "t" (measured in minutes). At time t=6 minutes, the position is d=5 km. If the bicyclists travels at 2 km for every 5 minutes, find the position of the bicyclist at t=8 minutes.
find the angle between a diagonal of a cube and an adjacent edge. (enter your answer in degrees. round your answer to two decimal places.)
The angle between a diagonal of a cube and an adjacent edge is 54.75°;
Assuming the length of a side of the cube as 1 unit, the three sides are given by the vectors;
a = (1, 0, 0)
b = (0, 1, 0)
c = (0, 0, 1)
The diagonal is given by the vector, v = (1, 1, 1)
The angle between the diagonal and one edge of the cube is given by
cos θ = v. a / |v|.|a|
v. a = (1, 1, 1).(1, 0, 0)
= 1(1) + 1(0) + 1(0
= 1 + 0 + 0
v. a = 1
Magnitude of vector V = √[(1)² + (1)² + (1)²]
|v| = √3
Similarly, |a| = √1;
So, |v|.|a| = √3.√1 = √3
Now, cos θ = 1/√3
So, θ = cos¹(1/√3)
θ = 54.75°
Therefore, the required angle is 54.75°.
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The angle below measures
__ degrees.
.
...........................
4. Identify the following according to the information above. Justify your answer.
The following figures are Line, Ray, Line Segment, Parallelogram and Cuboid in the sequential order.
a) Line - A line is a two-dimensional figure. It is a group of points joining together to form a single entity which extends in both directions infinitely. It has no end points.
b) Ray - A ray is a two-dimensional figure. It is a group of points joining together to form a single entity, but it extends infinitely in only one direction. It has one end point.
c) Line segment - A line segment is a two-dimensional figure. It is a group of points joining together to form a single entity, but it does not extend infinitely in any direction. It has two end points and a finite length.
d) Parallelogram - A parallelogram is a two-dimensional figure having 4 sides whose opposite sides are equal in length and also parallel to each other. The diagonals of the parallelogram intersect each other at equal distance.
e) Cuboid - A cuboid is a three-dimensional figure made up of rectangular faces of varying length, breadth and height. The opposite faces of a cuboid are similar in dimensions. It has 12 edges, 12 vertices and 6 faces.
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Please help me with this question I don't understand it. Please it must be easy for yall genius's
Answer:
Range is 12 and mean is -6
Step-by-step explanation:
To find the mean, add together all the numbers and divide by 7.
Please help!! Graph the image of the trapezoid
below using a scale factor of
k= 1/4
If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;
F'(-2/4, 8/4) = (-1/2, 2)
G'(4/4, 8/4) = (1, 2)
I'(-6/4, -4/4) = (-1.5, -1) and;
H(8/4, -4/4) = (2, -1)
Reduction and enlargement of figures using scale factors.A scale factor is is a number used to enlarge a shape and each side is multiplied by the same number.
The given trapezoid has the coordinate points F(-2, 8), G(4, 8), I(-6, -4) and H(8, -4).
If the coordinate points is reduced using the scale factor of 1/4, hence the resulting coordinate point will be;
F'(-2/4, 8/4) = (-1/2, 2)
G'(4/4, 8/4) = (1, 2)
I'(-6/4, -4/4) = (-1.5, -1) and;
H(8/4, -4/4) = (2, -1)
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Expressed as a product of its prime factors in index form, a number n is n = 3 times 5 squared times x cubed. express 5n squared as a product of prime factors in index form. give your answer in terms of x.
5n² can be expressed as, 5n² = 3² x 5⁵ x x⁶
Given that n can be written as the product of the primes as
n = 3 x 5² x x³
This expression for n is called the prime factorization of n.
We need to express 5n² as such a product of primes.
For that taking square of n, add the power 2 with the existing powers of 3,5 and x,
So, n² = ( 3 x 5² x x³)² = 3² x 5⁴ x x⁶
So 5n² = 5(3² x 5⁴ x x⁶)
Multiplying 5 with the existing power of 5, 5⁴,
⇒ 5n² = 3² x 5⁵ x x⁶
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A private jet flies the same distance in 7 hours that a commercial jet flies in 5 hours. If the speed of the commercial jet was 99 mph less than 2 times the speed of the
private jet, find the speed of each jet.
Answer
Answer:
Private jet - 165 mphCommercial jet - 231 mphStep-by-step explanation:
Let the speed of the private jet is p and commercial jet is c.
Set equations7p = 5cc = 2p - 99Solve by substitution7p = 5(2p - 99)7p = 10p - 49510p - 7p = 4953p = 495p = 495/3p = 165Find c:
c = 2*165 - 99 = 330 - 99 = 231How to solve the inequality -20 ≤5a-10 <25
Answer:
-4[tex]\leq[/tex]a<7
Step-by-step explanation:
-20[tex]\leq[/tex]5a -10<25 add 10
+10 +10 +10
-20 [tex]\leq[/tex]5a<35 Divide all the way through by 5
-4[tex]\leq[/tex]a<7
What is the range of the numbers below?
8.1
5.2
-8.4
0.9
-4.7
-8.1
In the figure below, m Z1 = (x+84)° and m2 = 2xº.
Find the angle measures.
Answer:
1. m ∠ 1 = 86°
m ∠ 2 = 4°
- Problem in the picture
2. m ∠ 1 = 6°
m ∠ 2 = 84°
Step-by-step explanation:
I'm confused, so I'll just solve both problems (assuming that they are the same type of angle)
1.
m Z1 = (x+84)° and m2 = 2xº.
m ∠ 1 = (x + 84)°
m ∠ 2 = 2x°
Complementary angles are equal to 90°
(x + 84) + 2x = 90
x + 84 + 2x = 90
3x + 84 = 90
-84 -84
----------------------
3x = 6
÷3 ÷3
-----------
x = 2°
m ∠ 1 = (x + 84)°
m ∠ 1 = (2 + 84)°
m ∠ 1 = 86°
m ∠ 2 = 2x°
m ∠ 2 = 2(2)°
m ∠ 2 = 4°
2. (Problem in the picture)
m ∠ 1 = (x - 6)°
m ∠ 2 = 7x°
Complementary angles are equal to 90°
(x - 6) + 7x = 90
x - 6 + 7x = 90
8x - 6 = 90
+6 +6
---------------------
8x = 96
÷8 ÷8
----------------
x = 12
m ∠ 1 = (x - 6)°
m ∠ 1 = (12 - 6)°
m ∠ 1 = 6°
m ∠ 2 = 7x°
m ∠ 2 = 7(12)°
m ∠ 2 = 84°
I hope this helps!
Find the value of k. The diagram is not to scale.
Answer:
[tex] \large{ \boxed{ \tt{answer : \boxed{ \tt{ k = 73 \degree}}}}}[/tex]
Please see the attached picture for full solution!
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Remy walked to a friends house, m miles away, at an average rate of 4mph. The m-mile walk home was at only 3mph. Remy spent 2 hours walking in all. Find the value of m.
Step-by-step explanation:
speed = mph or miles/hour
so, when we are dealing with a distance and compare the time spent on the distance, we have to divide distance by speed
miles / miles/hour = hour
so, we have
m/4 + m/3 = 2
as the sum of the time it took to walk the distance at 4mph and the time it took to walk the distance at 3 mph is 2 hours.
now we multiply by the denominators one after the other to eliminate the fractions.
m + 4m/3 = 8
3m + 4m = 24
7m = 24
m = 24/7 = 3.428571429... miles
Dwayne is selling hamburgers and cheeseburgers. He has 100 burger buns. Each hamburger sells for $3, and each cheeseburger sells for $3.50. Which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80?
h + c ≤ 80
3h + 3.5c ≤ 100
h + c ≤ 80
3h + 3.5c ≥ 100
h + c ≤ 100
3h + 3.5c ≤ 80
h + c ≤ 100
3h + 3.5c ≥ 80
The system of inequalities are:
h + c ≤ 100
3h + 3.5c ≥ 80
What are the system of inequalities?Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toHere are the system of inequalities :
number of hamburgers sold + number of cheeseburger sold ≤ total number of buns
(cost of one hamburger x number of hamburger sold) + (number of cheeseburger sold x number of cheeseburger sold) ≥ $80
h + c ≤ 100
3h + 3.5c ≥ 80
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Jenny polled her 35 co-workers to find out which type of candy they liked best. She found that 10 like chocolate, 8 like gumdrops, 2 like hard candy, and 3 like taffy. There were 5 people who said they like BOTH hard candy and taffy and the remaining co-workers said they like BOTH chocolate and gum drops. How many of Jenny’s co-workers enjoy gumdrops or chocolate?
a.
10
d.
7
b.
8
e.
25
c.
18
The number of co-workers that like gumdrops and chocolate is 7 (option b).
How many like chocolate and gumdrops?The mathematical operations that would be used to determine the answer are addition and subtraction.
Addition is determining the total value or summing two or more numbers. The sign used to represent addition is +. Subtraction is the process of determining the difference between two or more numbers. The sign used to denote subtraction is -.
The first step is to add the total number of people who like a particular type of candy : 10 + 8 + 2 + 3 + 5 = 28
The second step is to subtract that number gotten in the previous step from the total number of co-workers.
Co-workers that like both chocolate and gum drops = 35 - 28 = 7
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a tv show had 4,320,000 viewers for its season premiere. express this number using scientific notation.
Answer:
Step-by-step explanation:
See attachment
solve -15.4+25.2+(-10.4)=
Answer:The answer is -0.6
Step-by-step explanation: -15.4-10.4 is -25.8
-25.8+25.2 is -0.6
So therefore the answer is -0.6
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Need 2 submit by tonight need help asap please <3
Three angles add up to 180 degrees, angle one has a measure of 7x+6, angle two has a measure of 2x+3 and angle three has a measure of 10x+9.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
Step-by-step explanation:
please find attached file for the problem. hope it will help you , let me know if you have any further query
Limits and Piecewise functions help please
Answer: -2, 2
Step-by-step explanation:
The derivative of a function, f(x), at a point where f(x) has a sharp turn (or cusp) does not exist.
The derivative of a function, f(x), at a point where f(x) has a vertical tangent line does not exist.
Using this information, we can see that f(x) is not differentiable when x=3 since there is a vertical tangent line. We can also see that f(x) is not differentiable when x=-1 since there is a cusp.
100 points HELP!
A group of friends want to go to the amusement park. They have $416.75 to spend on parking and admission. Parking is $15.25, and tickets cost $36.50 per person including tax. Which equation could be used to determine x, the number of people who can go to the amusement park
A. 36.5 (15.25 + x) = 416.75
B. 416.75 = 36.5x + 15.25
C. 15.25x = 416.75 - 36.5
C. 15.25x + 36.5 = 416.75
Answer:
tyyyy is my final answer