Answer:
[tex]500,500\text{ and }500\sqrt{2}[/tex] feet
Step-by-step explanation:
GIVEN: The boundary of a field is a right triangle with a straight stream along its hypotenuse and with fences along its other two sides.
TO FIND: Find the dimensions of the field with maximum area that can be enclosed with [tex]1000[/tex] feet of fencing.
SOLUTION:
Let the other two sides of triangle be [tex]x[/tex] and [tex]y[/tex]
such that, [tex]x+y=1000 \implies x=1000-y[/tex]
Area of triangle [tex]A=\frac{1}{2}\times base\times height=\frac{1}{2}\times x\times y[/tex]
Area of triangle[tex]A=\frac{1}{2}\times(1000-y)\times y=\frac{(1000y-y^2)}{2}[/tex]
to maximize area, put [tex]\frac{d\ A}{d\ y}=0[/tex]
[tex]\implies 500-y=0[/tex]
[tex]\implies y=500\text{ feet}[/tex]
other side [tex]x=1000-y=500\text{ feet}[/tex]
[tex]\text{hypotenuse}^2=x^2+y^2[/tex]
[tex]=500^2+500^2\implies \text{hypotenuse}=500\sqrt{2}[/tex]
dimension of triangle are [tex]500,500\text{ and }500\sqrt{2}[/tex] feet
The problem is solved by using the optimization strategy in mathematics. The maximum area of the field is obtained when the triangular field is an isosceles right triangle with base 500 ft and the hypotenuse side 250 ft each.
Explanation:This problem involves optimization in mathematics. In a right triangle with hypotenuse (h) and other two sides as base (b) and height (h), we know that the hypotenuse is the longest side. The Pythagorean theorem applies which states that h² = b² + h².
Given that the total length of the fences is 1000 ft, we know that b + h + h = 1000. We then solve for h and substitute it into the area formula, A = 1/2 bh. We get a quadratic function upon simplification, and we maximize the function to get the base and the height.
Using the strategy of setting the derivative equal to zero, the dimensions that maximize the area are found to be base b = 500 ft and the two equal sides h = 250 ft each which form the hypotenuse. Therefore, the field will have it's maximum area when it's a isosceles right triangle.
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Monkey at the zoo eat 4 cups of food every day elephants eat 76 times as much which equation and solution represent the number of cups of food elephants eat per day ?
Answer:
X = 76*4
= 304 cups of food
Step-by-step explanation:
Given:
Monkey eat 4 cups of food / day Elephants eat 76 times as much as Monkey does / daySo Let X is the number of cups of food that elephants eat per day, we have the equation:
X = 76*4
= 304 cups of food
Hope it will find you well.
BRAINLIEST AWARDED TO FIRST CORRECT ANSWER NEED ASAP! AND 20 POINTS!! The table shows the cost for taxi rides of various distances. Which graph displays the same function?
Answer:
b because it cost u more for a certain distance
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Type an equation for the following pattern
Answer:
y = x + 2
Step-by-step explanation:
It looks like its adding 2 everytime.
y = x + 2
Autumn creates bracelets as a hobby and is planning to start selling them online for $10 per bracelet. Autumn has already sold 5 custom bracelets. Her bracelets are so popular that she expects to sell every bracelet that she makes. Write an equation for the amount of money Autumn makes. If Autumn makes and additional 24 bracelets, how much money will she make?
Answer:
(24*10)+50=290
Step-by-step explanation:
a) The equation for the amount of money Autumn makes is y = 10x , where x is the number of bracelets she sells and y is the total amount
b) The amount Autumn makes is $ 290
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
a)
Let the number of bracelets Autumn sells be = x
Let the cost of one bracelet be = $ 10
Now , the equation will be
So , the cost of x number of bracelets y = number of bracelets x cost of one bracelet
The cost of x number of bracelets y = 10x
So , the equation is y = 10x
b)
The equation is y = 10x
The cost of 5 bracelets = 10 x 5
= $ 50
Now , the cost of 24 bracelets = 24 x 10
= $ 240
So , the total amount Autumn makes = cost of 5 bracelets + cost of 24 bracelets
The total amount Autumn makes = 240 + 50
= $ 290
Hence ,
a) The equation for the amount of money Autumn makes is y = 10x , where x is the number of bracelets she sells and y is the total amount
b) The amount Autumn makes is $ 290
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Kevin makes several cone-shaped candles. He uses a cone mold that has a height of 15 centimeters and a diameter of 10 centimeters. How much wax is needed to make 3 cone-shaped candles?
Answer:
1,177.5cm^3 of candle wax will be required.
Step-by-step explanation:
The attached files contain further information so please check them.
10•f(7)+9•g(-1)? What’s the answerrr
Answer:
= 70f - 9g
Step-by-step explanation:
1. Remove parentheses
2. Multiply the numbers
3. Multiply the numbers
Answer:
-1
Step-by-step explanation:
How many times smaller is the volume of a cylinder if the diameter is multiplied by 1/2
Calculating the volume of a cylinder the radius is squared,
If the radius was 8 when 8 is squared you get 64
If the radius is multiplied by 1/2 the radius would become 4, 4 squared is 16
16 / 64 = 1/4
The volume would be 1/4 the original volume, so it would be 4 times smaller.
Final answer:
Halving the diameter of a cylinder makes its volume four times smaller, because the volume depends on the square of the radius, and reducing the diameter by half means the radius is also halved.
Explanation:
When the diameter of a cylinder is multiplied by 1/2, the radius of the cylinder is also reduced to half its original size. To understand the impact on the volume, we examine the volume formula for a cylinder: V = (pi = 3.1416) times r^2 times h, where V is the volume, r is the radius, and h is the height. If both the diameter and radius are reduced by half, the volume of the cylinder will be reduced by a factor of 1/2^2 for the radius squared part of the formula.
Volume is directly proportional to the square of the radius, so taking the original volume formula V =
times (original radius)^2 times h and then applying the radius reduction, we get the new volume V' =
times (1/2 times original radius)^2 times h = 1/4 times original volume. Therefore, the volume of the cylinder becomes four times smaller when the diameter (and thus radius) is halved.
Higher Order Thinking A recipe calls for
3 tablespoons of pineapple juice. A can of
pineapple juice is 12 fluid ounces. How many
teaspoons of juice are in the can?
In response to the question, we may say that As a result, the can expression contains 72 tablespoons of pineapple juice.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To begin, we must convert the provided measurements to the same unit.
2 tablespoons = 1 fluid ounce
3 teaspoons = 1 tablespoon
Thus, 12 fluid ounces of canned pineapple juice equals:
12 fluid ounces divided by 2 tablespoons per fluid ounce is 24 tablespoons
And because we need to know how much juice is in teaspoons, we can convert tablespoons to teaspoons by:
72 teaspoons = 24 tablespoons × 3 teaspoons/tablespoon
As a result, the can contains 72 tablespoons of pineapple juice.
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find the value of y in the given triangle
Given:
In the given triangle,
With respect to y, Perpendicular = 10 cm and Base = 8 cm
To find the value of y.
Formula
By Trigonometric Ratio we get,
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
Now,
Putting the values of perpendicular and base we get,
[tex]tan\theta = \frac{10}{8}[/tex]
or, [tex]\theta = tan^{-1} (\frac{10}{8})[/tex]
or, [tex]\theta = 51.34 ^\circ[/tex]
Rounding off to the nearest tenth, we have;
[tex]\theta = 51.3 ^\circ[/tex]
Hence,
The value of y is 51.3°.
There is a spinner with 11 equal areas, numbered 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 2?
Answer:
result if 3 would be 3 I think I hope it helps have a good day
Answer:
7/11
Step-by-step explanation:
17 POINTS WHOEVER ANSWERS THIS ASAP
Answer:
It's correct answer is A.
Answer:
A represents the connector of X and Y.
Step-by-step explanation:
answer??
ill give a brainliest
Answer:
r=7
Step-by-step explanation:
-30=12-6r
We move all terms to the left:
-30-(12-6r)=0
We add all the numbers together, and all the variables
-(-6r+12)-30=0
We get rid of parentheses
6r-12-30=0
We add all the numbers together, and all the variables
6r-42=0
We move all terms containing r to the left, all other terms to the right
6r=42
r=42/6
r=7
Answer:
-3 = r OR r = -3
Step-by-step explanation:
-30 = 12 - 6r
30+12 = -18 12+12 = (cancels out left with just 6r)
-18/6r = -3
-3 = r
Hope this helped :)
A ladder that is 20 feet tall is leaning against a building.Samuel measures that the base of the ladder touches the ground 12 feet from the base of the building.How far from the ground does the top of the ladder touch the building?
Answer:
The distance from the ground to the top of the ladder the building is touched is 16 feet.
Step-by-step explanation:
Given:
A ladder that is 20 feet tall is leaning against a building.Samuel measures that the base of the ladder touches the ground 12 feet from the base of the building.
Now, to find the distance from base of the building to the top of the ladder where building is touched.
Here, to understand the situation below is the figure attached:
Now, to get the distance from the ground to the top of the ladder where the building is touched we use pythagorean theorem:
[tex]AB^2+BC^2=AC^2\\\\AB^2+12^2=20^2\\\\AB^2+144=400\\\\Subtracting\ both\ sides\ by\ 144\ we\ get:\\\\AB^2=256\\\\Using\ square\ root\ on\ both\ sides\ we\ get:\\\\AB=16\ feet.[/tex]
Therefore, the distance from the ground to the top of the ladder the building is touched is 16 feet.
-2x^2+6x-3=0 with the quadratic formula
someone plz help
Answer:
a = -2 b = 6 c = -3
x = -6 +- sq root (6^2 -4 * -2 *-3) / 2 * -2
x1 = [-6 + sq root (36 - 24)] / -4
x1 = [-6 + sq root (36 - 24)] / -4
x1 = (-6 + sq root (12) ) / -4
x1 = (-6 + 3.4641016151 ) / -4
x1 = -2.5358983849 / -4
x1 = 0.6339745962
x2 = (-6 - sq root (12) ) / -4
x2 = (-6 - sq root (12) ) / -4
x2= (-6 - 3.4641016151 ) / -4
x2 = - 9.4641016151 / -4
x2 = 2.3660254038
Step-by-step explanation:
Simplify the following rational expression
Answer:
= 5 (-2y+3) / -y+3
Step-by-step explanation:
If you need more help, you can look at this website called "symbolab".
Of the last 230 new hires at a company, 220 had college degrees and 140 had prior experience. Only 10 new hires had prior experience without a college degree. What is the approximate probability that a new hire has a college degree but no experience?
Answer:
Step-by-step explanation:LOOK IN PG 1 OF PDF 3 QUESTION.
HOPES THIS WAS HELPFUL
The required probability is 9/23
What is probability?Probability is the chance of happening of an event.Probability is always ≤ 1How to find the approximate probability that a new hire has a college degree but no experience?According to the problem,
Of the last 230 new hires at a company, 220 had college degrees 140 had prior experienceOnly 10 new hires had prior experience without a college degreeNumber of students with experience and a degree = ( 140 - 10 ) = 130
Number of students with only degree = (220 - 130) = 90
Probability that a new hire has a college degree but no experience = 90/230 = 9/23
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Maura can buy daffodil bulbs in packages of 3 for $5.37 or in packages of 2 for $4.52. How much money does she save by buying 30 bulbs at the better price?
Final answer:
Maura saves $14.10 by purchasing 30 daffodil bulbs in the more economical 3-bulb packages instead of the 2-bulb packages.
Explanation:
To determine how much Maura saves by buying 30 daffodil bulbs at the better price, we first need to calculate the price per bulb for each package option and then find the total cost for 30 bulbs. Let's compare the two package options:
Package of 3 bulbs for $5.37: The price per bulb is $5.37 / 3 = $1.79 per bulb.Package of 2 bulbs for $4.52: The price per bulb is $4.52 / 2 = $2.26 per bulb.The package of 3 bulbs has a better price per bulb than the package of 2 bulbs. To buy 30 bulbs at the better price, Maura would need 10 packages of 3 bulbs, which will cost:
10 packages × $5.37 per package = $53.70
Now let's calculate how much it would cost if she bought the 2-bulb packages:
Since 30 is an odd number, Maura would need to buy 15 packages of 2 bulbs to get 30 bulbs. This will cost:
15 packages × $4.52 per package = $67.80
Maura saves by purchasing the 30 bulbs in 3-bulb packages:
$67.80 - $53.70 = $14.10
Therefore, Maura saves $14.10 by purchasing the 30 bulbs in the more economical 3-bulb packages.
What’s the answer to this ?
Answer:
16 ^3/4 = 8
Step-by-step explanation:
distribute the exponential fraction.
(1 point) Suppose F⃗ (x,y)=⟨2y,−sin(y)⟩ and C is the circle of radius 3 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation r⃗ (t) for the circle C that starts at the point (3,0) and travels around the circle once counterclockwise for 0≤t≤2π.
Answer:
The required vector parametric equation is given as:
r(t) = <3cost, 3sint>
For 0 ≤ t ≤ 2π
Step-by-step explanation:
Given that
f(x, y) = <2y, -sin(y)>
Since C is a cirlce centered at the origin (0, 0), with radius r = 3, it takes the form
(x - 0)² + (y - 0)² = r²
Which is
x² + y² = 9
Because
cos²β + sin²β = 1
and we want to find a vector parametric equations r(t) for the circle C that starts at the point (3, 0), we can write
x = 3cosβ
y = 3sinβ
So that
x² + y² = 3²cos²β + 3²sin²β
= 9(cos²β + sin²β) = 9
That is
x² + y² = 9
The vector parametric equation r(t) is therefore given as
r(t) = <x(t), y(t)>
= <3cost, 3sint>
For 0 ≤ t ≤ 2π
The vector parametric equation for the circle C that starts at the point (3,0) and travels around the circle once counterclockwise for 0≤t≤2π is:
[tex]r(t) = <3cost, 3sint>[/tex]
We have
[tex]f(x, y) = <2y, -sin(y)>[/tex]
As C is a circle centered at the origin (0, 0), with radius r = 3,
So, equation is:
[tex](x - 0)^2 + (y - 0)^2 = r^2[/tex]
[tex]x^2+ y^2 = 9[/tex]
As, cos²β + sin²β = 1
Take ,
x = 3cosβ
y = 3sinβ
Then
[tex]x^2 + y^2 = 3^2cos^2\beta + 3^2sin^2\beta\\= 9(cos^2\beta + sin^2\beta) \\= 9\\x^2 + y^2 = 9[/tex]
The vector parametric equation r(t) is therefore given as
[tex]r(t) = <x(t), y(t)>[/tex]
[tex]= <3cost, 3sint>[/tex]
For 0 ≤ t ≤ 2π
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I need help! Idk what the answer is.
The volume of the oblique cylinder is 24 ft^3. Which statements are true? Check all that apply.
-The height of the cylinder is 3.4 ft
-Diameter is about 4.5 ft
-Diameter is about 3 ft
-Radius is about 6 ft
-A right cylinder with the same height and radius of this oblique cylinder would also have a volume of 24 feet cubed
Answer:
The correct options are 1, 3, and 5
Step-by-step explanation:
Find the balance in an account after 8 years if $500 is invested at 7% interest compounded annually
Answer: 280
Step-by-step explanation:
??/500=7/100
7x500/100
35/500=7/100
35x8=280
I think this is the answer.
Answer:
$859.09
Step-by-step explanation:
A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is:________
a. 20.0 to 30.0
b. 20.5 to 26.5
c. 23.0 to 27.0
d. 24.4 to 25.6
Answer:
The correct option is;
d. 24.2 to 25.6
Step-by-step explanation:
Here we have a sample with unknown population standard deviation, we therefore apply the student t distribution at 64 - 1 degrees of freedom
Therefore, we have
[tex]CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex]
Where:
[tex]\bar x[/tex] = Mean = 25
σ = Standard deviation = 2
n = Sample size = 64
t = T value at 98% = [tex]\pm 2.387[/tex]
Which gives
[tex]CI=25\pm t_{63}\frac{2}{\sqrt{64}}[/tex]
That is the value is from
24.40325 to 25.59675 which gives,by rounding to one decimal place, is
24.4 to 25.6.
The 98% confidence interval for the true average age of all students at the university, given a sample mean age of 25, standard deviation of 2, and a sample size of 64, is approximately option (d) 24.4 to 25.6 years.
The 98% confidence interval for the true average age of all students in the university can be calculated using the sample mean, the sample standard deviation, and the size of the sample. Since the population standard deviation is unknown and the sample size is less than 30, we use the t-distribution to find the critical value (t).
First, we find the t-score corresponding to a 98% confidence level with 63 degrees of freedom (n-1 = 64-1). Using a t-distribution table or calculator, the t-score is approximately 2.390.
Next, we calculate the margin of error (ME) using the formula:
ME = t * (s/√n)
where s is the sample standard deviation and n is the sample size. Plugging in our numbers:
ME = 2.390 * (2/√64) = 0.5975
Finally, we add and subtract this margin of error from the sample mean to find the confidence interval:
CI = mean ± ME
CI = 25 ± 0.5975
CI = (25 - 0.5975, 25 + 0.5975)
CI = (24.4025, 25.5975)
Therefore, the 98% confidence interval for the true average age is approximately 24.4 to 25.6 years.
John is driving around town. When he reaches the gas station, he notes that he has traveled 10 miles. He reaches home 2 hours later and notes that he has traveled 30 miles.
If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
A. d = 10t - 10
B. d=20 + 10 t
C. d= 10t + 10
D. d= 10t + 40
Answer:
C. d = 10t + 10
Step-by-step explanation:
If d represents the distance, you know that the equation on the other side has to have +10 included in it because this was stated in the problem (he has traveled 10 miles). C is the only option with +10, but if you'd like a further explanation on the 10t part... by the end of his trip, he has traveled 30 miles total. Subtract the 10 he initially traveled before arriving at the gas station, and he has traveled 20 miles in two hours. 20 (miles) / 2 (hours) = 10, so after the gas station, he traveled at an average speed of 10 mph. We now know that he traveled 10 miles, plus another 10 miles for every additional hour (t) he travels after that. This gives us d = 10t + 10.
how many points appear in the figure
In Mr. Harold's class there are 12 students. They each have 5 pencils. Some of the students, s, each lost 2 pencils. Now, the students only have a total of 38 pencils left. Which equation represents this situation?
A. s × 2 = 38
B. (12 × 5) - s = 38
C.(12 × 5) - (s × 2) = 38
D. (s × 2) - 12 = 38
Write all functions that are symmetric about the y-axis. Choose from the following six circular functions. yequals=sine xsinx, y equals=cosine xcosx, y equals=tangent xtanx, yequals=cotangent xcotx, y equals=secant xsecx, and yequals=cosecant x
Answer:
Hence the function only :
Secx and Cosx functions are symmetric about y-axis
And remaining functions are not symmetric about y-axis.
Step-by-step explanation:
Given:
Six circular function as :
y= sinx ,y=cosx , y=tanx, y= cotx ,y=secx y=cosecx
To Find:
Which functions are symmetric about the y-axis
Solution:
The function is said to be symmetric about the y-axis is given by
f(x)=f(-x)
Now
1)For y=sinx i.e. f(x)=sinx
So put x=-x
f(-x)=sin(-x)
=-sinx
Hence f(x)≠f(-x)
This function is not symmetric about y-axis
2)For y=cosx ,i.e. f(x)=cosx
put x=-x
f(-x)=cos(-x)...............(as value for x and -x cos value remain the same )
=cosx
hence f(x)=f(-x)
This function is symmetric to the y-axis
3)For y=tanx i.e f(x)=tanx
put x=-x
f(-x)=tan(-x)
=-tanx
Hence f(x)≠f(-x)
This function is not symmetric about y-axis
4)For y=cotx i.e. f(x)=cotx
Using above observation,
f(x)≠f(-x)
This is not symmetric about y-axis
5)For y=secx i.e f(x)=secx
f(x)=f(-x)
This function is symmetric about y-axis.
6) for y=cosecx
f(x)≠f(-x)
This function is not symmetric about y-axis
for what values of xis x + 2x = 24 true?
4 and -6
6 and 4
-tland 6
-6 and -4
Answer:
-6 and 4
Step-by-step explanation:
the explanation is in the picture
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Find the percent increase. Round to the nearest percent. From 97 books to 120 books
Answer:
It's a 19 percent increase.
Step-by-step explanation:
Divide 97/120, then multiply it by 100. After that, you can subtract the answer by 100. The answer will be negative, so make it positive.
How many times did the team score 6 runs? Line plots and Histogram
Answer:
If you're asking about which graph would be better, you can show it by a histogram best.
Step-by-step explanation:
Sorry if this is not your question if not I misunderstood, but a line graph is to measure the changes between data, while histograms measure a single measurement for each subject matter. So the best graph to display this info would be through a histogram