Answers
Answer:
c
Step-by-step explanation:
the height is 3 so multiply everything by 3 (AFTER) THEN you add the 2 and 5 and get 10 then times by the 3 to get 30
Related Questions
Rewrite the following expression as the product of two binomials. Do not simplify the product.
(x-5)(4x+9) + (2x - 4)(x-5)
Answers
Answer:
x-5
Step-by-step explanation:
Using Lagrange multipliers, verify that of all triangles
inscribed in a circle, the
equilateral maximizes the product of the magnitudes of its
sides:
Answers
Among all triangles inscribed in a circle, the equilateral triangle maximizes the product of the magnitudes of its sides.
To prove this statement using Lagrange multipliers, let's consider a triangle inscribed in a circle with sides of lengths a, b, and c. The area of the triangle can be expressed using Heron's formula:
Area = √[s(s-a)(s-b)(s-c)],
where s is the semi-perimeter given by s = (a + b + c)/2. We want to maximize the product of the side lengths a, b, and c, which can be written as P = abc.
To apply Lagrange multipliers, we need to set up the following equations:
∇P = λ∇Area, where ∇P is the gradient of P and ∇Area is the gradient of the area function.
Constraint equation: g(a, b, c) = a^2 + b^2 + c^2 - R^2 = 0, where R is the radius of the inscribed circle.
Taking the partial derivatives and setting up the equations, we get:
∂P/∂a = bc = λ(∂Area/∂a),
∂P/∂b = ac = λ(∂Area/∂b),
∂P/∂c = ab = λ(∂Area/∂c),
a^2 + b^2 + c^2 - R^2 = 0.
From the first three equations, we have bc = ac = ab, which implies a = b = c (assuming none of them is zero). Substituting this back into the constraint equation, we get 3a^2 - R^2 = 0, which gives a = b = c = R/√3.
Therefore, the equilateral triangle with sides of length R/√3 maximizes the product of its side lengths among all triangles inscribed in a circle.
In conclusion, using Lagrange multipliers, we have shown that the equilateral triangle is the triangle that maximizes the product of its side lengths among all triangles inscribed in a circle.
To learn more about Lagrange multiplier, click here: brainly.com/question/24208980
#SPJ11
Kyle wants to find out how many textbooks his class has in total. He has discovered
that each student has an average of 5 textbooks. There are 30 people in his class. How many
textbooks does his class have in total?
Answers
Explanation: Because it is given that each student carries about 5 textbooks, with 30 students in the class, the equation would be 5 • 30 = 150. Some students may have more, while others may have less, so the average is given as 5 in order to simplify the equation.
can someone pls help!?
Answers
Answer:
the answer is G G(X)=F(X+2)
Write the expression in terms of a single trigonometric function. \[ \sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} \]
Answers
Let's start solving the expression using the product to sum formulae.
Here's the given expression,
\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]
Using the product-to-sum formula,
\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]
Applying the above formula in the first term,
\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]
Using the product-to-sum formula,
\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]
Applying the above formula in the second term,
\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]
Substituting these expressions back into the original expression,
we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]
Therefore, the given expression can be written in terms of a single trigonometric function as:
\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}
Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.
To learn more about trigonometric function click the below link
https://brainly.com/question/25618616
#SPJ11
3- Find all values of Z such that e² = 2+i√3
Answers
The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.
To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.
Given: 2 + i√3
To find r, we can use the modulus formula:
r = sqrt(a^2 + b^2)
= sqrt(2^2 + (√3)^2)
= sqrt(4 + 3)
= sqrt(7)
To find θ, we can use the argument formula:
θ = arctan(b/a)
= arctan(√3/2)
= π/3
So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).
Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.
ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik
Therefore, the values of Z are:
Z = ln(2 + i√3) + 2πik, where k is an integer.
The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.
To know more about polar form visit
https://brainly.com/question/30824428
#SPJ11
At time t=0, water begins to drip out of a pipe into an empty bucket. After 36 minutes, there are 12 inches of water in the bucket. Write a linear function rule to model how many inches of water w are in the bucket after any number of minutes
Answers
Answer:
y=1/3t
Step-by-step explanation:
For a linear function you can use the formula y=mx+b
m is the slope (also known as the rate of change)
b is the y intercept (the value y is at when x is 0). For this problem the bucket starts out empty so there is no y-intercept that needs to be written in the equation.
To find slope divide the inches of water by the total number of minutes given. 12/36=1/3
Plug your slope and y-intercept into the equation.
y=1/3t+0
Simplify
y=1/3t
Use function notation to represent the area of a circle with a radius of 2.11 inches
Answers
Answer:
f(2.11) = 13.9867 or 13.99 in²
Step-by-step explanation:
Given the radius ( r ) of 2.11 inches, we can determine the area of a circle by substituting the value of the radius into the following function:
f(r ) = πr²
f(2.11) = π(2.11)²
f(2.11) = π(4.4521)
f(2.11) = 13.9867 or 13.99 in²
Therefore, the area of the circle with a radius of 2.11 inches is 13.99 in².
Drag the point on the coordinate plane to the solution of the system of equations shown below: y=-2x-1 y = x + 2
Answers
Answer:
(1,-1)
Step-by-step explanation:
-2x-1 = x+2
-3x = 3
x = -1
substitute
y = (-1) + 2
y = 1
point: (1,-1)
the week, Carrie spent
$3.50 for a book. The next day
her father gave her $1.25. Then
she went to a movie, which cost
$7.50. If she now has $10.25,
how much money did she have
at the beginning of the week?
Answers
Answer:
$20.00
Step-by-step explanation:
Let x be the money Carrie had at the start of the week.
Add/Subtract from this amount (x) for the events occurring during the week:
x Start
-3.50 1 book
+1.25 Sugardaddy income
-7.50 Batman movie
===============
The end of the week Carrie has $10.25
Put this into one equation:
x - 3.50 + 1.25 - 7.50 = 10.25
x = 10.25 + 3.50 - 1.25 + 7.50
x = $20.00
Is this a function?
A) Yes
B) No
Answers
Answer:
B
Step-by-step explanation:
Answer:
No, it is not.
Step-by-step explanation:
X has 2 3's. X's shouldn't repeat for it to be a function or else it will overlap.
can you help me please
Answers
Answer:
13.5 in^2
Step-by-step explanation:
6 = 1/2(B)(H) = 1/2(2)(H)
H = 6
H x 1.5 =9
area = 1/2(3)(9) = 13.5
Answer:
2.7 square inches
Dante has a tent shaped like a triangular prism. The tent has equilateral triangle bases that measure 5 feet on each side. The tent is 8 feet long and 4. 3 feet tall
Answers
The tent has a volume of 86 cubic feet.
How we get the volume of tent?The tent owned by Dante is in the shape of a triangular prism, which means it has two identical equilateral triangle bases that measure 5 feet each. The tent's length is 8 feet, and its height is 4.3 feet.
To calculate the tent's volume, we can use the formula for the volume of a triangular prism, which is \(V = (1/2) * b * h * l\), where b is the base, h is the height, and l is the length of the prism.
Plugging in the given values, we get \(V = (1/2) * 5 * 4.3 * 8\) = 86 cubic feet. The volume of a tent is an important consideration when deciding which one to purchase or use for a particular activity, as it determines how much space is available inside for people and belongings.
Learn more about Volume
brainly.com/question/1578538
#SPJ11
suppose sean makes 10 tables a month, each of which he can sell for $200. given that the average cost of making each table is $150, should sean make more or fewer tables each month?
Answers
It's impossible to say Sean should base his decision on the marginal cost and marginal benefit of creating another table. The marginal cost of making a table is not the same as the average cost of making a table. As a result, there is insufficient information to determine what Sean should do.
The opportunity cost of an activity is the value of what must be sacrificed in order to engage in the activity (plus the cost). A cost that cannot be recovered at the time a decision must be made.
The science of decision-making is often used as a crude definition of economics. This stems from the fact that economics is frequently concerned with making the best decision in the most efficient manner. One way to quantify this is to consider total costs and total benefits.
To learn more about marginal benefit link is here
brainly.com/question/30529566
#SPJ4
if a is any integer, is a (a plus 1 )even or odd? say which it is (4 pts) and explain why (as a simple proof) (8 pts).
Answers
==================================================
Proof:
We'll break the proof into two cases which I'll label A and B
Case A: 'a' is evenCase B: 'a' is odd-----------
Case A: 'a' is even
k = some integer
a = 2k = some even integer
a+1 = 2k+1
a(a+1) = 2k(2k+1) = 2(2k^2+k) = 2*(some integer)
Since 2 is a factor of that last expression, this shows that a(a+1) is even when 'a' is even.
-----------
Case B: 'a' is odd
k = some integer
a = 2k+1 = some odd integer
a+1 = (2k+1)+1 = 2k+2
a(a+1) = (2k+1)(2k+2) = 2(2k+1)(k+1) = 2(some integer)
This shows that a(a+1) is even when 'a' is odd.
-----------
Therefore, for any integer 'a', the expression a(a+1) is always even.
Some examples:
a = 3, a+1 = 3+1 = 4, a(a+1) = 3*4 = 12 which is evena = 12, a+1 = 12+1 = 13, a(a+1) = 12*13 = 156 which is even-----------
Here's a slightly different way to interpret why the proof works.
a(a+1) consists of factors 'a' and 'a+1'
If 'a' was even, then a(a+1) is automatically even since 2 is a factor of 'a'.If 'a' was odd, then a+1 is even and we arrive at the same conclusion as before.Either way, we'll have 2 as a factor somewhere in a(a+1).
Room A and B were both cleaned today.- Room A is cleaned every 9 days.- Room B is cleaned every 6 days.What is the fewest number of days that will pass before both rooms are cleaned again on the same day?
Answers
Answer:
18 days
Explanation:
To determine the fewest number of days that will pass before both rooms are cleaned again on the same day, we list the multiple of each of the days.
\(\begin{gathered} 6=6,12,18,24,30,36,42,48\ldots \\ 9=9,18,27,36,45,54,\ldots \end{gathered}\)The next multiple 6 and 9 have in common is 18.
Therefore, after 18 days has passed, the two rooms will be cleaned on the same day.
Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
Answers
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is \(\mu = p\).The standard deviation is \(s = \sqrt{\frac{p(1 - p)}{n}}\)The shape is approximately normal.As long as these two conditions are respected:
\(n \leq 0.05N\)\(np(1 - p) > 10\)The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
\(\mu = p = 0.388\)
The standard error of the distribution is of:
\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184\)
More can be learned about the Central Limit Theorem at https://brainly.com/question/25800303
#SPJ1
PLS HELP! would really appreciate.
Answers
Answer:
Step-by-step explanation:
3^2*5^2= 225
9*25=225
Three to the 2nd power times 5 to the 2nd power.
I'm confused on what to do since I day dream during class, I know it's a bad thing but I have a hard time paying attention
Answers
Answer:17/20 answer a
Step-by-step explanation:
What is the inverse of function f? f(x)=10/9r+11
Answers
\(f(x) = \frac{10}{9}x + 11 \\ \)
So :
\(y = \frac{10}{9}x + 11 \\ \)
Subtract the sides of the equation minus 11
\(y - 11 = \frac{10}{9}x \\ \)
Multiply the sides of the equation by 9
\(9(y - 11) = 10x\)
\(9y - 99 = 10x\)
Divided the sides of the equation by 10
\( \frac{9y - 99}{10} = x \\ \)
So :
\( {f}^{ - 1}(x) = \frac{9x - 99}{10} \\ \)
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
find the area of the surface generated by revolving the given curve about the -axis. =36−2‾‾‾‾‾‾‾√,−4≤≤4
Answers
The surface area is approximately 161.47 square units.
To find the surface area generated by revolving the curve about the x-axis, we can use the formula:
S = 2π∫[a,b] f(x)√(1+[f'(x)]^2) dx
where f(x) is the given curve.
Here, f(x) = 36 - 2√(x^2+1) and we need to revolve it about the x-axis.
To find the limits of integration, we note that the curve is symmetric about the y-axis and therefore we can find the surface area of one half of the curve and multiply it by 2. So, we need to integrate from 0 to 4.
S = 2π∫[0,4] (36 - 2√(x^2+1))√(1+((x(-2x))/((x^2+1)^2))) dx
S = 2π∫[0,4] (36 - 2√(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx
Simplifying the integrand,
S = 2π∫[0,4] (36(x^4+1) - 2(x^2+1))√((x^4+4x^2+1)/(x^4+1)^2) dx
S = 2π∫[0,4] (36x^4-70x^2+34)√((x^4+4x^2+1)/(x^4+1)^2) dx
This integral is difficult to evaluate analytically, but it can be approximated using numerical integration techniques. Using a calculator or software, we find that the surface area is approximately 161.47 square units.
Learn more about surface area here
https://brainly.com/question/26403859
#SPJ11
There are 39 students in a class of which 14 are girls,
What fraction of the students is girls?20 points
Answers
Answer:
it would be 14/39
Step-by-step explanation:
Question 2 of 10
Which situation shows a constant rate of change?
A. The amount raised by a booster club compared with the number
of raffle tickets sold
B. The weight of a kitten compared with its age in months
C. The number of goals scored in a soccer game compared with the
minutes played
D. The height of a paper airplane over time
Answers
The amount raised by a booster club compared with the number of raffle tickets sold shows a constant rate of change;
A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.
To learn more about this; visit: https://brainly.com/question/5795738
#SPJ9
The hypotenuse of right angle triangle is 13cm. If one of the other side of the triangle is 1cm shorter than the hypotenuse, calculate the third side of the triangle
Answers
Greetings from Brasil....
From Pythagoras we have
AB² = AC² + BC²
13² = 12² + X²
X = 5
Answer:
5 cm
Step-by-step explanation:
Pythagoras theorem gives us:
\(hypotenuse^{2} = side^{2} + side^{2}\)
We know the hypotenuse is 13 cm.
We know one side is 12 cm.
\(13^{2} = 12^{2} + side^{2}\)
\(169= 144 + side^{2}\)
Subtracting 144 from both sides:
\(25 = side^{2}\)
Reversing the sides:
\(side^{2}=25\)
\(\sqrt{side^{2}}= \±\sqrt{25}\)
\(side = \±\sqrt{25}\)
\(side = \±5\)
Since a distance can't be negative:
\(side=5\)
The third side is 5 cm.
A rectangular farm has an area of 1.04 square kilometers. The length of the farm is 0.8 kilometer. What is the width, in kilometers, of the farm.
A) 13.0
B) 10.5
C) 1.3
D) 1.05
Answers
Answer:
\(\text{C. }1.3\)
Step-by-step explanation:
The area of a rectangle with width \(w\) and length \(l\) is given by \(A=lw\).
What we're given:
\(A\) of 1.04\(l\) of 0.8Substituting given values, we get:
\(1.04=0.8w,\\w=\frac{1.04}{0.8}=\boxed{\text{C. }1.3}\)
What is the rule for the following pattern by 9 18 12 24 18 36 30?
Answers
The rule for the pattern is to add 6 to each number.
What is the rule for the following pattern by 9 18 12 24 18 36 30?The pattern for this sequence is that it follows a multiplication by two rule. This means that each term in the sequence is twice the previous term. This rule is also known as the exponential rule, because each term is the result of multiplying the previous term by two.This pattern is an example of exponential growth, which is defined as a growth rate that increases by a fixed rate over a period of time. In this case, the fixed rate is a multiple of two, and the growth rate is increasing by a factor of two each time.Exponential growth is important in mathematics and science because it can be used to predict the growth of populations, the spread of disease, the growth of financial investments, and the growth of technology. It is also important in the study of natural phenomena such as climate change and the evolution of life.Exponential growth can be represented as a graph, which will show a curved line with a steep slope. This is because the growth rate is increasing exponentially. As the sequence progresses, the rate of growth will become increasingly steep.The rule for this pattern is that each term is twice the previous term, and this type of pattern is called exponential growth. It is important in mathematics, science, and other fields because it can be used to predict the growth of populations, the spread of disease, the growth of financial investments, and the growth of technology.To learn more about the exponential rule refer to:
https://brainly.com/question/11975096
#SPJ1
solve for w a/h= l • w
Answers
22.a) A fruit vendor bought 1948 oranges on a Thursday and sold 750 of them on the same day.
On Friday, he sold 240 more oranges than on Thursday. On Saturday, he bought 560 more
oranges. Later the day, he sold all the oranges he had at a price of Ksh. 8 each. Calculate the
amount of money the vendor obtained from the sales of Saturday. (5 marks).
Answers
Answer: Ksh 6144
Step-by-step explanation:
On Thursday, a fruit vendor bought 1948 oranges on a Thursday and sold 750. The number of oranges left will be: = 1948 - 750 = 1198
On n Friday, he sold 240 more oranges than on Thursday. This means the number of oranges sold is: = 240 + 750 = 990.
The number for f oranges left will then be: = 1198 - 990 = 208
On Saturday, he bought 560 more
oranges, the total oranges that the vendor has now will be:
= 208 + 560 = 768
Since sold all the oranges he had at a price of Ksh. 8 each, the amount if money made will be:
= Ksh 8 × 768
= Ksh 6144
The vendor made Ksh 6144
Which of the following is a counterexample to the given statement?
The name of every month ends in the letter y.
a. January
b. July
C February
d. December
Answers
The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right option is (c) February.
What is a counterexample?
In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.
Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."
Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.
For more questions on: counterexample
https://brainly.com/question/29197877
#SPJ8
Dave bought 8 boxes of chocolate candy and gave 2 boxes to his little brother. if each box has 17 pieces inside it, how many pieces did dave still have?
Answers
Answer:
17×6=102 because he gave 2 boxes to his brother so he have 6 boxes