Answers
===========================================================
Explanation:
Let x = length of side BC
This is the height of the cylinder. Think of a can that is laying on its side. The radius of this can or cylinder is CD
If point B has x coordinate of 12, and BC is 12 units long, this must mean point C has x coordinate of 12-x. This is plugged into the function to show that CD has a length of exactly [tex]\sqrt{12-x}[/tex]
This is the radius of the cylinder
The volume of a cylinder is [tex]V = \pi*r^2*h[/tex]
Plug in the radius and height mentioned to get this function in terms of x
[tex]V = \pi*\left(\sqrt{12-x} \ \right)^2*x[/tex]
That simplifies to
[tex]V = \pi(12-x)x[/tex]
or
[tex]V = \pi(12x-x^2)[/tex]
Ignore the pi portion for now.
We wish to maximize the function f(x) = 12x-x^2
Use either calculus (specifically derivatives) or a graphing calculator to find that the vertex is at (6, 36)
This means x = 6 leads to the largest f(x) value being 36.
Therefore, the volume V is maxed out when x = 6 and we get a max volume of 36pi cubic units.
Related Questions
What is the value of y in the equation 5x 2y = 20, when x = 0.3? 2.5 2.8 9.25 10.75
Answers
Hope that helps
Answer:
Y = 9.5
(option C)
Suppose you drive an average of 15,000 miles per year, and your car gets 24 miles per gallon. Suppose gasoline costs $3.20 a gallon. a. How much money do you spend each year on gasoline? b. You plan to trade in your car for one that gets x more miles per gallon. Write an expression to represent the new yearly cost of gasoline. c. Write an expression to represent your total savings on gasoline per year. d. Suppose you can save $600 a year with the new car. How many miles per gallon does the new car get?
Answers
Answer:
a) $2000
b) 15000(3.20)/(24+x) = new gasoline cost (replace with variable of your choice)
c) 2000-(15000(3.20)/(24+x)) = money saved (replace with variable)
d) ~34.29 miles (34.28571 miles)
Step-by-step explanation:
a) [15000(3.20)]/24 = 2000
b) use the formula above, but the denominator is 24+x (or variable of your choice) because the amount of mpg is increased
c) take the formula from a, then subtract formula in b from it
d) take formula c, replace the variable (variable = money saved) with 600
What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AC
Answers
The volume of the three-dimensional object (cone) formed is equal to 32π cubic units.
How to determine the volume of the three-dimensional object?In this scenario, the effect of rotating the right triangle around line segment AB would form a three-dimensional object known as a cone, with the following dimensions:
Radius, r = 4 units.Height, h = 6 units.How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Substituting the given parameters into the formula, we have;
V = 1/3 × π × 4² × 6
V = π × 16 × 2
V = 32π cubic units.
Read more on cone here: https://brainly.com/question/1082469
#SPJ1
Complete Question:
In the diagram below, right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AB?
(1) 32π
(2) 48π
(3) 96π
(4) 144π
Evaluate:
[tex]\bf{\sum^6_{n=0\:}(3)^n}[/tex]
Need help A.S.A.P., thank you! :)
Answers
Answer:
1093
Explanation:
Given expression:
[tex]\sf \huge{ \sum _{n=0}^6\left(3\right)^n}[/tex]Summation:
[tex]\sf a_0+\sum _{n=1}^63^n[/tex]Formula:
[tex]\sf \sum\limits_{i=1}^n x_i = x_1 + x_2 + \dots + x_n[/tex]Compute:
[tex]\rightarrow \sf 3^0 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6[/tex]
[tex]\rightarrow \sf 1 + 3 + 9 + 27 + 81 + 243 + 729[/tex]
[tex]\rightarrow \sf 1093[/tex]
Answer:
[tex] \boxed{\rm \: SUM = 1093 }[/tex]
Step-by-step explanation:
Given:
[tex] \huge\rm {{ \sum}^6_{n=0\:} (3)^n}[/tex]
To Find:
Sum of the given finite series
Solution:
We'll use this formula:
[tex] \boxed{\rm SUM = a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)}[/tex]
where,
a = first termr = ratio in between termsLet's find out the ratio R by using this formulae:
[tex] \rm \: r = \cfrac{a_{n + 1} }{a_n}[/tex]
According to the question,
[tex]\rm a_n = 3^n[/tex][tex]\rm a_{n+1}= 3^{n+1}[/tex]Substitute:
[tex] \rm \: r = \cfrac{3 {}^{n + 1} }{3 {}^{n} } [/tex]
Apply law of exponents:[a^m/a^n] = a^m-n
[tex] \rm \: r = {3}^{n + 1 - n} [/tex]
Rearrange it as:
[tex] \rm \: r = 3 {}^{n - n + 1} [/tex]
[tex] \rm \: r = 3 {}^{1} = 3[/tex]
So,the ratio R is 3.
Now let's find out the First term A.
To find, substitute the value of n in 3^n:
[It is given that n = 0][tex] \rm \: a = 3 {}^{0} [/tex]
[x^0 = 1][tex] \rm \: a = 1[/tex]
Hence, first term A is 1.
NOW Substitute the value of the first term A and ratio R onto the formulae of sum:
[tex] \rm \: a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)[/tex]
a = 1r = 3n = 7Simplify.
[tex] \rm SUM = \rm \: 1 \times \cfrac{1 - 3 {}^{7} }{ 1 - 1 \times 3} [/tex]
[tex] \rm \: SUM = \cfrac{ - 2186}{1 - 3} [/tex]
[tex] \rm \: SUM = \cfrac{ \cancel{ - 2186} \: \: {}^{1093} }{ \cancel{ - 2} \: \: ^{1} } [/tex]
[tex] \rm \: SUM = 1093[/tex]
We're done!
Hence, the sum of the given Finite series is 1093.
[tex] \rule{225pt}{2pt}[/tex]
find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive
Answers
The smallest number of terms of the AP that will make the sum of terms positive is 73.
Since we need to know the number for the sum of terms, we find the sum of terms of the AP
Sum of terms of an APThe sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where
n = number of terms, a = first term and d = common differenceSince we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.
The common difference, d = a₂ - a
= -52.5 - (-54)
= -52.5 + 54
= 1.5
Number of terms for the Sum of terms to be positive
Since we require the sum of terms , S to be positive for a given number of terms, n.
So, S ≥ 0
n/2[2a + (n - 1)d] ≥ 0
So, substituting the values of the variables into the equation, we have
n/2[2(-54) + (n - 1) × 1.5] ≥ 0
n/2[-108 + 1.5n - 1.5] ≥ 0
n/2[1.5n - 109.5] ≥ 0
n[1.5n - 109.5] ≥ 0
So, n ≥ 0 or 1.5n - 109.5 ≥ 0
n ≥ 0 or 1.5n ≥ 109.5
n ≥ 0 or n ≥ 109.5/1.5
n ≥ 0 or n ≥ 73
Since n > 0, the minimum value of n is 73.
So, the smallest number of terms of the AP that will make the sum of terms positive is 73.
Learn more about sum of terms of an AP here:
https://brainly.com/question/24579279
#SPJ1
For what values of x and y is quadrilateral ABCD a parallelogram?
Answers
Answer:
x = 6 y = 4Step-by-step explanation:
AB = DC
AD = BC
we use AB and DC
6x - 26 = 8x - 38
-26 + 38 = 8x - 6x
12 = 2x
x = 12 : 2
x = 6
---------------
check
6 * 6 - 26 = 8 * 6 - 38
36 - 26 = 48 - 38
10 = 10
the answer is good
now we use AD and BC
6y + 12 = 3x + 24
-3x + 6y - 12 = 0
3y - 12 = 0
3y = 12
y = 12 : 3
y = 4
----------------------
check
6 * 4 + 12 = 3 * 6 + 24
24 + 12 = 12 + 24
36 = 36
the answer is good
Evaluate the expression 2(8-4)2-10/2
Answers
Step-by-step explanation:
here is your answer
hope it help u
Answer:
16
Step-by-step explanation:
2(8 - 4) 2
first, you'll subtract 4 from 8 to get 4.
Next 2 X 4 X 2
Multiply 2 and 4 by doing that you'll get 8
lastly 8 X 2
Multiply 8 and 2 to get your answer 16.
Pls mark brainiest pls
What is the equation of a line with a slope of -3 and a y-intercept of 4?
A. y= 4x+3
B. y= 4x-3
C. y=-3x-4
D. y=-3x+4
Answers
Answer:
y = -3x+4
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = -3x+4
Step-by-step explanation:
We have,
Slope (m) = -3y-intercept (c) = 4We know that,
y = mx+c
y = -3x+4
Hence, option (D) is correct.
compare the graph of g(x) = x^2 + 6 with the graph of f(x)=x^2
Answers
If the parent graph is transformed to x^2 + 6, this shows that the parent function translated 6 units up the graph to create the graph x^2+6
What are quadratic graphsThese are graph with function of leading degree of 2. The parent function for a quadratic graph is x^2
f(x)= x^2
If the parent graph is transformed to x^2 + 6, this shows that the parent function translated 6 units up the graph to create the graph x^2+6
Learn more on translation here; https://brainly.com/question/12861087
#SPJ1
Find the area of the shade regions. Give your answer as a completely simplify exact value in terms of pie(no approximation). a=
Answers
Answer:
41.87 cm²
Step-by-step explanation:
Area of shaded region :
Area (sector of radius 7 cm) - Area (sector of 3 cm)π × θ/360° (r₁² - r₂²)3.14 x 120/360 (49 - 9)3.14 x 1/3 x 40125.6/341.87 cm²Using a volume of 20000 and an angle of 10 can you find the base and height of a right triangular prism
Answers
Answer:
No, I don't think so....
Step-by-step explanation:
Volume = 1/2 * Base * Height * Length
Height = Base * tan 10
The underlined items you have,but there is still 2 unknowns and only one equation to solve them <===== so I think you need one more piece of the puzzle to solve.... either the base or the length of the prism.
Evaluate. Write your answer as a whole number or as a simplified fraction.
12-².4³ =
Submit
Answers
[tex]12^{-2} \times 4^3\\\\=(4 \times 3)^{-2} \times 4^3\\\\=4^{-2} \times 4^3 \times 3^{-2}\\\\=4^{-2+3} \times 3^{-2}\\\\=4^1 \times \dfrac1{3^2}\\\\=\dfrac 49[/tex]
Combine the radicals 4√7+3√28.
Answers
Answer:
10√7
Step-by-step explanation:
[tex]4 \sqrt{7} + 3 \times 2 \sqrt{7} \\ 4 \sqrt{7} + 6 \sqrt{7} \\ 10 \sqrt{7} [/tex]
Answer:
10√7
Step-by-step explanation:
To combine the radicals, you must have the same number under both radicands. Luckily, you can simplify one of the radicands. This is done by separating the radicand (√28) into its common factors (√4 x √7) and taking the square root of one of the factors (√4 = 2).
4√7 + 3√28 <---- Original expression
4√7 + 3(√4 x √7) <---- Expand √28
4√7 + (3 x 2)√7 <----- Take √4
4√7 + 6√7 <---- Multiply coefficients
10√7 <---- Add both terms
In a cafeteria there is one large 10 seat table
Answers
Which of the following could be the equation of a line perpendicular to the line 2x−5y=7?
Answers
The equation of a line perpendicular to the line 2x − 5y = 7 is y = (-5/2)x + b
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
Two lines are said to be perpendicular if the product of their slopes is equal to -1.
The slope of the line:
2x - 5y = 7
5y = 2x - 7
y = (2/5)x - 7
The slope of the line 2x - 5y = 7 is 2/5. The slope of the line perpendicular is -5/2
Hence:
The equation of a line perpendicular to the line 2x − 5y = 7 is y = (-5/2)x + b
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
The table below shows the different combinations of honey and oats that can be used in making granola
Answers
Answer:
10:4
Step-by-step explanation:
it can be simplified
We can actually deduce here that the honey to oats ratio that doesn't follow the pattern in the table is: 10:4.
What is ratio?Ratio actually refers to the way that two or more numbers are compared in relation to their size to each other. It shows how much of one number is found in another.
From the honey to oats ratio, we can see that the pattern goes thus:
5 - 2 = 3 (this should be the number of cups of oat for the next role of ratio).This is because 10 - 3 = 7
Then 15 - 7 = 8
Therefore, the ratio that doesn't follow the pattern is 10:4.
Learn more about ratio on https://brainly.com/question/2328454
#SPJ6
How can this subtraction problem be solved using friendly numbers?
57−38
Enter your answers in the boxes.
Step 1: Use a friendly number for the subtrahend: 38 +
= 40
Step 2: Adjust the minuend: 57 +
=
Step 3: Subtract: The difference is
.
So, 57−38 =
.
Answers
Answer:
Because the part is missing, this is a subtraction problem. Example: There are 98 hats, 20 of them are pink and the rest are yellow.
Step-by-step explanation:
In a shoe store window, Sandy sees a sign announcing 25% off all sandals in stock. She finds a pair she likes that was originally priced at $45. If Sandy buys this pair of sandals on sale, how much will she pay
Answers
Answer:
$11.12
Step-by-step explanation:
Since the sale is 25% and the shoe was originally priced at $45; you can find the price of the sandal on sale by knowing that 25% means 1/4, so you can just find 1/4 of 45 which is 11.12. 45 * 1/4
Answer:
C. $33.75
Step-by-step explanation:
I took the test
A unit circle has angle θ
in standard position. Point P is on the unit circle at the coordinates ( 2√2, 2√2)
.
What is the angle in degrees?
Answers
[tex]P=(\stackrel{\stackrel{x}{adjacent}}{2\sqrt{2}}~~,~~\stackrel{\stackrel{y}{opposite}}{2\sqrt{2}}) \\\\\\ tan(\theta )=\cfrac{\stackrel{opposite}{2\sqrt{2}}}{\underset{adjacent}{2\sqrt{2}}}\implies \theta =tan^{-1}\left( \cfrac{2\sqrt{2}}{2\sqrt{2}} \right)\implies \theta =tan^{-1}(1)\implies \theta =45^o[/tex]
Make sure your calculator is in Degree mode.
Kevin evaluated the expression below.
75 - 6 (8 - 6) + 3
Step 1: 75 - 6 x 2 + 3
Step 2: 75 - 6 x 5
Step 3: 75 - 30
Step 4: 45
Kevin made an error in solving the expression. What error did Kevin make?
Which step contains the error?
What error did Kevin make?
Explain how you would correct Kevin's error.
Be sure to include the correct answer in your explanation.
Answers
From the solution, Kevin made an error in step 3 by adding 2 and 3 instead of multiplying 6 and 2. The correct solution is 66
Expressions. and functionsGiven the expression solves by Kevin below;
75 - 6 (8 - 6) + 3
Step 2: Simplify the expression in parenthesis
75 - 6(2) + 3
Step 3: Solve the product (PEMDAS)
75 - 12 + 3
75 - 9
Step 4: 66
From the solution, Kevin made an error in step 3 by adding 2 and 3 instead of multiplying 6 and 2
Learn more on expressions here: https://brainly.com/question/2833285
#SPJ1
Solve for the x in the inequality 6(2−6x)≤4−35x 6 ( 2 − 6 x ) ≤ 4 − 35 x .
Answers
Answer:
8 ≤ x
Step-by-step explanation:
6(2 − 6x) ≤ 4 − 35x
Expand bracket;
12 - 36x ≤ 4 − 35x
Add 36x to both sides to get;
12 ≤ 4 + x
Subtract 4 from both sides to get;
8 ≤ x
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to solve the inequality 6(2-6x)≤4-35x.
[tex]\triangle~\fbox{\bf{KEY:}}\star[/tex]
[tex]\star[/tex] We need to get x all by itself.First, we can use the distributive property and distribute 6:
[tex]\star\large\pmb{12-36x\leq4-35x}[/tex]
Now, add 35x to both sides:
[tex]\star\large\pmb{12-x\leq 4}[/tex]
And now, subtract 12 from both sides:
[tex]\star\large\pmb{-x\leq-8}[/tex]
Divide both sides by -1 and watch what happens:
[tex]\star\large\pmb{x\geq 8}[/tex]
Have you noticed that the inequality sign changed from "less than" to "greater than"?
Well, that happened because we divided both sides by a negative number, -1.
Thus, [tex]\star~\large\pmb{x\geq 8}[/tex]
Hope this helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
[tex]\pmb{M^ar_ib^el\:P^eri}[/tex]
a student is asked to solve the equation below and to justify her steps identify what if anything is incorrect in her math or justification j-6=-10
Answers
Answer:
B
Step-by-step explanation:
If a, a²+ 1 and a+6 are in an AS, find the possible values of a.
it's of optional math. If someone know how to solve this. please help me I have been trying this for like half hour
Answers
a, a² + 1 and a + 6 are all in arithmetic progression, in which there is a fixed difference d between consecutive terms. This mean we have
a² + 1 = a + d
a + 6 = a² + 1 + d
Eliminate d and solve for a :
(a² + 1) - (a + 6) = (a + d) - (a² + 1 + d)
a² - a - 5 = -a² + a - 1
2a² - 2a - 4 = 0
a² - a - 2 = 0
(a - 2) (a + 1) = 0
a - 2 = 0 or a + 1 = 0
a = 2 or a = -1
i rlly need helpp due in 2 dayssss
Answers
Answer:
84 R4
Step-by-step explanation:
Answer:
84 R4
Step-by-step explanation:
[tex]9\sqrt{760}[/tex]
multiply 9 by each answer choice then pick the one that makes sense
9×84= 756 9×83=747 9×85=765
756+4= 750 747+3= 750
I start a walk at 2.47pm. The walk takes 85 minutes. What time does the walk finish?
Answers
Answer:
4:12pm
Step-by-step explanation:
85 minutes = 1 hour and 25 minutes
2:47pm + 1 hour 25 minutes = 3:72 pm
72 minutes = 1 hour 12 minutes so add another 1 hour to 3 and the balance is 12 minutes so walk ends at 4:12pm
Another way to look at it is as follows:
After 13 minutes, the time is 2:47 + 0:13 = 3pm
Remaining time left is 85-13 = 72 minutes = 1 hour: 12 minutes. Add that to 3pm and you get 4:12pm
Complete the steps to identify all potential rational roots of f(x) = 3x2 – x – 4.
Answers
De vergelijking moet je gelijk zetten aan 0. Vervolgens bereken je discriminant.
Beide x zijn de snijpunten met de x-as.
-4 is de snijpunt met de y-as
Iam sorry for this language.
its dutch, you can translate it to english
Which term describes the set of all possible output values for a function
Answers
Answer:
range
Step-by-step explanation:
,domain describes the input values and range describes the output
The spin and dine restaurants ice cream for dessert Chloe actually won a bet and gets to spin two spinners disliked one random flavor of ice cream and one random topping. A, how many different possible combinations can she spin. B what is the probability of spinning Chloe's preference vanilla ice cream with chocolate a rainbow sprinkles,
Answers
The probability of spinning vanilla ice cream with chocolate a rainbow sprinkles is 1/12
The missing part of the questionFlavor of ice cream: Vanilla, Strawberry, Chocolate
Topping: Rainbow sprinkles, Caramel sauce, Nuts, Cherries
The number of different combinationsUsing the dataset above, we have:
Ice cream = 3
Topping = 4
The number of different combinations is calculated as:
Combination = ice cream * Topping
Evaluate
Combination = 3 * 4
Combination = 12
Hence, the number of different combinations is 12
The probability of spinning vanilla ice cream with chocolate a rainbow sprinklesThe vanilla ice cream with chocolate a rainbow sprinkles is just one of the 12 combinations.
So, the probability is:
P = 1/12
Hence, the probability of spinning vanilla ice cream with chocolate a rainbow sprinkles is 1/12
Read more about probability at:
https://brainly.com/question/27116549
#SPJ1
Evaluate the following limit:
[tex]\displaystyle \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}}[/tex]
Answers
If we evaluate the function at infinity, we can immediately see that:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle L = \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}} = \frac{\infty}{\infty}} \end{gathered}$}[/tex]
Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.
We can solve this limit in two ways.
Way 1:By comparison of infinities:
We first expand the binomial squared, so we get
[tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{x^4 - x^2 + 4}{x^3 - 5}} = \infty \end{gathered}$}[/tex]
Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.
Way 2Dividing numerator and denominator by the term of highest degree:
[tex]\large\displaystyle\text{$\begin{gathered}\sf L = \lim_{x \to \infty}\frac{x^{4}-x^{2} +4 }{x^{3}-5 } \end{gathered}$}\\[/tex]
[tex]\ \ = \lim_{x \to \infty\frac{\frac{x^{4} }{x^{4} }-\frac{x^{2} }{x^{4}}+\frac{4}{x^{4} } }{\frac{x^{3} }{x^{4}}-\frac{5}{x^{4}} } }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=\lim_{x \to \infty}\frac{1-\frac{1}{x^{2} } +\frac{4}{x^{4} } }{\frac{1}{x}-\frac{5}{x^{4} } } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{0}=\infty } \end{gathered}$}[/tex]
Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.
Which choices are equivalent to the exponential expression below? Check all
that apply.
□A.0.0
OB. 25
O C. 125
OD. 195
E. 3.
53
33
5/3
OF.
ი|ო
Answers
The expression equivalent to this sentence expression is (5/3) . (5/3) . (5/3). Letter A
.
We know that a power is a multiplication of equal factors - according to the exponent.
A power is represented by aⁿ, where: 'a' indicates base and 'n' indicates exponent.
To represent this expression in multiplication, let's just:
repeat the expression three times (according to its exponent). Resolution[tex] \large \sf ( \dfrac{5}{3} ) {}^{3} [/tex]
[tex] \blue { \boxed{ \large \sf \dfrac{5}{3} \times \dfrac{5}{3} \times \dfrac{5}{3} }} \\ [/tex]
So, the answer correct is (5/3) . (5/3) . (5/3).