Answers
Answer:
[tex]{ \rm{V(x) = 4x {(10 - x)}^{2} }} \\ \\ { \rm{ \frac{dv}{dx} = 4 {(10 - x)}^{2} + 4x( - 2(10 - x))}} \\ \\ { \rm{ \frac{dv}{dx} = 4 {(10 - x)}^{2} + 4x( - 20 - 2x) }} \\ \\ { \rm{ \frac{dv}{dx} = 4(100 - 20x + {x}^{2} ) + ( - 80x - 8 {x}^{2} ) }} \\ \\ { \rm{ \frac{dv}{dx} = - 4 {x}^{2} - 160x + 400}}[/tex]
• But at maximum volume, dv/dx is 20 square inches.
[tex]{ \rm{ - 4 {x}^{2} - 160x + 400 =2 0}} \\ \\ { \rm{ {x}^{2} + 40x - 95 = 0}}[/tex]
• Using the quadratic formula:
[tex]{ \underline{ \rm{ \: \: x \approx3\: \: squares \: \: }}}[/tex]
• Therefore,
For maximum volume,
[tex]{ \rm{V(x) = 4x(10 - x) {}^{2} }} \\ \\ { \rm{V(3) = (4 \times 3)(10 - 3) {}^{2} }} \\ \\ { \rm{V(3) = 12 \times 49}} \\ \\ { \boxed{ \rm{V = 588 \: {in}^{3} }}}[/tex]
Related Questions
Evaluate.
−|a+b|/2−c when a=1 7/8 , b=−1 , and c=−4
Enter your answer as a simplified fraction in the box.
Answers
a= 1 7/8 {Given}
b=-1
c=-4
Putting values;[tex] \frac{ - | 1\frac{7}{8} + ( - 1)| }{2} - ( - 4)[/tex]Convert the mixed number to an improper fraction[tex] \frac{ - | \frac{15}{8} + ( - 1) | }{2} - ( - 4)[/tex]When there is a + in front of an expression in parentheses, the expression remains the same&When there is a - in front of an expression in parentheses, change the sign of each term in the expression[tex] \frac{ - | \frac{15}{8} - 1| }{2} + 4[/tex]Calculate the difference[tex] \frac{ - | \frac{7}{8} | }{2} + 4[/tex]The absolute value of any expression is always positive or zero[tex] \frac{ - \frac{7}{8} }{2} + 4[/tex]
Use [tex] \frac{ - a }{b} = \frac{a}{ - b} = - \frac{a}{b} [/tex] to rewrite the fraction[tex] - \frac{ \frac{7}{8} }{2} + 4[/tex]Simplify the complex fraction[tex] - \frac{7}{16} + 4[/tex]Calculate the sum[tex] \frac{57}{16} [/tex]Solved ✔︎An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of -|a + b| / 2 - c when a = [tex]1\frac{7}{8}[/tex], b = -1, and c = -4 in a mixed fraction is [tex]3\frac{9}{16}[/tex].
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
- |a + b| / 2 - c
The value of -|a + b| / 2 - c
when,
a = [tex]1\frac{7}{8}[/tex] = 15/8
b = -1
c = -4
= [- |a + b| / 2 ]- c
= [ - | 15/8 + (-1) | / 2] - (-4)
= [ - | 15/8 - 1 | / 2 ] + 4
= [ - | (15-8)/8 | / 2 ] + 4
= [ - | 7/8 | / 2 ] + 4
= { -7/(8 x 2) ] + 4
= -7/16 + 4
= (-7 + 16x4) / 16
= (-7 + 64) / 16
= 57 / 16
We have to write in a mixed fraction.
= [tex]3\frac{9}{16}[/tex]
Thus,
The value of -|a + b| / 2 - c when a = [tex]1\frac{7}{8}[/tex], b = -1, and c = -4 in a mixed fraction is [tex]3\frac{9}{16}[/tex].
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2. Carlie graphed a line with a negative slope.
What must be true about the graph?
a. The graph decreases from left to right.
b. The graph increases from left to right.
c. The graph must cross (0,0).
d. The graph must be contained in Quadrants
III and IV.
Answers
Answer:
A. The graph decreases from left to right
Evaluate. 1 1/2+3/4÷(−1/3)−2/3 Enter your answer as a mixed number in simplest form
Answers
Answer:
-1 5/12
Step-by-step explanation:
1 1/2+3/4÷(−1/3)−2/3
3/2-2/3+3/4*3/-1
9-4/6-9/4
5/6-9/4
20-54/24
-34/24
-17/12
-1 5/12
The price of a gallon of gas went from $2.34 to $2.99. What is the percent increase?
Answers
Answer:
64
Step-by-step explanation:
99-34=64
the two stays the same
Need helpppppppppppppppppp
Answers
Answer:
Add all the numbers in the data set together, then divide by the number of items in the data set. The result is the median value.
So:
70+61+50+48+45+43+40+39+35+32=x
x÷10=?
A jacket is on sale for 15% off. If
the original price is $165, how much
would you save by buying it on sale?
A. $ 15.00
B. $ 24.75
C. $140.25
D. $189.75
E. $247.50
Answers
Answer:
$24.75
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 165 × 15/100
Discount = 165 x 0.15
You save = $24.75
Final Price = Original Price - Discount
Final Price = 165 - 24.75
Final Price = $140.25
A worker makes 220 for 8 hours of work. At this rate, how much does the worker make per hour
Answers
Answer:
22.5
Step-by-step explanation:
8hrs=220
1hr=220÷8
1hr=22.5
According to the question,
The worker makes,
[tex]8 \ hours = 220[/tex]then,
Per hour, worker will make,
→ [tex]1 \ hour = \frac{220}{8}[/tex]
By applying division, we get
→ [tex]1 \ hour = 22.5[/tex]
Thus the solution above is appropriate.
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Point E is 5 units to the right of point A, point D is 4 units down and 1 unit to the right of point E, point C is 2 units down and 1 unit to the left of point D, point B is 5 units to the left of point C, and point A is 6 units above point B. A point has been translated left and down. Based on the graph, which could be true? Check all that apply. A is the image of C. A is the image of D. B is the image of D. B is the image of E C is the image of A. C is the image of D. D is the image of E.
Answers
Answer:
There are three answers
Step-by-step explanation:
B is the image of D
B is the image of E
C is the image of D
Answer:
B is the image of D
B is the image of E
C is the image of D
Step-by-step explanation:
100x+300y=1.200
(2/3x+10)/100=(y+20)/300
Answers
Answer:
x= -4.284 and y= 1.432
Step-by-step explanation:
1.- Write two words that mean addition
Answers
Answer:
the two words that means addition are
plus, sum and calculation..............
Place the following numbers in order from least to greatest -4.5, -3 5/6, square root of 16, -8/3, -2 pie
Answers
Answer: -2 pi, -4.5, -3 5/6, -8/3, square root of 16
Step-by-step explanation:
The number which would be the smallest would be the largest negative number sense its farthest from 0 and the greatest would by the biggest positive number in this case being square root of 16.
square root of 16 is 4 sense (4 times 4 is 16)
-8/3= -2.67
-2 pi= -6.28
-3 5/6= -3.834
-12 is an element of what sets of numbers?
Answers
Answer:
real numbers, integers, and rational numbers
Step-by-step explanation:
Write the scale without units: 1 in:9 yd
Answers
Answer:
1:9
Step-by-step explanation:
that's how you write scale
10) A community college student interviews everyone in a particular statistics class to
determine the percentage of students that own a car.
A) convenience B) random
C) cluster
D) systematic
E) stratified
Answers
ANSWER QUICK PLEASE!
Which of the following is NOT an expression?
A. 3x + 4 = 7
B. 6 - i/5
C. x + 8
D. 2x - 3
Answers
Answer:
A. 3x + 4 = 7
Step-by-step explanation:
Expressions do not have an equal sign.
Hopefully this helps!
Brainliest please?
Which of the functions below could have created this graph?
A. F(x) = x2 + x2+x+1
B. F(x)= x2 +5
F*+6
c. - *-+*
(-)y-
D
Answers
Answer:
only D is negative on the leading term
Hi hope you’re have a great day can I get some help please
Answers
Answer:
the function is odd
Step-by-step explanation:
functions that are symmetric with respect to the y axis are even functions
functions that are symmetric with respect to the origin (the 0,0 point) are odd functions (which means that if you flipped it 180 degrees it will still look the same)
have a nice day!
A park has a grassy section that covers 2 1/3 acres. Denny mowed half of the grassy section. What is the number of acres that Danny mowed?
Answers
So hi I hate school okay bye
Answer:
7/6 (1 1/6)acres
Step-by-step explanation:
The grassy section covers 2 1/3 acres overall. To find half of that, we divide it by two because half of an amount or object is one of the two equal parts that together make up the whole amount or object.
To turn a mixed number (in this case, 2 1/3) into an improper fraction, multiply the whole number with the denominator of the proper fraction.
2*3 = 6Add the numerator to this product to obtain the numerator of the improper fraction.
6 + 1 = 7
so the improper fraction is 7/3
then we multiply that fraction by 1/2 because we are trying to find half of the overall section
7/3 * 1/2 = 7/6
(2) Below is the graph of a function, y = f (x).
(a) Draw a secant line on the graph above from x = 0 to x = 4. (copy the graph if you are writing your answers on a separate paper)
(b) What is the average rate of change of f (x) from x = 0 to x = 4? Show how you get your answer.
Answers
Answer:
Step-by-step explanation:
a. To draw a secant line, just draw a straight line connecting the 2 points at x = 0 and x = 4.
b. The average rate of change of this line is going to be the change in y / the change in x. The equation will be (f(4) - f(0))/(4 - 0) = (0 - 3) / 4 = -3/4.
A line is 4.5” long is divided into 6 equal parts. How long is each part?
Answers
Answer:
0.75"
Step-by-step explanation:
4.5÷6
please mark me brainliest
thankyousm!! please help me
Answers
Step by Step What do I do
Answers
Answer:
7:46
Step-by-step explanation:
The clock says 9:20. I am assuming that the question is related to the clock on the left. It asks for the time an hour and 34 minutes ago. One hour from 9:20 is 8:20. Now we work with the minutes. 8:20 minus 34 minutes is 7:46.
Answer:
7:46
Step-by-step explanation:
Estimate 53.8-27.6. circle the compatible numbers to substitute
54-28 53-28 55-27 55-25
Answers
Answer:
54 - 28
Hope this helps :)
The compatible numbers to substitute is 54 - 28
How to determine the compatible numbers to substituteFrom the question, we have the following parameters that can be used in our computation:
Estimate 53.8 - 27.6
This means that we approximate the numbers in the expression
using the above as a guide, we have the following:
53.8 = 54
27.6 = 28
Hence, the compatible numbers to substitute is 54 - 28
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Use graphing technology to find the range of the function
f(x) = –x^2 – 10x – 27
Answers
five times a number is 120, what is the number
Answers
Explanation: 24x5 = 120
Answer:
Step-by-step explanation:
24
Consider the graph of f(x)=13x−2. How do the graphs of 2f(x), f(x+2), and f(x)+2 compare to the graph of f(x)? Drag tiles to the empty boxes to correctly complete each sentence. The graph of 2f(x) Response area the graph of f(x). The graph of f(x+2) Response area the graph of f(x). The graph of f(x)+2 the graph of f(x).
Answers
Using translation concepts, it is found that:
2f(x) is a vertical stretch by a factor of 2 of f(x).f(x + 2) is a shift left of 2 units of f(x).f(x) + 2 is a shift up of 2 units of f(x).What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
As for this problem, we have that:
For 2f(x), f(x) is multiplied by 2, hence it is a vertical stretch by a factor of 2 of f(x).For f(x + 2), x -> x + 2, hence f(x + 2) is a shift left of 2 units of f(x).For f(x) + 2, f(x) -> f(x) + 2, hence it is a shift up of 2 units of f(x).More can be learned about translation concepts at https://brainly.com/question/4521517
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Dịch các câu sau đây thành các biểu thức logic bằng cách sử dụng các vị từ, lượng từ và các liên từ: a) Không có ai là hoàn hảo h) Không phải mọi ngươi đều hoàn hảo c) Tất cả các bạn của bạn là hoàn hảo. d) Một trong sỐ các bạn của bạn là hoàn hảo. e) Mọi người đều là bạn của bạn và đều hoàn hảo. ) Không phải mọi người đều là bạn của bạn hoặc có ai đó không hoàn hảo.
Answers
Answer:
that's alot but no english speak english it is long
[tex]f(x)=x^{2} -3x-10[/tex]
Answers
Answer:
Given
f(x) = 3x + 2
g(x) = (x + 3) / (2x - 10)
#1
g · f(x) =
g(f(x)) =
(3x + 2 + 3)/ (2(3x + 2) - 10) =
(3x + 5) / (6x - 6)
#2
f · g(x) =
f(g(x)) =
3[(3x + 2) / (2x - 10)] + 2 =
(9x + 6) / (2x - 10) + 2 =
(9x + 6 + 4x - 20)/ (2x - 10) =
(13x - 14) / (2x - 10)
Step-by-step explanation:
Ethan is cutting a 36-inch sub into slices that are
2- inches thick. How many slices will he cut?
Answers
Answer:
He can cut 18 slices!
Step-by-step explanation:
Answer:
18
Step-by-step
ive learned this before
4. k(x) × g(x) × f(x)
Answers
[tex]k(x) \times f(x)[/tex]
[tex](2x + 5) \times (x - 1)[/tex]
[tex]2 x(x - 1) + 5(x - 1)[/tex]
[tex] ({2 x }^{2} - 2x) + (5x - 5)[/tex]
[tex] {2x}^{2} - 3x - 5[/tex]
________________________________
[tex]k(x) \times g(x) \times f(x)[/tex]
[tex]g(x) \times (k(x) \times f(x))[/tex]
[tex] ({6x }^{2} - 4x + {3x}^{4} ) \times ( {2x}^{2} - 3x - 5)[/tex]
[tex] {6x}^{2} ( {2x}^{2} - 3x - 5) - 4x ( {2x}^{2} - 3x - 5) + {3x}^{4} ( {2x}^{2} - 3x - 5)[/tex]
[tex]12 {x}^{4} - 18 {x}^{3} - 30 {x}^{2} - {8x}^{3} - 12 {x}^{2} - 20x + {6x}^{6} - 9x {}^{5} - {15x}^{4} [/tex]