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
5th grade math. correct answer will be marked brainliest
Answers
Answer:
Step-by-step explanation:
The answer is 4/8 or 1/2 pie
Answer:
The answer is 4/8 or 1/2 pie
Have an amazing day :)
A triangle with angles of 74° and 16° is?
A. equilateral
B. obtuse
C. isosceles
D. right
E. impossible to draw
Answers
Which is the correct mapping statement for a rotation 180∘ about the origin?
(x,y)↦(y,x)
(x,y)↦(−x,−y)
(x,y)↦(−y,x)
(x,y)↦(y,−x)
Answers
Answer:
B
Step-by-step explanation:
it moved twice to the left hand side because it's 180 anticlockwiseAnswer:(x,y)↦(−x,−y)
Step-by-step explanation:
Help me with this please
Answers
Answer:
6
Step-by-step explanation:
The question indicates that the triangles are similar. The sides of FGH are 12, 15, and 20. The measured side of MNP is 10, which is 1/2 of 20. So since NM is the shortest side, it corresponds to the shortest side of FGH, which is 12. 1/2 of 12 is 6.
Please let me know if you have questions.
triangle DEF is formed by connecting the midpoints of the sides triangle ABC. The lengths of the sides of DEF are shown. what is the length of AB
Answers
The requried length of the AB is given as AB = 16.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Since triangle DEF is formed by connecting the midpoints of the sides of triangle ABC, the length of the sides of triangle DEF is half the length of the corresponding sides of triangle ABC. That is:
DE = 1/2 AB
EF = 1/2 BC
FD = 1/2 AC
We can use the information about the lengths of the sides of triangle DEF to find the length of AB.
Since DE = 8 and EF = 10, we can use the triangle inequality to find FD:
FD + DE > EF
FD + 8 > 10
FD > 2
Similarly, since EF = 10 and FD = 12, we can use the triangle inequality to find DE:
DE + EF > FD
DE + 10 > 12
DE > 2
Finally, since DE = 8 and FD = 12, we can use the triangle inequality to find EF:
EF + FD > DE
EF + 12 > 8
EF > -4
Since all sides of a triangle must have positive lengths, EF cannot be negative. Therefore, the inequalities we have found imply that:
2 < FD < 12
2 < DE < 8
0 < EF < 10
Since DE = 1/2 AB and EF = 1/2 BC, we can write:
AB = 2DE = 2(8) = 16
BC = 2EF = 2(10) = 20
Therefore, the length of AB is 16.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ7
Three friends all have ages that are consecutive integers. The sum of their
ages is 57. What is the age of the oldest friend?
Answers
Answer:
Friend C would be 20 years old
Step-by-step explanation:
Consecutive integers are integers that follow each other
In this case, we have three friends (let's call them A, B, and C) who's total age sum is 57:
A + B + C = 57
If Friend B is one year older than Friend A and Friend C is two years older than Friend A (or one year older than Friend B), then we write and solve for Friend A:
A + (A + 1) + (A + 2) = 57
3A + 3 = 57
3A = 54
A = 18
So if Friend A is 18 years old, then Friend B is 19 years old, and Friend C is 20 years old, making Friend C the oldest.
Answer:
20 years old
Step-by-step explanation:
3x + 3 = 57
3x = 54
x = 18
X + 2 = 18 + 2
Answer = 20 years old
A submarine travels 5.5 km due East from its base and then turns and travels due North for 3.4 km.
How far away is the submarine from its base?
Give your answer rounded to 1 DP.
Answers
Answer:
6.5km
Step-by-step explanation:
If you make a diagram, you'll see the submarine forms a right angle triangle with the base, where the hypotenuse is the length from the submarine to its base, and 5.5 and 3.4 are the side lengths. To find the hypotenuse, use the formula a^2+b^2=c^2.
5.5^2+3.4^=c^2
41.81=c^2
6.466=c
Round it to one decimal point and you get 6.5km.
Answer:
6.5km
Step-by-step explanation:
I think is this I am not really sure
If map=1, Prove that
1+
It man
Itntpt 1tpam
+
Answers
Answer:
hi I didn't understand the question
can you please help me to understand.
I will try to give my best
What is the value of y in the parallelogram below
Answers
If the length of a rectangle is (x + 7) inches and the width is (3x+2) inches. Which expression represents the rectangle's area? HINT: Area = width * length
Answers
Answer:
The answer is no 1:
[tex]3x ^{2} + 23x + 14[/tex]
A concession stand charges $5.75 for 5 muffins. What is the cost per muffin?
A
$1.00
B
$1.15
С
$28.75
D
$10.75
Answers
Answer:
B- $1.15
Step-by-step explanation:
5.75 divided by 5 equals 1.15
10 POINTS!!!!Which polynomial represents the sum below?
Answers
Answer:
B
Step-by-step explanation:
if you combine like terms, you'll get B
Kevin has 6 pounds of ham to make 12 sandwiches. He puts the same amount of ham on each sandwich. Which statement about Kevin’s sandwiches is true?
Answers
Answer:
what are the options? But assuming he put the same amount in each sandwich he would put half a pound in each sandwich
Mr.Rosenthal wants to make gumbo a type of soup he buys some shrimp for $7.95 an onion for 0.26 and a bunch of celery for $1.03 how much dose he spend on the ingredients
Answers
Answer:
$9.24
Step-by-step explanation:
7.95+1.03+.26 = 9.24
explainatiom
Sevilya bought a new computer. She had to pay 8% in sales tax. The cost of the computer is $1,000. How much did she pay in total? Show all work
Answers
Answer:
1080
Step-by-step explanation:
1000*8%=80
1000+80=1080
pls help!!
find the area of then triangle
Answers
Answer:
B, 11.7
Step-by-step explanation:
2.9x8.1/2 11.745, round to the nearest tenth, 11.7
okay this makes 0 sense... Show how you can solve the equation 3x=9 by multiplying each side by the reciprocal of 3... need to be the full steps pls
Answers
Answer:
x=3
Step-by-step explanation:
3x=9
Divide both sides by 3 and you get 1x=3 or basically x=3.
So the answer would be x=3.
HELPPP WIILLLL MAKR BRAINLIEST IF RIGHTTTT
Answers
Answer:
I think the answer is letter B
Answer:
4π yd²
Step-by-step explanation:
Area of a circle = πr²
πr²=4π
r²=4
r=2
Circumference of a circle = 2πr = 2π(2) =4π
Carmen's father is 28 years older than her and 3 years ago he was 5 times her age. What are their ages?
Answers
28-3=25
so 25/5=5
she is 5 year old
By the question,
x = y+28 equation i
Three years ago;
x-3 = 5 ( y- 3 ) equation ii
y + 28 - 3 = 5y - 15 ( substitute x in eq’n 2 )
y + 25 = 5y - 15
40 = 4y
y= 10
Thus daughter is 10 years old.
Father is 10 + 28 = 38 years.
Help if you can :)
Also, show work
thxx <3
Answers
Answer:
3. The answer is B: 315 dm³
4. It is A: 47,786 2/3 ft³
Step-by-step explanation:
3.I multiplied Length x Width x Height and then divided by 3
4. I did 64 to the second power and then multiplied it by 35/3
Find the 12th term of the geometric sequence 2, 10, 50, ...
Answers
Answer:
488281250 is the Twelfth
Step-by-step explanation:
The geometric sequence is multiplying by 5
2, 10, 50,
2 times 5 is 10 (First)
10 times 5 is 50 (Second)
50 times 5 is 250 (Third)
250 times 5 is 1250 (Fourth)
1250 times 5 is 6250 (Fifth)
6250 times 5 is 31250 (Sixth)
31250 times 5 is 156250 (Seventh)
156250 times 5 is 781250 (Eighth)
781250 times 5 is 3906250 (Ninth)
3906250 times 5 is 19531250 (Tenth)
19531250 times 5 is 97656250 (Eleventh)
97656250 times 5 is 488281250 (Twelfth)
Answer:
−97656250
Step-by-step explanation:
Thank me later
Mr. Esposito is 5 foot 11 inches tall. Mrs. Humbert is 63 inches tall. Who is taller and by how much?
Answers
Answer:
Mr. Esposito is taller By 8 inches
Step-by-step explanation:
5 feet and 11 inches is equal to 71 inches. And 71 inches is greater than 63 inches. Therefore, Mr. Esposito is taller.
(71-63=8)
DON'T FORGET TO DOUBLE-CHECK!
Answer:
Mr. Esposito is taller by 8 inches
Step-by-step explanation:
Mr. Esposito
12x5 = 60 + 11 = 71
Mrs. Humbert
63 inches = 5 foot and 3 inches
71 - 63 = 8
32) If somebody has a monthly income of $2,543, what should their monthly auto expense be?
Answers
Answer:
$211.916
Step-by-step explanation:
help please i need it asap
Answers
Answer:
x = 5
Step-by-step explanation:
[tex]\frac{4.5}{7.5}[/tex] = [tex]\frac{3}{x}[/tex]
cross multiply
4.5x = 7.5(3)
4.5x = 22.5
divide
x = 5
if the area is 48 square meters what is the length of side R in meter
Answers
Answer:
12 m
Step-by-step explanation:
the area of a rectangle is length x width
we know the width, so we can proceed like this:
Lenght = A/width
Lenght = 48/4 = 12 m
ZABD and ZDBC are supplementary angles,
What is the measure of x?
X = [?]°
7D
110%
AK
B
>C
Angles are not drawn to scale.
Finter
Answers
Answer:
x=70°
Step-by-step explanation:
x+110=180 linear pair
x=180-110=70
find the value of x in the triangle shown below 9 and 8 and x
Answers
Answer:
x=5.8
Step-by-step explanation:
I kinda guessed on this due to the fact you didn't provide a photo. I used the pythagorean equation to solve this.
Start by identifying you a, b, and c sides.
Please help immediately! also don't use a link to a website
Answers
Answer:
Step-by-step explanation:
the radius is half the diameter:
7/2 : 2 = 7/2 x 1/2 = 7/4 cm
the circumference is:
diameter x π = 7/2π cm
the approximate circumference is
7/2 x 3,14 = 10,99 cm
Help please 20 points for anyone
Answers
Answer:
The answer is B!
Step-by-step explanation:
I hope this helps! Have a great rest of your day!
Will give brainliest!! PLEASE HELP NEED THIS NOW DUE TODAYYY!!!
My math students challenged me, their math teacher, to play a dice game with them. They will give me 10 cents for each odd sum I roll with two dice, but I have to give them 10 cents for each even sum they roll with the two dice. I do not think this game is fair. I think I am going to get cheated! I noticed that I cannot roll one of my odd numbers: 1!
Should I play this game with the students? Use your mathematical thinking to convince me whether or not this is a fair game.
Answers
Answer:
No
Step-by-step explanation:
You can if you want, but there is a total of 6 on the dice. And there are 3 odds. Each odd you role you gain 10 cents, but each time a student roles a even they also get 10 cents. So you will get paid and in a game of chance and gambling. You won't gain anything if ALL of the students are together and going against you. Its like 1 vs 25 and you would have to pay a lot of students at one time to play this game. So logically no, because you won't gain money. But also you could if you always get odds, but again. That's a 3/6 or 1/2 each time you role to get a odd number.
Hope that helped, or even made sense xD