Answer:
Step-by-step explanation:
Let x = base side length
y = side height
volume V = x²y
y = V/x²
surface area
A = x² + 4xy
A = x² + 4x(V/x²)
A = x² + 4V/x
Solving for volume
V = (A - x²)(x/4)
V = ¼(Ax - x³)
a maximum will occur when the derivative equals zero
V' = ¼(A - 3x²)
0 = ¼(A - 3x²)
0 = A - 3x²
3x² = A
3x² = 1100
x² = (1100 / 3)
x = √(1100/3)
V = (A - x²)(x/4)
V = (1100 - √(1100/3))²(√(1100/3)/4)
V = 3,510.56606...
V = 3510.6 cm³
The box height will be half of the base side length.
y = ½√(1100/3)
Write $1.50 to $12.00 as a ratio in fraction form in lowest terms.
Answer:
1/8
Step-by-step explanation:
June, Gavyn and Alex share some sweets in the ratio 5:3:2. June gets 42 more sweets than Alex. How many sweets does Gavyn get?
Answer:
42 sweets
Step-by-step explanation:
The ratios are 5 : 3 : 2 = 5x : 3x : 2x (x is a multiplier )
June gets 42 more sweets than Alex , then
5x = 2x + 42 ( subtract 2x from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Gavyn = 3x = 3 × 14 = 42 sweets
Answer:
42 sweets.
Step-by-step explanation:
First work out the number of parts:
5 + 3 + 2 = 10.
So June gets 5/10 = 1/2 of the sweets.
Alex gets 2/10 = 1/5.
Gavyn gets 3/10.
If the total number of sweets was x, then:
1/2 x - 1/5 x = 42
5/10x - 2/10 x = 42
3/10 x = 42
x = 42*10/3 = 140.
So Gavyn has 3/10 * 140 = 42.
(b) Notice that x=0.5 meter when θ = 45o. By approximately how many radians should you increase θ if you want the x coordinate of the point R to decrease to x = 0.45 meters? Use the tangent line approximation.
The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].
Based on the statement we construct the geometric diagram, by definition of tangent we have expressions for the initial and final angles ([tex]\theta_{1}[/tex], [tex]\theta_{2}[/tex]), in radians, of the figure:
Initial triangle
[tex]\tan \theta_{1} = \frac{y_{1}}{x_{1}}[/tex] (1)
Final triangle
[tex]\tan \theta_{2} = \frac{y_{2}}{x_{2}}[/tex] (2)
By using (2), the equivalence [tex]\theta_{2} = \theta_{1}+\Delta \theta[/tex] and trigonometric identities we have the following expression:
[tex]\frac{y_{2}}{x_{2}} = \frac{\tan \theta_{1}+\tan \theta_{2}}{1-\tan \theta_{1}\cdot \tan \theta_{2}}[/tex] (3)
By (1), we simplify the expression:
[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}} + \tan \Delta \theta}{1-\frac{y_{1}}{x_{1}}\cdot \tan \Delta \theta}[/tex] (3b)
If [tex]0 \le \Delta \theta \le \frac{\pi}{6}[/tex], then we can use the following approximation:
[tex]\tan \Delta\theta \approx \Delta \theta[/tex] (4)
Then, we reduce (3b) into an entirely algebraic expression:
[tex]\frac{y_{2}}{x_{2}} = \frac{\frac{y_{1}}{x_{1}}+\Delta \theta }{1-\frac{y_{1}}{x_{1}}\cdot \Delta \theta }[/tex] (3c)
Where [tex]y_{2} = \sqrt{r^{2}-x_{2}^{2}}[/tex].
Now we clear [tex]\Delta \theta[/tex] within the formula:
[tex]\Delta \theta = \frac{\frac{y_{2}}{x_{2}}-\frac{y_{1}}{x_{1}}}{\frac{y_{1}}{x_{1}}\cdot \left(1+\frac{y_{2}}{x_{2}} \right) }[/tex] (5)
If we know that [tex]x_{1} = y_{1} = 0.5[/tex], [tex]r = 0.707[/tex] and [tex]x_{2} = 0.45[/tex], then we estimate the angle change:
[tex]y_{2} = \sqrt{0.707^{2}-0.45^{2}}[/tex]
[tex]y_{2} \approx 0.545[/tex]
[tex]\Delta \theta = \frac{\frac{0.545}{0.45}-1 }{1\cdot \left(1+\frac{0.545}{0.45} \right)}[/tex]
[tex]\Delta \theta = 0.095[/tex]
As [tex]\Delta \theta < \frac{\pi}{6}[/tex], then the result seems to be reasonable. The angle is increased in approximately 0.095 radians (5.443°) for [tex]x = 0.45\,m[/tex].
We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845
Fdgbfrgrth Rheu Hyueheuhuhuhuheeuhuhuhe
solve the equation and justify each step using the algebraic properties of equality
Answer:
-5
Step-by-step explanation:
3x=-13-2
3x=-15
x=-5
3x-1 over 5 = x+1 over 3
I need asap
Answer:
(3x-1)/5= (x+1)/3
3(3x-1)=5(x+1)
then solve which the final answer will give you x=8
Craig has a job waiting tables where he earns $3.45 per hour plus tips. Craig earned $73.68 in tips during his shift yesterday.
If x represents the number of hours Craig worked yesterday, which of the following equations can be used to find the amount of money Craig earned yesterday?
A. y = 3.45x - 73.68
B. y = 73.68x + 3.45
C. y = 3.45x + 73.68
D. y = 73.68x - 3.45
Angle ABC And BCA a are complementary angle ABC is 85° if angle BCA is named as 3b -7 what could be the value of b?
Michael paid an entrance fee of $8 plus an additional $2.25 per game at the bowling alley. He spent $50.00. Write and solve an equation to determine how many games Michael played.
Answer:
4
Step-by-step explanation:
$8.00+$2.25 = $10.25
$50.00÷$10.25= 4.
Third question please need help
Answer:
add 6 time 8 and get the answer like that.
Step-by-step explanation:
just keep adding that what you need to do ok.
Jack bought a 1/4 pound of salami and 1 2/3 pounds of Ham at the deli. Both items are on sale for $12 per pound. What is the total cost?
Answer:
Salami: $3.00
Ham: $ 8.00
Step-by-step explanation:
12 * 1/4 = 12/4 = $3.00
12 * 2/3 = 24/3 = $8.00
*What is the correct value of b?
~50/100 = b/28
-b=14
-b=20
-b=10
*What is the value of n?
~25/100 = 7/n
-n=28
-n=24
-n=32
Answer:
-b = 14
-n = 28
Step-by-step explanation:
For b
50/100=b/28 cross-multiply
1400= 100b divide both sides by hundred
-b = 14
For n
25/100= 7/n cross multiply
25n = 700 divide both sides by 25
-n = 28
Please help me with this question. What formula would you use to find the missing lengths of the right triangles?
a2 + b2 = c2 can be use to find missing lengths of the right triangles
Log2(x-1)+Log2(x+2) =2
Find X
Please answer right!
Answer:
Step-by-step explanation:
5x + 2 - 3x - 1 = 3x + 2
5x - 3x - 3x = - 2 + 1 + 2
5x - 6x = 1
-1x = 1
x = 1 / -1
x = -1
Angles 1 and 2 are coresponding angles angle 1 is 3x+15 angle 2 is 4x-5 degrees.
what is the value of x
Answer:
10
Step-by-step explanation:
3x+15+4x-5=180
7x+10=180
7x=170
x=10
Give the digits in the hundred thousands place and the ten thousands place.
746,089
Answer:
Hundred thousands - 7
Ten Thousands- 4
Step-by-step explanation:
For a project in his Geometry class, Ryan uses a mirror on the ground to measure the height of his school’s football goalpost. He walks a distance of 12.15 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. He then walks 3.4 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
9514 1404 393
Answer:
4.82 m
Step-by-step explanation:
The mirror reflects light at the same angle the light hits it, so the triangles formed by the line of sight, the ground, and the objects involved are similar. This means corresponding lengths are proportional.
height/mirror distance = T/12.15 = 1.35/3.4
Multiplying by 12.15, we find the top of the goalpost to have a height of ...
T = 12.15(1.35/3.4) ≈ 4.82 . . . meters
The goalpost is about 4.82 meters high.
The circle graph shows a family budgets it’s annual income.if the total annual income is 140,000, what amount is budgeted for auto expenses?
Answer: The amount budgeted for Auto Expenses is $18,200
Step-by-step explanation:
13 Percent of $140,000 is $18,200
0.13 times 140,000 :-)
Refer to the map shown in exercise.2. If m.angle 1 os 64° what is the measure of angle.2?
Answer:180
Step-by-step explanation:
If 20% of the students were boys, what fraction were girls?
Answer:
Girls are 4/5 of the students.
Step-by-step explanation:
boys + girls = 100% of students.
If 20% of the students are boys then 80% are girls
80% = 80/100 = 4/5
Pleased help math experts urgent
Answer:
1. get closer to 0
2. symmetrical across y=-x
3. x cannot be equal to 0
4. decreasing if x<0, increasing if x>0
Step-by-step explanation:
yes
Solve the inequality 10y−3(y+2)>2y+4, and write the solution in interval notation.
Step-by-step explanation:
10y - 3(y + 2) > 2y + 4
10y - 3y - 6 > 2y + 4
(10 - 3 - 2)y > 4 + 6
5y > 10
y > 10/5
y > 2
[tex] \: [/tex]
Solution → y > 2
Interval Notation → [tex] \lang 2 , \infty\rang[/tex]
The solution in interval notation is: (2, ∞)
To solve the inequality 10y - 3(y + 2) > 2y + 4, follow these steps:
Step 1: Distribute the -3 on the left side of the inequality:
10y - 3y - 6 > 2y + 4
Step 2: Combine like terms:
(10y - 3y) - 6 > 2y + 4
7y - 6 > 2y + 4
Step 3: Get all the y terms on one side by subtracting 2y from both sides of the inequality:
7y - 2y - 6 > 2y - 2y + 4
5y - 6 > 4
Step 4: Get the constant term on the other side by adding 6 to both sides of the inequality:
5y - 6 + 6 > 4 + 6
5y > 10
Step 5: Finally, solve for y by dividing both sides by 5:
y > 10/5
y > 2
The solution to the inequality is y > 2. Now, let's write it in interval notation.
To know more about interval:
https://brainly.com/question/29126055
#SPJ2
I need to know that answer please help if you can
Answer:
$180
Step-by-step explanation:
y = 30x +150
30(1) + 150
= 180
Which of the following is not a solution of the equation below (3x(x-1)(x-2)=0
What is the options?
Hello can someone please help me with this
Answer:
I would assume it is c. 1, because of rounding, but I'm only 70% sure.
plz plz heelp me i need heelp
Question 5 - Last night 20 mm of rain fell in 4 h. If it continues raining at the same rate, how
long will it take for 45 cm of rain to fall?
Answer:
Step-by-step explanation:
45 divided by two
The lcm of 5^3 and 5^2 is?
Answer:
5³
Step-by-step explanation:
5³ is the answer since it's the greater between the two numbers
Answer:
125
Step-by-step explanation:
This is because 5^2 *5 is 125 and 5^3 * 1 = 125 and the findings are both numbers have to be multiplied by a whole number to quantify a same identical multiple total number - we can check this by dividing by the smallest 125/5^2 = 5 and then the largest is 125/5^3 = 1 and we know there could not be a smaller whole number - The other workings would be to do a prim e factor tree of 125 = 5 25 5 and 5 = 5^3 and here we are told 5^3 is a multiple of 125 and 5^2 is also a multiple of 5^3 as it square fits 5 times into 125 as 5*25 is 125
6x+3>15 solve for a please
Answer:
x>2
Step-by-step explanation:
1) 6x+3 > 15
2) 6x > 15-3
3) 6x > 12
4) x > 12÷6
5) x > 2
