If a total of 1100 square centimeters of material is to be used to make a box with a square base and an open top, find the largest possible volume of such a box.

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

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

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

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

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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  

Answer:

I would assume it is c. 1, because of rounding, but I'm only 70% sure.

Answer:180

Step-by-step explanation:

Answer:

$180

Step-by-step explanation:

y = 30x +150

30(1) + 150

= 180

Answer:

-5

Step-by-step explanation:

3x=-13-2

3x=-15

x=-5

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

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

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

Answer:

(3x-1)/5= (x+1)/3

3(3x-1)=5(x+1)

then solve which the final answer will give you x=8

Answer:

4

Step-by-step explanation:

$8.00+$2.25 = $10.25

$50.00÷$10.25= 4.

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.

Answer:

Hundred thousands - 7

Ten Thousands- 4

Step-by-step explanation:

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.

Answer:

10

Step-by-step explanation:

3x+15+4x-5=180

7x+10=180

7x=170

x=10

Answer:

1/8

Step-by-step explanation:

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

a2 + b2 = c2 can be use to find missing lengths of the right triangles

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.

Answer:

Step-by-step explanation:

45 divided by two

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 :-)

What is the options?