What is the value of y?

Answer:

The dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm

Step-by-step explanation:

The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.

Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are

A = 2lh + lw + 2wh

Now for a box of square base, l = w = x.

So, A = 2xh + x² + 2xh

A = x² + 4xh

Since V = x²h and V = 171500 cm³,

h = V/x² = 171500/x²

substituting h into A, we have

A =   x² + 4xh

A =  x² + 4x(171500 cm³/x²)

A =  x² + 4 × 171500 cm³/x

A =  x² + 686000 cm³/x

To find the value of x that minimizes A, we differentiate A with respect to x

So, dA/dx = d[x² + 686000 cm³/x]/dx

dA/dx = 2x - 686000 cm³/x²

equating this to zero, we have

2x - 686000 cm³/x² = 0

2x = 686000 cm³/x²

2x³ = 686000

x³ = 686000 cm³/2

x = ∛(343000 cm³)

x = 70 cm

To determine if this in a minimum dimension for A, we differentiate dA/dx and insert x = 70 cm

So, d²A/dx² = d[2x - 686000 cm³/x²]/dx

d²A/dx² = 2 + 3 × 686000 cm³/x³

d²A/dx² = 2 + 2058000 cm³/x³

with x = 70 cm, we have

d²A/dx² = 2 + 2058000 cm³/(70 cm)³

d²A/dx² = 2 + 2058000 cm³/343000 cm³

d²A/dx² = 2 + 6

d²A/dx² = 8 > 0

So, x = 70 is a minimum value for the dimension

Since h = 171500 cm³/x²

h = 171500 cm³/(70 cm)²

h = 171500 cm³/4900 cm²

h = 35 cm

So, the dimensions of the box that minimize the amount of material used is length of square base x = 70 cm and height of box = 35 cm

Step-by-step explanation:

given,

m1=23°

m2=32°

hope it helps

Answer:

the diameter of the circle is ⅓ of the height

so the radius is 1/6 of the height

the area of the flag is 1*1.5 of the height

(we need to consider this)

pi*(1/6)² / 1.5

= 0.058177

so the percentage is

5.82 %

So, the required percentage is  [tex]5.81\%[/tex].

To understand the calculations, check below.

The area of the disk is defined as the ‘ measure of surface ‘ surrounded by the round edge (circumference) of the disk. The area of a disk can be derived by breaking it into a number of identical parts of disk as units — calculating their areas and summing them up till the disk is reformed.

That is [tex]Area=\pi \frac{d^2}{4}[/tex]

Let the width and the length of the flag be [tex]2x[/tex] and [tex]3x[/tex] respectively.

So, the diameter of the gold-colored disk will be [tex]\frac{2x}{3}[/tex]

Now, by using the above formula the area of the gold disk will be,

[tex]\pi \frac{d^2}{4}=\pi\times\frac{4x^2}{4\times 9} \\ =\frac{\pi x^2}{9}[/tex]

And the area of the flag will be,

[tex]Area=l\times b\\=2x\times 3x\\=6x ^2[/tex]

So, the required percentage is,

[tex]\frac{(\frac{\pi x^2}{9} )}{6x^2} \times 100=\frac{\pi}{54}\times 100\\ =5.81\%[/tex]

Learn more about the topic Area of the disk:

https://brainly.com/question/21881629

Answer:

53,901

Step-by-step explanation:

The value given is: 245,093.

5 is in the thousands place. Multiply the thousands place with ten:

1,000 x 10 = 10,000

This means that the number with 5 in the ten thousands place will be your answer.

53,901 is your answer.

~

Answer:

656.3844

Step-by-step explanation:

Area of squares = [tex]s^{2}[/tex]

s = measure of a side, all sides are the same.

[tex]25.62^{2}[/tex] use a calculator

Answer:

a = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]c^{2}[/tex] = [tex]18^{2}[/tex]    (pythagoras theorem)

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]4^{2}[/tex]      (pythagoras theorem)

[tex]c^{2}[/tex] + [tex]b^{2}[/tex] = [tex]22^{2}[/tex]      (pythagoras theorem)

From these 3 equations we can find the value of a

Answer:

I believe it’s 20

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

The sum of the angles of a triangle are 180

128+ 2x-3 +23 = 180

Combine like terms

2x+148=180

Subtract 148 from each side

2x+148 -148 = 180-148

2x = 32

Divide by 2

2x/2 = 32/2

x =16

Answer:

[tex]252 \: sq \: feet = 2 \: lbs \\ 1008 \: sq \: feet = ( \frac{1008 \times 2}{252} ) \\ = 8 \: lbs[/tex]

Answer:

8lbs of fertilizer

Step-by-step explanation:

1008 ÷ 252 = 4

2 × 4 = 8

Answer:

x=00

Step-by-step explanation:l

nnm

Answer:

The perimeter of the garden would be 93 feet, meaning you would need 93 feet of fencing.

Step-by-step explanation:

To find the perimeter of a shape you first need to know how long each side of the shape is and then add those sides together, once you have that number, you have your perimeter. I hope this helps.

Answer:

a 4,1. helpful answer

Answer:

Part a:

The null and alternate hypotheses are

i) H0:  ud  ≥ u    vs          Ha: ud < u

ii) As the significance level is ∝= 0.025 and it is one tailed test then the critical region R < - 1.96

iii) The test statistics is  =−9.15

iv) We accept the alternate hypothesis.

​

Part b:   CI = (−3.637,−2.163)

​

Step-by-step explanation:

AS the sample sizes are sufficiently large (n1,n2> 30) we can use the sample standard deviations in place of population standard deviations.

Part a:

The null and alternate hypotheses are

i) H0:  ud  ≥ u    vs          Ha: ud < u

where

ud is the mean of the days missed  per year by mothers working for companies that provide day-care facilities on premises

and

u is the mean number of days missed per year by mothers working for companies that do not provide day-care facilities on premises

ii) As the significance level is ∝= 0.025 and it is one tailed test then the critical region R < - 1.96

iii) The test statistics is

z= xˉ1 − xˉ2/√ s 1² /n 1 +s 2² /n 2

​=  6.4−9.3/ √1.2 ² /45+ 1.85² /50​

=−9.15

iv) The calculated z = −9.15 values lies in the critical region= R < - 1.96 and the null hypothesis is rejected. Hence the  mean of absentees for companies that provide day-care facilities on premises  is less than the

the mean number of absentees for companies that do not provide day-care facilities on premises.

We accept the alternate hypothesis.

​

Part b:

The confidence interval can be calculated using the formula

CI = ( xˉ1 − xˉ2) ± z∝/2 √ s 1² /n 1 +s 2² /n 2

CI = (6.4−9.3) ± 2.326 * √1.2 ² /45+ 1.85² /50​

CI = (−3.637,−2.163)

​

Step-by-step explanation:

Volume of cylinder: πr²h

= π(6)² x 15

= 36π x 15

= 1620 cm³

Answer: A

Answer:

B. 540 picm3

Step-by-step explanation:

(6)2 X 15= 540

Answer:

(0,4)

Step-by-step explanation:

Answer:

a = (r/x) -b

x = -14

Step-by-step explanation:

r=x(a+b)

Divide each side by x

r/x = a+b

Subtract b

r/x  -b = a

x/2=-7

Multiply each side by 2

x/2*2 = -7*2

x = -14

Answer:

1.) a = r / x - b

2.) x = - 14

Step-by-step explanation:

1.) r = x ( a + b )

r / x = x / x ( a + b) ...( Divide each side by x )

r / x = a + b

r / x - b = a + b - b ... ( Subtracting each side by b) r / x - b = a

2.) x / 2 = -7

x / 2 × 2 = -7 × 2 .. ( multiplying each side by 2 )

x = - 14

Answer:

[tex]1 : 4\frac{1}{2} \\ = 1 : \frac{9}{2} \\ = \frac{1}{ \frac{9}{2} } \\ = \frac{2}{9} [/tex]

Answer:

C

Step-by-step explanation:

All others can be proved false.

Answer:

all the angles add up to 180 degrees

So 180÷6=30

(i got 6 cuz 1+2+3)

so 1=30

2=30*2=60

3=30*3=90

The answer would be (3,2) because you would do (x,-y)

9514 1404 393

Answer:

  3. $0.45

  4. 50%

  5. -5°, -1°, 1°, -2°, 5°

Step-by-step explanation:

3. The difference in tip amounts is ...

  15%($25) -15%($22) = 15%($25 -22) = 15%($3.00) = $0.45

  Jasmine paid $0.45 more tip than Candice.

__

4. If 25% were sick, then the crew that showed up was 75% of the full crew. If 1/3 of those 75% went home early, then the remaining (2/3)(75%) = 50% were the fraction working at the end of the day.

__

5. The Fridays in January were Jan 2, 9, 16, 23, and 30. The middle of the month was the 16th. For something like this, it can help to read through a couple of times, as the relations are not given in a way that gives a solution without skipping around.

We are given that the temp on the 30th was 5°, and that the 23rd was 7° less, so -2°. The low on the 2nd was 3° lower than on the 23rd, so was -5°. The temp on the 16th was 6° higher than on the 2nd, so was -5+6 = 1°, and the temp on the 9th was 2° lower than that, so -1°.

The low temperatures were ...

Complete question:

The base of a pyramid covers an area of 14.0 acres (1 acre = 43, 560 ft²  ) and has a height of 481 ft. If the volume of a pyramid is given by the expression V = bh/3, where b is the area of the base and h is the height. If the height of the pyramid were increased to 512 ft and the height to base area ratio of the pyramid were kept constant, by what percentage would the volume of the pyramid increase

Answer:

The percentage increase of the volume is 6.45 %

Step-by-step explanation:

The volume of pyramid is calculated as;

V = bh/3

The initial volume of the pyramid is calculated as follows;

[tex]V = \frac{bh}{3} \\\\V_0 = (\frac{1}{3} ) \times (14 \ acres \ \times \frac{43,560 \ ft^2}{1 \ acre} ) \times (481 \ ft)\\\\V_0 = 97,777,680 \ ft^3[/tex]

The final volume of the pyramid when the height is increased to 512 ft.

[tex]V_1 = (\frac{1}{3} ) \times (14 \ acres \ \times \frac{43,560 \ ft^2}{1 \ acre} ) \times (512 \ ft)\\\\V_1 = 104,079,360 \ ft^3[/tex]

The percentage increase of the volume;

[tex]= \frac{104,079,360 - 97,777,680}{97,777,680} \times 100\%\\\\= 6.45 \ \%[/tex]

The volume of the pyramid will increase by 11.79%

The volume of a Pyramid is calculated using:

[tex]V = \frac{Bh}3[/tex]

Where:

When the height is increased from 458 to 512, then the initial and the final volumes are:

[tex]V_1 = \frac{458}{3}b[/tex]

[tex]V_2 = \frac{512}{3}b[/tex]

The percentage change is then calculated as:

[tex]\% Change = \frac{V_2 -V_1}{V_1} \times 100\%[/tex]

This gives

[tex]\% Change = \frac{512b/3 -458b/3}{458b/3} \times 100\%[/tex]

Simplify the numerator

[tex]\% Change = \frac{54b/3}{458b/3} \times 100\%[/tex]

Evaluate the quotient

[tex]\% Change = 0.1179 \times 100\%[/tex]

Express as percentage

[tex]\% Change = 11.79 \%[/tex]

Hence, the volume of the pyramid will increase by 11.79%

Read more about volumes at:

https://brainly.com/question/1972490

Answer:

-27/7

Step-by-step explanation:

Replace x with 19,

f(19)=3/(19+2) - root(19-3)

      =3/21 - root(16)

      =1/7 - 4

      =1/7 - 28/7

      = -27/7

Answer:

Step-by-step explanation:

In a parallelogram,

i) opposite sides are equal and parallel.

So, DC = AB

DC = 28 units

ii) Diagonals bisect each other.

AC bisects BD

DE =  EB = [tex]\frac{1}{2}[/tex] BD

DE = [tex]\frac{1}{2}*91[/tex] = 45.5

DE = 45.5 units

Answer:

I guess it would go

Ben did:+10

Gail:-8

Nathaniel:0

Step-by-step explanation:

hope this was what you wanted

best of luck

Answer:

33.55 m³

Step-by-step explanation:

volume is base area times height.

the base area is a right-angled triangle (a×b/2).

At = 2.5×4.4/2

the height is 6.1

the total volume is then

2.5×4.4×6.1/2 = 33.55 m³