Which net can be folded to form a triangular pyramid?

Answer:

The length of the ladder is 7.21 feet

Step-by-step explanation:

Let

y = Height of the wall

x = Distance between the wall and the ladder (bottom)

L = Length of the ladder

So, the given parameters are:

[tex]\frac{dy}{dt} = -2ft/s[/tex]

When [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]

The ladder, the wall and the ground forms a right-angled triangle where the hypotenuse is the length of the ladder; So:

[tex]L^2 = x^2 + y^2[/tex]

Differentiate with respect to time

[tex]2L\frac{dL}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

The length of the ladder does not change with time. So:

[tex]2L*0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

[tex]0 = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

Rewrite as:

[tex]2x\frac{dx}{dt} =- 2y\frac{dy}{dt}[/tex]

Divide both sides by 2

[tex]x\frac{dx}{dt} =- y\frac{dy}{dt}[/tex]

Recall that:

[tex]\frac{dy}{dt} = -2ft/s[/tex] and  [tex]x = 4; \frac{dx}{dt} = 3ft/s[/tex]

So:

[tex]4 * 3 = -y * -2[/tex]

[tex]12 = 2y[/tex]

[tex]6 = y[/tex]

[tex]y = 6[/tex]

Substitute [tex]y = 6[/tex] and [tex]x =4[/tex] in: [tex]L^2 = x^2 + y^2[/tex]

[tex]L^2 =4^2 + 6^2[/tex]

[tex]L^2 =52[/tex]

[tex]L = \sqrt{52[/tex]

[tex]L = 7.21ft[/tex]

Answer:

D

Step-by-step explanation:

Answer:

athe correct answer of this question is 6x + 3y = 5

Answer:

28

Step-by-step explanation:

1/4 can be rewritten as  1 / (2^2)

or 2^-2.

using the 2nd form,

we have 2^-2 * 2^30 = 2^x

By exponent rule

2^28 = 2^x

So we can observe now that x = 28

Answer:

23

Step-by-step explanation:

Answer:

Step-by-step explanation:

GXI with three points sounds like a triangle and a triangle angle equals 180 degrees.

Add picture and I'll try to solve full problem

Answer:

x = 1

x = -9

Step-by-step explanation:

(2x2 +  16x) -  18  = 0

2x2 + 16x - 18  =   2 • (x2 + 8x - 9)

x2 + 8x - 9

 -9    +    1    =    -8

     -3    +    3    =    0

     -1    +    9    =    8

 2 • (x + 9) • (x - 1)  = 0

2   =  0

x+9 = 0  

x = -9

x-1 = 0

x = 1

x2 + 8x - 9  = 0

  x2+8x = 9

(x+4) • (x+4)  =

 (x+4)2

x2+8x+16 = 25 and

  x2+8x+16 = (x+4)2

(x+4)2 = 25

x = -4 + √ 25

 x2 + 8x - 9 = 0

has two solutions:

 x = -4 + √ 25

  or

 x = -4 - √ 25

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

A   =     1

                     B   =    8

                     C   =   -9

B2  -  4AC   =

                    64 - (-36) =

                    100

 -8 ± √ 100

  x  =    —————

                   2

  x  =  ( -8 ± 10) / 2

x =(-8+√100)/2=-4+5= 1.000

or:

x =(-8-√100)/2=-4-5= -9.000

Answer:  x = 1

x = -9

Answer:

the constant of proportionality would be 9

Answer:

Step-by-step explanation: Three line segments can form a triangle, if the sum of any two lengths is greater than the third length. In A), 8 + 7 = 15 < 16. So, A cannot form a triangle.

Step-by-step explanation:

you have to study

Answer:

A,B and D form a triangle

Step-by-step explanation:

A - Side = 16 cm, side = 8 cm, side = 7 cm

16>8+7=15 form a triangle

B.- Side = 16 cm, side = 9 cm, side = 7 cm

16>9+7=16 form a triangle

C - Side = 17 cm, side = 12 cm, side = 7 cm

18>12+7=19 not form a triangle

D - Side = 17 cm, side = 11 cm, side = 5 cm

17>11+5=16 form traingle

Answer:

Y = 2

Step-by-step explanation:

Answer:

confess and believe are the two main words.

Step-by-step explanation:

Just got this right :')

Answer:

Equation - $1000=$300+$7.50x

Answer - Mr. Chamberlain can included 93 Student Entries

Step-by-step explanation:

$1000 (budget)

$300 (cost to rent bus)

$7.50 (cost of each student entry)

$1000-$300= $700

Now we have found out that Mr. Chamberlain has $700 left to spend on student entries.

$700/$7.50 = 93.333

Round 93.333 down to 93 because you can't have 1/3 of a student (obviously)

93 = the max number of student entries that Mr. Chamberlain can have for the museum field trip

I hope this helps :)

Answer:

30.2  sq cm

Step-by-step explanation:

bass times height 10 cm bottom and 3.2 height

Answer:

13.16

Step-by-step explanation:

formula= (absin∅)/2

= (4×9×sin47)/2

= 13.16

Answer:

24 square yards

Step-by-step explanation:

Find the diagram attached.

The area of the diagram = Area of rectangle + Area of triangle

Area of rectangle = 3 * 4

Area of rectangle = 12 square yards

Area of triangle = 1/2 * base * height

Area of triangle = 1/2 * 6 * 4

Area of triangle = 12 square yards

Area of the diagram = 12 + 12

Area of diagram =  24 square yards

Hence 24 square yards of carpeting is needed

Answer:

x=6,1,5 is your answer look it once

Answer:

Step-by-step explanation:

Radius r = 12.5/2 = 6.25 cm

Height h = 7 cm

volume = πr²h = 3.14⋅6.25²⋅7= 858.6 cubic cm

Answer:

8.5

Step-by-step explanation:

When you write out the data set, it looks like this:

5, 8, 8, 8, 8, 9, 9, 9, 10, 10

The median means the exact middle of the data set. In this case, it falls between the 8 and the 9, so the middle would be 8.5, so that's the median of the set. I hope this helps :)

Answer:

The median is 8.5

Step-by-step explanation:

The median is the middle number in a data set. For example, if you had a data set:

2, 2, 3, 4, 4

You would go forwards and backwards in the set until you found the middle number, which is 3. 3 would be the median.

However, if there is no middle number (there are an even number of points in the set), you add the two remaining numbers and divide it by two.

For example, if the final two numbers were:

2, 6

You would add 2 and 6 to get 8, and divide by 2, and you get the median 4.

In this set, we have

5, 8, 8, 8, 8, 9, 9, 9, 10, 10.

The final two numbers are 8 and 9, so you add 8+9=17, divided by 2 = 8.5.

Answer:

1/4

Step-by-step explanation:

Answer:

First add 3 to each side

Then divide each side by 5

Step-by-step explanation:

5x - 3 = 12

First add 3 to each side

5x-3+3 = 12+3

5x = 15

Then divide each side by 5

5x/5 = 15/5

x = 3

Answer:

3

Step-by-step explanation:

5x = 12 + 3

x = 15/5

x = 3

9514 1404 393

Answer:

  a) S(p) = -97.78p +2977.78

  b) about 98 fewer shirts per week will be sold for each $1 increase in price

  c) 533 shirts per week

  d) $15.63

Step-by-step explanation:

a) You are given two ordered pairs: (p, s) = (10, 2000) and (19, 1120). The two-point form of the equation for a line can be used.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  s = (1120 -2000)/(19 -10)(p -10) +2000

  s = -97.78(p -10) +2000

  S(p) = -97.78p +2977.78

__

b) The slope is shirts/dollar, meaning about 98 fewer shirts will be sold for each dollar increase in price.

__

c) S(25) ≈ 533

At a price of $25, the store would sell about 533 shirts per week.

__

d) 1450 = S(p) = -97.78p +2977.78

  -1527.78 = -97.78p

  15.625 = p ≈ 15.63

The store should charge $15.63 per shirt to maintain sales of 1450 shirts per week.

Answer:

Step-by-step explanation:

cylinder

Step-by-step explanation:

the basses is top and bottom so if there circular on top and bottom and curved surface for the body its a cylinder

Answer:

I think its gonna be 35 I'm not sure

Answer:

C

Step-by-step explanation:

Pentagon

Hope this helps (:

Answer

C). pentagon is the correct answer.

Step-by-step explanation:

A pentagon has 5 congruent sides and 5 angles.

Answer:

The third option 56

Step-by-step explanation:

56 is the middle number but I'm sorry if I'm wrong

Answer:

households

Step-by-step explanation:

An observational units are defined as the entity for which the information is received and the statistics are compiled of in the process of collecting the statistical data. It is also known as the statistical unit.

In the context, National Retail Federation is conducting a survey asking various households how much they are planning to spend on the memorial day. So the observational units in this study are the household because the information are collected on the basis of each household going to spend on the Memorial day.  

The observational units in this will be households.

An observational unit is defined as the entity for which the data is received and the statistics are collected in the process of collecting the statistical data. It is also known as the statistical unit.

In this context, National Retail Federation is executing a survey asking various households how much they are planning to spend on memorial day.

So the observational units in this study are the household because the information is gathered on the basis of each household going to expend on Memorial day.  

Thus the observational units in this will be households.

To know more about Observation follow

https://brainly.com/question/25843544

Answer:

[tex]\mathbf{ \dfrac{128}{3}}[/tex]

Step-by-step explanation:

Given that:

[tex]y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0[/tex]

[tex]Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16[/tex]

[tex]Then;[/tex]

[tex]y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4[/tex]

[tex]\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y[/tex]

∴

[tex]\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy[/tex]

[tex]Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0[/tex]

∴

[tex]V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\[/tex]

[tex]= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )[/tex]

[tex]= - \dfrac{2}{3} \Big(64\Big )[/tex]

∴

[tex]\mathbf{V = \dfrac{128}{3}}[/tex]