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3 years ago

Savvas Texas Algebra II

Mathematics

1 answer:

Elan Coil [88]3 years ago

3 0

Answer:

The number of small balloons = 46

The number of large balloons = 159

The number of bottles of helium gas = 5

The total cost of the supplies = $68.97

Step-by-step explanation:

The volume of each small balloon = 300 in.³

The volume of each large balloon = 1000 in.³

The cost of one package of 50 small balloons = $2.59

The cost of one package of 24 large balloons = $1.99

The volume of one small tank of pressurized helium = 20 ft³

The volume cost of one small tank of pressurized helium = $10.49

By conversion

20 ft³ = 34,560 in.³

The volume of 30 small balloons = 30 × 300 in.³ = 9,000 in.³

The volume of 30 large balloons = 30 × 1000 in.³ = 30,000 in.³

The volume taken by 24 large balloons = 24,000 in.³,

24 large balloons cost = $1.99

The volume taken by 50 small balloons = 15,000 in.³

50 small balloons cost = $2.59

Therefore, we buy more large balloons

We have;

A×300 + B×1000 = C×34,560

Given that all the helium will be used, the volume of helium will be a multiple of 300, therefore, when 5 bottles of helium is used, we have;

A×300 + B×1000 = 5×34,560 = 172,800 in.³

Given that there will be at least 30 of each balloon, gives;

We remove the minimum possible quantity (more than 30) of small balloons from 172,800 in.³ leaving multiples of 1,000s as follows;

Using Excel, the quantities of 36 and 46 small balloons give the same cost

For 46 small balloons

The volume of 46 small balloons = 13,800 in.³

Therefore, 172,800 in.³ - 13,800 in.³ = 159,000 in.³ = The volume of the large balloons

The quantity of the large balloons = 159,000 in.³/(1,000 in.³/balloon) = 159 balloons

Therefore, we have 46 small balloons, and 159 large balloons, with 5 small bottles of helium gas

The number of package of large balloons is 159/24 = 6.625 ≈ 7 packages

The cost of the 7 packages of large balloons = 7 × $1.99 = $13.93

The number of package of small balloons is 46/50= 0.92 ≈ 1 package

The cost of the 1 packages of small balloons = 1 × $2.59 = $2.59

The cost of the five bottles of helium = 5 × $10.49 = $52.45

$68.97

The number of small balloons = 46

The number of large balloons = 159

The number of bottles of helium gas = 5

The total cost of the supplies = $68.97

At the same cost, we can also have;

The number of small balloons = 36

The number of large balloons = 162

The number of bottles of helium gas = 5

The total cost of the supplies = $68.97

Therefore, we can have 36 or 46 small balloons and 162 or 159 large balloons along with 5 bottles of helium gas with a total cost of $13.93 + $2.59 + $52.45 = $68.97.

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A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per

pishuonlain [190]

Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

$y=a(t-h)^2+k$

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

$y=ax^2+bx+c$

then the x-coordinate of the vertex is

$h=-\frac{b}{2a}$

Now in our case b = 32 and a = -16; therefore,

$h=\frac{-32}{2(16)}=1$

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

$k=-16(1)+32(1)+96=112$

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

$h(t)=a(t-1)^2+112$

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

$h(0)=-16(0)^2+32(0)+96=96$

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

$96=a(0-1)^2+112$ $96=a+112$

subtracting 112 from both sides gives

$a=-16$

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

$\boxed{h\mleft(t\mright)=-16\left(t-1\right)^2+112.}$

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

$h(t)=0.$

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

$-16\left(t-1\right)^2+112=0$

Now subtracting 112 from both sides gives

$-16(t-1)^2=-112$

Dividing both sides by -16 gives

$(t-1)^2=\frac{-112}{-16}$ $(t-1)^2=7$

taking the square root of both sides gives

$t-1=\pm\sqrt{7}$

adding 1 to both sides gives

$t=\pm\sqrt{7}+1$

Hence, the two solutions we get are

$t=\sqrt{7}+1=3.6$ $t=-\sqrt{7}+1=-1.6$

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

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1 year ago

Hellppppppp plllz T^T

xenn [34]

I’m not sure but i hope you get it correct : )

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3 years ago

Determine the displacement of end A with respect to end D if the diameters of each segment are dAB = 0.85 in ., dBC = 1.1 in .,

ipn [44]

Answer / Step-by-step explanation:

It should be noted that the question is incomplete due to the fact that the diagram has not been provided. However, the diagram has been complementing the question has been provided below.

To solve the question in the narrative, we recall the equation used in solving for displacement:

Thus, δₙₐ = Σ pL/AE

Where:

P is applied axial force.

E is the young's modulus of elasticity.

A is the area of cross-section.

L is length of the bar

Therefore, -8 (80) ÷ π/4 ( 0.85)² (18) (10³) + 2(150) ÷ π/4 (1.1)² (18) (10³) + 6(100) ÷ π/4 (0.45)² (18) (10³)

Solving further,

we have,

-8 (80) ÷ 0.7853( 0.85)² (18) (10³) + 2(150) ÷ 0.7853(1.1)² (18) (10³) + 6(100) ÷ 0.7853 (0.45)² (18) (10³)

= -640÷ 0.7853( 0.85)² (18) (10³) + 300 ÷ 0.7853(1.1)² (18) (10³) + 600 ÷ 0.7853 (0.45)² (18) (10³)

Solving further, we arrive at 0.111 in answer.

The positive sign indicates that end A moves away from end D.

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3 years ago

Mixed numbers from 3 to 7 with an interval of 1/3

disa [49]

4 1/3 there you go hope I helped

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Something added by -8 equals 20

LiRa [457]

Answer:

28 is added by -8 equals 20

Step-by-step explanation:

The equation to calculate something added by -8 equals 20 is as follows:

x-8 = 20

x = 20+8

x = 28

28 is added by -8 equals 20

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3 years ago

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