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Mashcka [7]
3 years ago
10

Elam is packing his room to move into a new house. A small box can hold 8 books without breaking, while a large box can hold 12

books without breaking. He has at most 160 books to pack and less than 30 boxes total. Let s represent the number of small boxes and l represent the number of large boxes. The inequalities s ≥ 0 and l ≥ 0 are part of the system that models this scenario. Which inequalities complete the system? s – l < 30 8s – 12l ≤ 160 s + l < 30 8s + 12l ≤ 160 s + l > 30 8s + 12l ≤ 160 s + l < 30 8s + 12l ≥ 160
Mathematics
2 answers:
gtnhenbr [62]3 years ago
7 0

the answer is

s + l < 30

8s + 12l ≤ 160

or B on e d g e n u i t y

lora16 [44]3 years ago
5 0

\text{Elam ispacking his room to move into a new house.}\\&#10;\\&#10;\text{let the number of small box is s and the number of large box be l.}\\&#10;\\&#10;\text{since he has at most 160 books to pack and less than 30 boxes total.}\\&#10;\\&#10;\text{so the total number of small and large boxes is less than 30. so}\\&#10;\\&#10;s+l

\text{hence the system that models this scenario is given by the inequalities}\\&#10;\\&#10;s+l

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g 1.32 Two points on a sphere of radius 3 are given as P1(3,0,30) and P2(3,45,45): (a) Find the position vectors of P1 and P2. (
Rama09 [41]

Answer:

a) P.V  of is OP₁ = [ 1.5i + 0j + 2.6k ],   P.V  of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

b) Vector connecting P₁ to P₂ is [ 0i + 1.5j + 0.48k ]  

c) cylindrical coordinates are (1.5, π/2, 0.48)

Step-by-step explanation:

Given that;

r = 3

P₁ ( 3, 0°, 30° ),   P₂ ( 3, 45°, 45° )

a)

P.V of P₁

x = rcos∅sin∅ = 3(cos0°) ( sin30°) = (3 × 1 × 0.5) = 1.5

y = rsin∅sin∅  = 3(sin0°) (sin30°)   = (3 × 0 × 0.5) = 0

z = rcos∅        = 3(cos30°)             = ( 3 × 0.866)  = 2.6

∴ P.V  of is OP₁ = [ 1.5i + 0j + 2.6k ]

P.V of P₂

x = rcos∅sin∅ = 3(cos45°) ( sin45°) = (3 × 0.7071 × 0.7071) = 1.5

y = rsin∅sin∅  = 3(sin45°) (sin45°)   = (3 × 0.7071 × 0.7071) = 1.5

z = rcos∅        = 3(cos45°)                 = ( 3 × 0.7071)            = 2.12

∴ P.V  of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

b)

Vector connecting P₁ to P₂ is given by

OP₂ - OP₁ = [ 1.5i + 1.5j + 2.12k ] - [ 1.5i + 0j + 2.6k ]

= [ 0i + 1.5j + 0.48k ]  

c)

P₁P₂ → = [ 0i + 1.5j + 0.48k ]  = [ 1.5j + 0.48k ]  

so in a cylindrical coordinate, it should be

r = √(o² + 1.5²) = 1.5

∅ = tan⁻¹[y/π] = π/2

z = 0.48

cylindrical coordinates are (1.5, π/2, 0.48)

5 0
3 years ago
There are 400 silver dollars in two bags. If 275 are in one bag, how many are in the other bag?
xz_007 [3.2K]
If there are 400 silver dollars in all, and there are 275 in one bag, to find the amount in the other bag, just subtract:

400-275=125

There are 125 in the other bag.
4 0
3 years ago
Read 2 more answers
For which values of P and Q does the following equation have Infinity many solutions? P×+57=-75x+Q​
Semenov [28]

earrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  

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In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

Unless there is none then in that case there very well may be infinite solutions

7 0
3 years ago
What is the measure of angle "A"?
Zolol [24]

Answer:

Step-by-step explanation:

The given figure is an isosceles trapezoid, this means that the two non-parallel sides in the trapezoid are congruent. One of the properties of an isosceles triangle is that opposite angles are supplementary. This means that the sum of angles opposite each other in an isosceles trapezoid is (180) degrees. One can apply this here by stating the following,

Substitute,

Inverse operations.

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3 years ago
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lys-0071 [83]
Here we are going to use the equation y=15x2+3x+56.
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8 0
3 years ago
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