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yuradex [85]
3 years ago
15

Suppose u=<2,−1> and v=<1,−8> are two vectors that form the sides of a parallelogram. Then the lengths of the two di

agonals of the parallelogram are?
Mathematics
1 answer:
tigry1 [53]3 years ago
8 0
| u | = √(2² + (-1²)) = √5
| v | = √ ( 1² + (-8)² = √65
cos (u,v) = ( u * v ) / (| u | * | v |) =
 (2 * 1 + ( -1 ) * ( - 8 )) / √5 √ 65 = (2 + 8) / √5 √65 = 10 / (√5 √ 65 )
The length of a larger diagonal:
d 1² = | u |² + 2 |u| |v| + | v |² = 5 + (2 √5 √65 * 10 / √5 √65 )+65
d 1² = 70 + 20 = 90
d 1 = √ 90 = 3√10
d 2² = 70 - 20 = 50
d 2 = √50 = 5√2
Answer:
The lengths of the diagonals are: 3√10 and 5√2 .
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y varies inversely with x. k, the constant of inverse variation, is 9.62. When y is 2.6, what is x? Round your answer to the nea
Ksivusya [100]

Answer:

3.7

Step-by-step explanation:

2.6  = 9.62/x

2.6x = 9.62     Multiplied each side by x

     x = 3.7       Divided each side by 2.6.

5 0
3 years ago
How are greater than and greater than or equal to similar?<br> How are they different
anzhelika [568]
Greater than means it can only be greater than the value give for example x is greater than 10, x can only be a number greater than 10. Greater than or equal to is similar because the answer can be greater than the value given or equal to it. For example x is greater than 10, x could be equal to 10 or any value greater than it.
5 0
3 years ago
What steps to get the principle of a 30 year loan at 5.5%?
hoa [83]
Multiply 30 -- the number of years of the loan -- by the number of payments you make each year. For example, 30 X 12 = 360. You are making 360 payments over the course of the loan. Divide your mortgage interest rate by your total payments.
8 0
2 years ago
A stand is a frustum shape, formed by removing a small square-based pyramid from the top of
kupik [55]

The frustum can be considered as consisting of a square pyramid, less the

cut volume.

  • The mass of the stand, is approximately 18.60905 kg

Reasons:

The given parameter of the frustum are;

The density of the frustum, ρ = 85 g/cm³

Height of pyramid, h = 9 cm

Side length of base = 10 cm

Height of frustum

By proportional shapes, the side length of the top of the frustum can be found as follows;

\dfrac{4 \, cm}{9 \, cm} = \dfrac{x}{10 \, cm}

x = \dfrac{4 \, cm}{9 \, cm} \times 10 \, cm = 4\frac{4}{9} \, cm

V = \dfrac{h}{3} \times \left(B_1 + B_2 + \sqrt{B_1 \times B_2} \right)

B₁ = 10², B₂ = \left(4\frac{4}{9} \right)^2

Therefore;

V = \dfrac{4}{3} \times \left(10^2 + \left(4\frac{4}{9}  \right)^2  + \sqrt{10^2 \times  \left(4\frac{4}{9}  \right)^2} \right) \approx 218.93

The volume of the stand, V ≈ 218.93 cm³

Mass = Volume × Density

∴ Mass of the stand, m = 218.93 cm³ × 85 g/cm³ = 18,609.05 grams = 18.60905 kg.

Learn more here:

brainly.com/question/24323975

8 0
3 years ago
HELP ME, PLZ. 100 POINTS !!!
marta [7]

Answer:

x=2√5/5

x=-2√5/5

Step-by-step explanation:

13√(2√5/5)^2-(2√5/5)^4+9√(2√5/5)^2+(2√5/5)^4=16

13√(4×5/25)-(16×25/625)+9√(4×5/25)+(16×25/625)

13√(4/5)-(16/25)+9√(4/5)+(16/25)

13√(4/25)+9√(36/25)

13×2/5+9×6/5

26/5+54/5

16=16 (proven)

3 0
3 years ago
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