Ask question

Ask question

All categories

3 years ago

9

Suppose u=⟨2,−2u=⟨2,−2⟩ and v=⟨6,2⟩v=⟨6,2⟩ are two vectors that form the sides of a parallelogram. then the lengths of the two d

iagonals of the parallelogram are

1 answer:

Alex Ar [27]3 years ago

5 0

91.7
44.6
is the answer

You might be interested in

Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

<em>F'(x)</em> = 3<em>x</em>² + 7

and

<em>F</em> (0) = 5

and you're asked to find <em>F(b)</em> for the values of <em>b</em> in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, <em>F</em> (0) = 5.

For the remaining <em>b</em>, you can solve for <em>F(x)</em> exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then <em>F</em> (0.1) = 5.701, <em>F</em> (0.2) = 6.408, <em>F</em> (0.5) = 8.625, and <em>F</em> (2.0) = 27.

On the other hand, if you're expected to <em>approximate</em> <em>F</em> at the given <em>b</em>, you can use the linear approximation to <em>F(x)</em> around <em>x</em> = 0, which is

<em>F(x)</em> ≈ <em>L(x)</em> = <em>F</em> (0) + <em>F'</em> (0) (<em>x</em> - 0) = 5 + 7<em>x</em>

Then <em>F</em> (0) = 5, <em>F</em> (0.1) ≈ 5.7, <em>F</em> (0.2) ≈ 6.4, <em>F</em> (0.5) ≈ 8.5, and <em>F</em> (2.0) ≈ 19. Notice how the error gets larger the further away <em>b </em>gets from 0.

A <em>better</em> numerical method would be Euler's method. Given <em>F'(x)</em>, we iteratively use the linear approximation at successive points to get closer approximations to the actual values of <em>F(x)</em>.

Let <em>y(x)</em> = <em>F(x)</em>. Starting with <em>x</em>₀ = 0 and <em>y</em>₀ = <em>F(x</em>₀<em>)</em> = 5, we have

<em>x</em>₁ = <em>x</em>₀ + 0.1 = 0.1

<em>y</em>₁ = <em>y</em>₀ + <em>F'(x</em>₀<em>)</em> (<em>x</em>₁ - <em>x</em>₀) = 5 + 7 (0.1 - 0) → <em>F</em> (0.1) ≈ 5.7

<em>x</em>₂ = <em>x</em>₁ + 0.1 = 0.2

<em>y</em>₂ = <em>y</em>₁ + <em>F'(x</em>₁<em>)</em> (<em>x</em>₂ - <em>x</em>₁) = 5.7 + 7.03 (0.2 - 0.1) → <em>F</em> (0.2) ≈ 6.403

<em>x</em>₃ = <em>x</em>₂ + 0.3 = 0.5

<em>y</em>₃ = <em>y</em>₂ + <em>F'(x</em>₂<em>)</em> (<em>x</em>₃ - <em>x</em>₂) = 6.403 + 7.12 (0.5 - 0.2) → <em>F</em> (0.5) ≈ 8.539

<em>x</em>₄ = <em>x</em>₃ + 1.5 = 2.0

<em>y</em>₄ = <em>y</em>₃ + <em>F'(x</em>₃<em>)</em> (<em>x</em>₄ - <em>x</em>₃) = 8.539 + 7.75 (2.0 - 0.5) → <em>F</em> (2.0) ≈ 20.164

4 0

3 years ago

Joni has a circular garden with a diameter of 14 1/2 feet if she uses 2 teaspoons of fertilizer for every 25 square feet of gard

alina1380 [7]

Answer:

13.20 teaspoon of fertiliser needed for entire garden.

Step-by-step explanation:

Diameter of the garden = 14.50 ft

Radius of the garden = 7.25 ft

Area

[tex]A=\pi r^2[/text]

[tex]A=\pi \times 7.25 \times 7.25[/text]

[tex]\pi=3.14[/text]

[tex]A=\pi \times 7.25 \times 7.25[/text]

[tex]A=3.14 \times 7.25 \times 7.25[/text]

Hence

[tex]A=165.046[/text]

Area is 165.046 Sq Ft

For 25 sq ft of fields the fertiliser needed = 2 tea spoon

For 1 sq ft of fields the fertiliser needed =

[tex]\frac{2}{25}[/text] tea spoon

For 165.046 sq ft of fields the fertiliser needed =

[tex]\frac{2 \times 165.046 }{25}[/text] tea spoon

For 165.046 sq ft of fields the fertiliser needed = 13.20 tea spoon

6 0

3 years ago

Find the area of ABC with the side lengths a=8 and b= 12, and the included angle C =84 degrees. Round your answer to the nearest

spin [16.1K]

Answer:

47.7 square units

Step-by-step explanation:

The area of triangle ABC with two given sides and an inclusive angle =

1/2absinC

Where : a = 8, b = 12, C = 84

Area of Triangle ABC = 1/2 × 8 × 12 × sin 84

Area of Triangle ABC = 47.737050978 square units

Approximately to the nearest tenth = 47.7 square units.

6 0

3 years ago

At Pizza Pi, 68% of the pizzas made last week had extra cheese. If 17 pizzas had extra cheese, how many pizzas in all were made

Andrei [34K]

Answer: 50

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

the coordinates A(5,-2) B(3,-1) C(-4,-4) D(-3,8), and E(-1,4) form the verices of a polygon when they are connected in order for

abruzzese [7]

E, B, D, C, A in correct order

Your welcome!!!

~Shantiicakes

7 0

3 years ago