<img src="https://tex.z-dn.net/?f=a2%20%5Cdiv%20a%20-%20b%20%2B%20b2%20%5Cdiv%20b%20-%20a" id="TexFormula1" title="a2 \div a

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11Alexandr11 [23.1K]

3 years ago

+ b2 \div b - a" alt="a2 \div a - b + b2 \div b - a" align="absmiddle" class="latex-formula">

Mathematics

2 answers:

Zigmanuir [339]3 years ago

7 0

Answer:

Step-by-step explanation:

=a^2/a-b+b^2/b-a

=here denominator which divides a^2 and b^2 gets cancelled

=a-b+b-a

=+a-a and +b -b gets cancelled

and answer is 0

ikadub [295]3 years ago

5 0

Answer:

Step-by-step explanation:

Given

a² ÷ a - b + b² ÷ b - a ← perform the division calculations

= a - b + b - a ← collect like terms

= 0

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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

F'(x) = 3x² + 7

and

F (0) = 5

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

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) 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 F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

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

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

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

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

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

3 years ago

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting t

timama [110]

Step-by-step explanation:

Using Pythagorus theorem :

(A)

$PR = \sqrt{ {PQ}^{2} + {QR}^{2} }$

$PR = \sqrt{196 + 81} = \sqrt{277} = 16.64 \: cm$

(B)

$QR = \sqrt{ {PQ}^{2} + {PR}^{2} } = \sqrt{196 +324 } = 22.8 \: cm$

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4 years ago

the length of a rectangle is 9 units more than the width of the rectangle, w. if the width of the rectangle is more than 20 unit

Delvig [45]

Answer:

$W>20$

Step-by-step explanation:

Let

L-----> the length of a rectangle

W---> the width of a rectangle

we know that

$L=W+9$ -----> equation A

$W>20$ -----> inequality B

The inequality B represent the equation that could be used to find the possible values of the width

The solution for the width of the rectangle is all real numbers greater than 20 units

3 0

3 years ago

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soldi70 [24.7K]

Answer:

y=1/2x

Step-by-step explanation:

math is math ‍

7 0

3 years ago

Read 2 more answers

Help help i need help with this

aliina [53]

Answer:

1) 8 2) -33/9

Step-by-step explanation:

1) (1/2)x = -1/2 + 9/2

(1/2)x = 4 x = 8

2) distributing 3/2, 9x/2 - 15/2 = -24

9x/2 = -24 + 15/2

9x/2 = -33/2

9x = -66/2

9x = -33

x = -33/9

5 0

3 years ago