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3 years ago

Midpoint of (2,4) to (8,2)

Mathematics

1 answer:

omeli [17]3 years ago

5 0

Answer:

midpoint of (2,4) and (2,8) is ( 5 , 3 )

Step-by-step explanation:

your answer!

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If anyone knows about definite integrals for calculus then please I request help! I

kicyunya [14]

Answer:

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 4x^{-2}$
[u] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = \frac{-8}{x^3} \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du$
[Integral] Exponential Integration: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)$
Simplify: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

4 0

3 years ago

Which unit would be best for measuring the thickness of a coin

choli [55]

Answer: Milimeters (mm)

Step-by-step explanation:

8 0

4 years ago

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Are the following figures similar? Rectangles ABCD and EFGH are shown. AB equals 5. BC equals 25. EF equals 3. FG equals 15. Yes

Tatiana [17]

Answer:

Yes; the corresponding sides are proportional

Step-by-step explanation:

If two figures are similar, the lengths of their sides are proportional. This means if we set up a proportion with the sides we are given and cross-multiply, we get a true statement at the end of it.

Using the similarity statement ABCD~EFGH, we will compare AB to EF and BC to FG:

5/3 = 25/15

Cross multiply:

5(15) = 3(25)

75 = 75

We got a true statement, so the sides are proportional.

8 0

3 years ago

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45% as fraction in the simplest form

Kobotan [32]

Answer:9/20

Step-by-step explanation: 45/100=9/20, 45÷5=9, 100÷5=20 both the denominater and the numerator are divisible by 5.

7 0

3 years ago

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Which transformations can be used to carry ABCD onto itself? The point of

dmitriy555 [2]

Answer:

A and B

Step-by-step explanation:

For A, y=2 is the axis of vertical symmetry, meaning a reflection would map the shape onto itself.

For B, x=3 is the axis of horizontal symmetry, meaning a reflection would map the shape onto itself.

For C, a rotation of 90 degrees would make the shape taller vertically and shorter horizontally, therefore it would be wrong.

For D, a translation two units down would move all points down, even though some would need to go up, therefore it would be wrong.

7 0

3 years ago