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3 years ago

Find the length of "C" using the Pythagorean Theorem. 14 48

Mathematics

1 answer:

Charra [1.4K]3 years ago

7 0

Answer:

Step-by-step explanation:

the formula for Pythagorean theorem is A^2+B^2=C^2

14 squared is 196 48 squared is 2304 add them together u get 2500 and u have u get the sqrt of 2500 which is 50.

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Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

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

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

∴ we have used u-solve (u-substitution) to find the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

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

Unit: Integration

5 0

2 years ago

Please helpppppppppppppppppppppppppp

adell [148]

Answer:

the answer is D or A

Step-by-step explanation:

step-by-step explanation

I hope this helps

5 0

3 years ago

A tree farmer Planet 3 types of trees on 22 acres of land .he planted 48 trees per acre.what was the total number of trees the f

Alja [10]

Answer:

The total number of trees the farmer planted = 1056 trees

Step-by-step explanation:

It is given that,

A tree farmer Planet 3 types of trees on 22 acres of land and,

he planted 48 trees per acre

To find total number of plants

There are 22 acres of land.

In one acre he planted 48 trees.

Therefore total number of plants in 22 acers = 22 * 48 = 1056 trees

5 0

3 years ago

Given: BC bisects DBE. Prove: ABD is congruent to ABE

Arada [10]

Answer:

See below

Step-by-step explanation:

BC bisects <DBE and if AC is a straight line then you have that:

<ABD + <DBC = 180 (straight angle because of line AC)

<ABE + <CBE = 180 ( straight angle because of line AC)

Because BC bisects <DBE => < DBC = <CBE

So <ABD and <ABE must be the same to both sum 180 when added < DBC

7 0

3 years ago

Gina looked at the architectural plan of a room with four walls in which the walls meet each other at right angles. The length o

Lerok [7]

For a better understanding of the solution provided here, please find the diagram attached.

In the diagram, ABCD is the room.

AC is the diagonal whose length is 18.79 inches.

The length of wall AB is 17 inches.

From the given information, we have to determine the length of the BC, which is depicted a $x$ , because for the room to be a square, the length of the wall AB must be equal to the length of the wall BC.

In order to determine the length of the wall BC, or $x$ , we will have to employ the Pythagoras' Theorem here. Thus:

$x=\sqrt{(AC)^2-(AB)^2}$

$x=\sqrt{(18.79)^2-(17)^2}\approx\sqrt{64.06} \approx8$

Thus, $BC\approx 8$ inches

$\therefore AB\neq BC$ and hence, the given room is not a square.

8 0

3 years ago