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3 years ago

Write an equation of the line passes through the given points (6,-3),(1,2)

Mathematics

2 answers:

adoni [48]3 years ago

6 0

Answer:

y = -x+3

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

= ( 2 - -3)/( 1 - 6)

( 2+3)/( 1-6)

5/ -5

-1

The slope is -1

We can use slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -x+b

Substitute a point into the equation

2 = -1 +b

Add 1 to each side

2+1 = -1+1+b

3 = b

y = -x+3

Vadim26 [7]3 years ago

5 0

y = -x + 3

$m = \frac{y_{1} - y_{2} }{x_{1} - x_{2}}$

$m = \frac{6 - 1 }{-3 - 2}$

$m = \frac{5 }{-5}$

$m=-1$

y = mx + b

substitute

2 = -1(1) + b

2 = -1 + b

3 = b

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Insert grouping symbols so that the given expression has a value of 25. 12 – 7 + 2 • 4 + 6

katovenus [111]

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4 0

2 years ago

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

Evaluate the expression 2x - 5 when x = -5 C) 5 D) 15 A)-5 B) -15

IRINA_888 [86]

Answer:

B) -15

Step-by-step explanation:

8 0

3 years ago

What two-dimensional figure will result from slicing this rectangular prism parallel to its base?

alina1380 [7]

Answer:

We will obtain a rectangle on slicing this rectangular prism parallel to it's base.

Hence, option 1) is true.

RECTANGLE.

Step-by-step explanation:

On slicing this geometrical figure; which is a rectangular prism parallel to it's base then we will obtain a figure similar to it's base of the same dimensions as it's base.

As the base of the rectangular prism is a rectangle so on slicing this 3-dimensional figure parallel to it's base we will obtain rectangles.

Hence, option 1 is true.

RECTANGLE.

8 0

2 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!

Marrrta [24]

Answer:

Fist one:

x−2=−3

Second one: a=63b/23

Third one: x=−a/2+3b/2

7 0

3 years ago