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3 years ago

Y=6x+5 is the equation. what is its gradient

1 answer:

8 0

Gradient is synonymous to slope.

y = 6x + 5 is an example of a slope-intercept form of a straight-line equationl.

The slope-intercept equation is like this:

y = mx + b

where : m = slope ; b = "y-intercept"

y = 6x + 5

6 is the slope
5 is the y-intercept.

Since slope and gradient are synonymous, 6 is the gradient of the above equation.

You might be interested in

65 inches is how many feet? (Round to nearest hundredth) *

nalin [4]

Answer:

5.42 feet

Step-by-step explanation:

12 inches=1 foot

65/12=5.41667

5.41667=5.42 feet

7 0

3 years ago

Read 2 more answers

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

Given f(x)=1/x+5 and g(x)=x-2

vladimir1956 [14]

For this case we have the following functions:

$f (x) = \frac {1} {x + 5}\\g (x) = x-2$

We must find f (g (x)). So:

$f (g (x)) = \frac {1} {(x-2) +5} = \frac {1} {x-2 + 5} = \frac {1} {x + 3}$

Finally we have to:

$f (g (x)) = \frac {1} {x + 3}$

For the function to be defined the denominator must be different from 0. That is x different from -3.

Answer:

Option B

3 0

3 years ago

Matt Bonner has 8 dimes, 9 pennies, and 4 quarters in his pocket. If each coin is equally likely to be pulled out of his pocket

Lesechka [4]

Answer:

B. 0.602%

Step-by-step explanation:

Probability is essentially (# times specific event will occur) / (# times general event will occur). Here, we have a few specific events: draw a quarter, draw a second quarter, draw a penny, and draw another penny. The general event will just be the number of coins there are to choose from.

The probability that the first draw is a quarter will be 4 / (4 + 8 + 9) = 4/21.

Since we've drawn one now, there's only 21 - 1 = 20 total coins left. The probability of drawing a second quarter is: (4 - 1) / (21 - 1) = 3/20.

The probability of drawing a penny is: 9 / (20 - 1) = 9/19.

The probability of drawing a second penny is: (9 - 1) / (19 - 1) = 8/18.

Multiply these four probabilities together:

(4/21) * (3/20) * (9/19) * (8/18) = 864 / 143640 ≈ 0.602%

The answer is B.

8 0

3 years ago

Read 2 more answers

I’m confused?????????

QveST [7]

Answer:

The equation of the line is y - 3 = 2.5(x - 2) ⇒ D

Step-by-step explanation:

The rule of the slope of a line is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

The point-slope form of a line is y - y1 = m(x - x1), where

(x1, y1) is a point on the line

From the given figure

∵ The line passes through points (2, 3) and (0, -2)

∴ x1 = 2 and y1 = 3

∴ x2 = 0 and y2 = -2

→ Substitute them in the rule of the slope to find it

∵ m = $\frac{-2-3}{0-2}=\frac{-5}{-2}=2.5$

∴ m = 2.5

→ Substitute the values of m, x1, y1 in the form of the equation above

∵ m = 2.5, x1 = 2, y1 = 3

∵ y - 3 = 2.5(x - 2)

∴ The equation of the line is y - 3 = 2.5(x - 2)

6 0

3 years ago