Determine the equation of the line that has a slope of 8 and has a y-intercept of -9

Given amn 45 and abc 45 the triangles are similar by

Sever21 [200]

Answer:

JUST DOING THIS FOR POINTS

Step-by-step explanation:

LOL

8 0

3 years ago

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

Laden bought 10 bags of small marbles and 8 bags of large marbles.There were 12 marbles in each bag.How many Marbles did Karen b

mihalych1998 [28]

Answer:

216 marbles bought altogether

Step-by-step explanation:

small m- 10

large m- 8

10×12+8×12=

120+96

= 216

6 0

3 years ago

Read 2 more answers

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. The volleyball team

almond37 [142]

Answer: After washing 20 cars together, each team will have raised the same amount in total.

Step-by-step explanation:

Let x represent the number of cars that each each teams will wash for them to raise the same amount in total.

The volleyball team gets $4 per car. In addition, they have already brought in $24 from past fundraisers. This means that the total amount raised by the volleyball team after washing x cars would be

4x + 24

The wrestling team has raised $84 in the past, and they are making $1 per car today. This means that the total amount raised by the wrestling team after washing x cars would be

x + 84

For both amounts to be equal, the number of cars would be

4x + 24 = x + 84

4x - x = 84 - 24

3x = 60

x = 60/3

x = 20

4 0

3 years ago

The width of a rectangle is the length minus 4 units. The area of the rectangle is 12 units. What is the width, in units, of the

marusya05 [52]

Answer:

Step-by-step explanation:12-4=8

4 0

2 years ago