All categories

3 years ago

Use the distributive property of multiplication to find 7×32.

Mathematics

1 answer:

prisoha [69]3 years ago

4 0

Answer:

224

Step-by-step explanation:

7 × 32 = 7 × (30 + 2) = 7 × 30 + 7 × 2 = 210 + 14 = 224

You might be interested in

The price of a video game at Game Word has increased from $36 to $45 each. What was the percent change?

andriy [413]

Step-by-step explanation:

price difference= $45-$36

=$9

now,

x% of $45=$9

or, x/100 ×45 =9

or, x/20 ×9=9

or, x/20=1

therefore, x= 20%

3 0

3 years ago

4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received. How many slices of

atroni [7]

Answer:

Step-by-step explanation:

6 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

2 years ago

The formula V=Bh, where B represents the area of the base, can be used to find the volume of a cylinder. Which formula is equiva

Karo-lina-s [1.5K]

Answer:

Explanation:

B=Base Area

In a cylinder, the base area is a circle.

Area Circle=pi r^2

Replace base area with area of circle:

V=pi r^2 H

7 0

3 years ago

Read 2 more answers

2. If AB = 4x + 9. BC = 5x + 2, and AC = 56, then find the value for . AB, BC. A B

inysia [295]

Answer:

AB=29; BC=27

Step-by-step explanation:

So they told us AB=4x+9 and that BC=5x+2, and AC=56 , now to help with the question you can draw this information on a number line. Now on a number you can see that basically AC=AB+BC.

So you would write it as such,,

4x+9+5x+2=56

Combine like terms

9x+11=56

Now you have to isolate the x by itself but first get rid of the 11.

9x+11-11=56-11

You would get

9x=45

Here you can divide 9 by both sides to isolate x.

9x/9=45/9

{x=5}

Now to find the value for both substitue x in the equations for both

1. AB=4x+9 where x is 5

4(5)+9 =AB

20+9 =AB

29=AB

You would do the same with BC

2. BC= 5x+2 where x is 5

5(5)+2= BC

25+2= BC

27=BC

If you want to check your answers you can just substitute x for 5 in the first equation we did where AC=AB+BC

6 0

3 years ago