What exponent will make this true? Enter your naswer in the box 10?=1,000

What is 20% of $10

Mama L [17]

10 * 0.20 = 2
20% of 10 is 2

4 0

3 years ago

Evaluate the following definite integral

mihalych1998 [28]

Answer:

$\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}$

General Formulas and Concepts:

Symbols

e (Euler's number) ≈ 2.71828

Algebra I

Exponential Rule [Multiplying]: $\displaystyle b^m \cdot b^n = b^{m + n}$

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals
Definite Integrals
Integration Constant C

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

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

U-Solve

Integration by Parts: $\displaystyle \int {u} \, dv = uv - \int {v} \, du$

[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, Trig

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx$

Step 2: Integrate Pt. 1

[Integrand] Rewrite [Exponential Rule - Multiplying]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \int\limits^1_0 {x^5e^{x^3}e} \, dx$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = e\int\limits^1_0 {x^5e^{x^3}} \, dx$

Step 3: Integrate Pt. 2

Identify variables for u-solve.

Set u: $\displaystyle u = x^3$
[u] Differentiate [Basic Power Rule]: $\displaystyle du = 3x^2 \ dx$
[u] Rewrite: $\displaystyle x = \sqrt[3]{u}$
[du] Rewrite: $\displaystyle dx = \frac{1}{3x^2} \ du$

Step 4: Integrate Pt. 3

[Integral] U-Solve: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = e\int\limits^1_0 {x^5e^{(\sqrt[3]{u})^3}\frac{1}{3x^2}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {x^5e^{(\sqrt[3]{u})^3}\frac{1}{x^2}} \, du$
[Integral] Simplify: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {x^3e^u} \, du$
[Integrand] U-Solve: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {ue^u} \, du$

Step 5: integrate Pt. 4

Identify variables for integration by parts using LIPET.

Set u: $\displaystyle u = u$
[u] Differentiate [Basic Power Rule]: $\displaystyle du = du$
Set dv: $\displaystyle dv = e^u \ du$
[dv] Exponential Integration: $\displaystyle v = e^u$

Step 6: Integrate Pt. 5

[Integral] Integration by Parts: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3} \bigg[ ue^u \bigg| \limits^1_0 - \int\limits^1_0 {e^u} \, du \bigg]$
[Integral] Exponential Integration: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3} \bigg[ ue^u \bigg| \limits^1_0 - e^u \bigg| \limits^1_0 \bigg]$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}[ e - e ]$
Simplify: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}$

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

Unit: Integration

Book: College Calculus 10e

8 0

3 years ago

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained i

alex41 [277]

Answer:

sample size if he uses a previous estimate of 32% is 523

sample size if he does not use any prior estimates is 601

Step-by-step explanation:

estimate E = 4 percentage = 0.04

confidence Cl = 95% = 0.95

previous estimate p = 32% = 0.32

q = 1 - 0.32 = 0.68

to find out

size of sample

solution

first we calculate z value for 95% confidence E = 0.04 is 1.96

from probability P(-1.96 < z < 1.96) = 0.95)

here z = 1.96

so in 1st part size of sample we know

E = z × $\sqrt{pq/n}$

put all value E, z p and q and we get n

n = (z/E)² ×p×q

n = (1.96/0.04)² ×0.32×0.68

n = 523

sample size if he uses a previous estimate of 32% is 523

now in 2nd part we take p = 0.5

so n will be

n = (z/E)² ×p×q

n = (1.96/0.04)² ×0.5×0.5

n = 601

sample size if he does not use any prior estimates is 601

6 0

3 years ago

What is the true solution to 3In2+In(4x)

stepladder [879]

Answer:

x=2

Step-by-step explanation:

7 0

3 years ago

Find the value of x and y.

suter [353]

Answer:

5,6

Step-by-step explanation:

5 0

3 years ago

What exponent will make this true? Enter your naswer in the box 10?=1,000​

What exponent will make this true? Enter your naswer in the box 10?=1,000