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3 years ago

Y = 1/2 x + 2 in both graphs

Mathematics

1 answer:

Mazyrski [523]3 years ago

3 0

Answer:

x=2y-4

Step-by-step explanation:

Step number 1: 1/2x + 2 = 1 . y
step number 2: 1/2x + 2 = y
step number 3: 1/2x + 2 - 2 = y - 2
Step number 4: 1/2x =y
Step number 5: 2 . 1/2x= 2y - 2 .2
Step number 6: x=2y-4

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I WILL MARK AS BRAINLIEST! Solve for X and Y

konstantin123 [22]

Answer:

a) 40 b) 8 c) 27 2/3 d) 4

a) 93 b) -95 c) -87 d) -81

5 0

3 years ago

Read 2 more answers

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

If y varies inversely with x and y=2 when x=8 what is K the constant of proportionality

777dan777 [17]

Y=k/x
2=k/8
k=16
the answer is A

7 0

3 years ago

The diameter of the moon is 2,160 miles. A model has a scale of 1 in : 150 mi. What is the diameter of the model?

Charra [1.4K]

Answer:

The diameter of the model is 14.4 inches.

Step-by-step explanation:

The Diameter of the moon = 2,160 miles

The scale on the model represents 1 in = 150 miles

Let the model represents k inches in 2,160 miles.

So, by the Ratio of Proportionality:

$\frac{1}{150} = \frac{k}{2160}$

⇒ $k = \frac{2160}{150} \\\implies k = 14.4$

or, k = 14.4 inches

⇒On the scale 2160 miles is represented as 14.4 inches

Hence the diameter of the model is 14.4 inches.

3 0

3 years ago

1000 students participated in a survey on a university campus about their TV watching habits. All

nasty-shy [4]

Hi, you've asked an unclear question. However, I inferred you may want to know the actual number of students represented by the percentages of 27%, and 61%.

Explanation:

Finding percentage usually involves performing two operations; multiplication and division.

First, all (100%) of respondents said they watched TV at least at some point during the day.

Next, 27% of respondents stated that they only watched television during prime time hours, in which the actual number of students represented by the percentage is calculated by dividing 27 by 100 and multiplying by 1000 =

$\frac{27}{100} * 1000 = 270$ .

Finally, we are told 61% of respondents stated that they spend prime time hours in their dorm rooms. The actual number of students represented by the percentage is calculated by dividing 61 by 100 and multiplying by 1000 =

$\frac{61}{100} * 1000 = 610$

5 0

3 years ago