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wariber [46]
4 years ago
8

Write an equation that expresses the following relationship. p varies jointly with the square of d and the cube of u In your equ

ation, use k as the constant of proportionality.
Mathematics
1 answer:
Veronika [31]4 years ago
5 0

Answer:

p= kd^{2}u^{3}

Step-by-step explanation:

Using k as the constant of proportionality.

The expression that expresses the relationship : p varies jointly with the square of d and the cube of u.

Varies jointly means that p will change as 'd' and 'u' will change together with respect to their powers.

We get the expression as:

p= kd^{2}u^{3}

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Jenna found a pair of sneaker that cost $64.She has a 15% off coupon. How much will she pay for the sneakers?(without Tax?)
S_A_V [24]
First, do 100-14 to find out how much percent doesn't get the coupon= 85
then find 85% of 64= 54.4
finally, your answer is: 54.4
3 0
4 years ago
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:
<u>Calculus</u>

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]:

  1. f(x) = cxⁿ
  2. 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:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution/u-solve</em>.

  1. Set <em>u</em>:
    \displaystyle u = 4 - x^2
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = -2x \ dx
  3. [<em>du</em>] Rewrite [U-Solve]:
    \displaystyle dx = \frac{-1}{2x} \ du

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Apply U-Solve:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du
  2. [Integrand] Simplify:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du
  3. [Integral] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du
  4. [Integral] Apply Integration Rule [Reverse Power Rule]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C
  5. [<em>u</em>] 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 <em>find</em> the indefinite integral.

---

Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

---

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

Unit: Integration

5 0
2 years ago
The area of a rectangle is 72 cm square. The length of the rectangle is 6 cm longer than the width. What is the width of the rec
miskamm [114]

The correct option will be :  B) 6 cm.

<u><em>Explanation</em></u>

Suppose, the width of the rectangle is x cm.

As, the length is 6 cm longer than the width, so the length will be: (x+6) cm.

<u>Formula for the Area of rectangle</u> is: (Length)*(Width)

Given that, the area of a rectangle is 72 cm²

So....

x(x+6)=72\\ \\ x^2+6x-72=0\\ \\ (x+12)(x-6)=0

Using zero-product property, we will get...

x+12=0\\ x= -12 <em>(Negative value is ignored as width can't be negative)</em>

and

x-6=0\\ x=6

So, the width of the rectangle is 6 cm.

6 0
3 years ago
I'm not sure what the answer is but I'm leaning toward A. Can someone help?​
Flauer [41]

Answer:

Yea im pretty sure that it is A

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The solution of 2x2 + x = 3 is shown below.
Yanka [14]

Answer:

b. {(-1.5, 9.5), (1,7)}

Step-by-step explanation:

brainliest please? :)

9 0
3 years ago
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