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3 years ago

Explain if you can

Mathematics

2 answers:

Savatey [412]3 years ago

7 0

Ist c hope you had your

Mashutka [201]3 years ago

4 0

Part A: C part B: C. I hope this helps

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Hannah's school hosted a book donation. There are 150 students at her school, and they donated a total of b books! Hannah donate

svetoff [14.1K]

Answer:

$x=3*\dfrac{b}{150}$

Step-by-step explanation:

Let x = number of books that Hannah donated

We know that the number of students is 150 and the total number of books is represented by b, we can write that as:

Average number of books donated by each student = $\dfrac{b}{150}$

Now we know that Hannah donated 3 times as much as the average. We can write that as:

$x=3*\dfrac{b}{150}$

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3 years ago

The ratio of boys to girls at a movie is 4:7. If there are 21. girls, how many boys are

IrinaVladis [17]

Answer:

Step-by-step explanation:

7*3=21 so 4*3=12

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3 years ago

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Step-by-step explanation:

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Sara threw her math book off a building . The height of the book, seconds after being thrownis modeled by the equation below. Th

Vikentia [17]

Answer: 70 ft

Step-by-step explanation:

Given

height of book is measured by the function is

$h(x)=-5(x+2)(x-7)$

when the book is thrown $x=0$

$\therefore h(x=0)=-5(0+2)(0-7)\\\Rightarrow h(x=0)=70\ ft$

The height of the book is $70\ ft$

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3 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:
Calculus

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]:

f(x) = cxⁿ
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:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

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

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

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

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

Unit: Integration

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2 years ago