1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sholpan [36]
3 years ago
14

Courtney got 64 out of 75 correct on a test. What is the best estimate of the percent Courtney got correct?

Mathematics
1 answer:
Radda [10]3 years ago
7 0
To find the best estimate for the percentage just divide 64/75 and you should get 85.3% and you can round that to 85%.
You might be interested in
Evaluate the integral, show all steps please!
Aloiza [94]

Answer:

\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x

Rewrite 9 as 3²  and rewrite the 3/2 exponent as square root to the power of 3:

\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x

<u>Integration by substitution</u>

<u />

<u />\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}

\textsf{Let }x=3 \sin \theta

\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}

Find the derivative of x and rewrite it so that dx is on its own:

\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta

\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta

<u>Substitute</u> everything into the original integral:

\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & =  \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}

Take out the constant:

\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta

\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}

\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta

\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}

\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}

\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}

\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}

\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:

\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}

\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:

\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}

Learn more about integration by substitution here:

brainly.com/question/28156101

brainly.com/question/28155016

4 0
2 years ago
Simplify: 5 -3 • 5 5<br><br> 25 8<br> 25 -15<br> 5 -3<br> 5 2
Lostsunrise [7]
5 -3 * 5 5 simplified = 160!!!
7 0
2 years ago
6th-grade math help on geometry.
denis23 [38]

Answer:

okay , attach a file .

Step-by-step explanation:

7 0
2 years ago
How do u do this with answer plz
Whitepunk [10]

Answer:

i guess u know how to calculate a rectangle

Step-by-step explanation:

https://sciencing.com/area-triangular-prism-8165114.html

6 0
2 years ago
Read 2 more answers
Ok need help please help Thank you
Step2247 [10]
96 1/2 

there is ur answer i think :)
7 0
3 years ago
Other questions:
  • What is the range of the numbers 5,5,7,5,9,11,18?
    15·1 answer
  • What is the quotient?
    11·1 answer
  • What is the constant of the variation for the inverse variation?
    15·1 answer
  •  
    15·1 answer
  • Help please.................................................
    5·1 answer
  • Hurry what is your guys Xbox name
    6·2 answers
  • Plz help i have 3 mins it for 25 points
    5·2 answers
  • Write 96% as a fraction.
    7·2 answers
  • 33) Given the graphs of f(x) = x - 1 and g(x) = -x - 7, what is the solution to the equation f(x) = g(x)?
    13·1 answer
  • Write the equation using function notation f(x). then find f(0)<br><br> 2x^2 - 3y = 6
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!