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3 years ago

9

The price of a visit to the dentist is $50. If the dentist fills any cavities, an additional charge of $100 per cavity gets adde

d to the bill.
If the dentist finds n cavities, what will the cost of the visit be?
Write your answer as an expression.
So the answer is 50+100n
You can see the step by step answer below.

2 answers:

RUDIKE [14]3 years ago

7 0

50+100n is the answer, hope I helped :D

iren2701 [21]3 years ago

3 0

50 + 100n is answer

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This is a timed quiz. Pls, help. 50 points. 6th-grade math.

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2 years ago

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:

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2 years ago

Please help me, I will give brainliest

ipn [44]

Answer:

8w² < 4w(150-w)

Step-by-step explanation:

Square area of living : w · w = w²

Money spent : 8 · w²

Square area of artichokes : (150 - w) · w

Money earned : 4 · w · (150 - w)

Julia manages to save some money every week. That means that the money earned is bigger than the money spent ( the money spent is less than the money earned)

8 · w² < 4 · w · (150 - w)

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2 years ago

a cell phone company charges a monthly fee plus a 0.35 for text messages sent they charge 25.00 monthly fee and your bill is 58.

riadik2000 [5.3K]

Hey,

So first we are told that they charg a fixed fee of 25:00 right?That means even if you didn’t send any text messages you still have to pay 25:00.

So first we have to subtract that 25:00 form 58.25 right?This means the rest of the bill is for text messages OK?
So he spent 33.25(this is the answer to the subtraction) on the text messages right?
And for every text he sent he was charged 0.35 right? So we have to divide 33.25 by 0.35 right?
And that gets us 95.

Now we can double check the answer by multiplieng 95 by 0.35 and adding 25.

So th answer is 95

Hope this helps !!

6 0

3 years ago