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2 years ago

Hurry i need your help

Mathematics

2 answers:

worty [1.4K]2 years ago

8 0

Answer:

IM READY FOR ACTION!

Step-by-step explanation:

GaryK [48]2 years ago

6 0

Answer: 10

Step-by-step explanation:

A. 2.50 + 2.50 + 2.50 + 2.50

the sum of 2.50, 4 times

B. The sum is 10, Maila's friends tell her to sell each wristband for 2.50. And 4 were bought, so add 2.50+2.50+2.50+2.50.

10 9 8 7 6 5 4 3 2 1 0

---0----|----|--•--|----|----•----|----|--•--|----|---

<----------- <---------- <----------- <------

+ + + +

2.50 2.50 2.50 2.50

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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:

Fundamental Theorem of Calculus

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

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:

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

Integration by substitution

$\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}$

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

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

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

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

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

Substitute 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

Sonji paid $25.00 for two scarves, which were different prices. When she got home she could not find the receipt. She

Nimfa-mama [501]

Let the less expensive scarf be x

expensive scarf = $3 + x

According To The Question,

x+x+$3=$25

2x+$3=25

2x=22

x=$11

expensive scarf = x + $3 = $11 + $3 = $14

HOPE THIS WILL HELP YOU

8 0

3 years ago

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Write down the number eleven thousand,eleven hundred and eleven in figures

Tomtit [17]

Answer:

12,111

Step-by-step explanation:

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2 years ago

Compound Inequalities Solve the following compound inequality 12 < 2x-4/3 < 16

Lana71 [14]

The answer is 20/3, 26/3.

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2 years ago

Y=-5x+1, in this equation the slope is -5 and the y-intercept is 1. What is the slope and y-intercept of y=4x-7?

irina [24]

Answer:

Step-by-step explanation:

1. the slope is 4 and the y-intercept is -7 or (0, -7)

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2 years ago