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3 years ago

What’s the correct answer for this?

Mathematics

2 answers:

algol [13]3 years ago

7 0

Answer:

Step-by-step explanation:

Since AB is a diameter, MO = NO

7x - 4 = 6x

7x - 6x = 4

= 4

MN = MO + NO

= 7x - 4 + 6x

= 7 * 4 - 4 + (6 * 4)

= 28 - 4 + 24

= 48

Hope this helps!

joja [24]3 years ago

6 0

Answer:

MN = 48

Step-by-step explanation:

Since AB is a diameter , so it divides MN into 2 equal parts i.e. MO = NO

7x-4 = 6x

7x-6x = 4

x = 4

Now

MN = MO + NO

MN = 7x-4+6x

MN = 7(4)-4+6(4)

MN = 28-4+24

MN = 48

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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:

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4 0

2 years ago

The farmer has a problem with too many mice in his barn. He brought in 363636 cats to catch the mice. Each cat caught 111 mice,

FromTheMoon [43]

Answer:

40585818

Step-by-step explanation:

thats an insane amount of anything but like, dam n

363636*111 to find out how many were caught, then that number plus 222222

6 0

3 years ago

Please help me solve this and its about dot plots

Lubov Fominskaja [6]

Answer:

Step-by-step explanation:

Number of blue cars = 28

Number of dots in blue cars = 7

one dot = 28÷ 7 = 4

One dot equals 4cars

Number of tan cars = 5*4 = 20

7 0

2 years ago

Find the equation of the line using the point-slope formula. Write the final equation using slope-intercept form. (1,2) with a s

Lilit [14]

Answer:

$y-2=\displaystyle -\frac{3}{4}(x-1)$

$y=\displaystyle -\frac{3}{4}x+\frac{11}{4}$

Step-by-step explanation:

Hi there!

Point-slope form: $y-y_1=m(x-x_1)$ where m is the slope of the line and $(x_1,y_1)$ is a given point

Given that the slope is -3/4, we can plug it into $y-y_1=m(x-x_1)$ as m:

$y-y_1=\displaystyle -\frac{3}{4}(x-x_1)$

We can also plug in the given point (1,2):

$y-2=\displaystyle -\frac{3}{4}(x-1)$

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

To write the equation in slope-intercept form, isolate y:

$y-2=\displaystyle -\frac{3}{4}(x-1)\\\\y=\displaystyle -\frac{3}{4}(x-1)+2\\\\y=\displaystyle -\frac{3}{4}x+\frac{3}{4}+2\\\\y=\displaystyle -\frac{3}{4}x+\frac{11}{4}$

I hope this helps!

8 0

2 years ago

Please help and explain why, so that I understand.

chubhunter [2.5K]

Hello there!

The number of people in different cities should be represented on a graph as Two-dimensional.

I'll explain why: The number of dimensions you need on a graph is equal to the number of variables that you are studying. In this case, you have two variables in the study:

1)The number of people
2)The city where they live

You'll need a two-dimensional graph with two axes in which one of the axes represents the number of people and the other axis represents the city. If you were also studying the age of those people, you'll need one more dimension to include this new variable.

Have a nice day!

8 0

3 years ago