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2 years ago

Khalid invests $500 in an account that earns 1.5% interest per year, compounded annually. Which of the following is

Mathematics

2 answers:

Inessa [10]2 years ago

6 0

<h2>D. Geometric Sequence </h2>

For your question: "Khalid invests $500 in an account that earns 1.5% interest per year, compounded annually. Which of the following is

formed by the amount in his account from year to year?"

The geometric sequence is formed.

cupoosta [38]2 years ago

6 0

Answer:

Step-by-step explanation:

took quiz and cuz i milk da kows on da farm

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Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

4 0

2 years ago

Help pleasee and thanks

Assoli18 [71]

Answer if D hope it helps!

3 0

3 years ago

The number of students who chose lunch was 5 more than the number of students who chose breakfast. Write a system of linear equa

Papessa [141]

Answer:

The system of linear equations are $y=5+x$ and $x+y=25$

Step-by-step explanation:

Given : The number of students who chose lunch was 5 more than the number of students who chose breakfast. Let x represent the number of students who chose breakfast and y represent the number of students who chose lunch.

(50 students picked, 25 picked dinner the rest picked lunch and breakfast)

To find : Write a system of linear equations that represents the numbers of students who chose breakfast and lunch ?

Solution :

The number of students who chose breakfast be 'x'

The number of students who chose lunch be 'y'.

The number of students who chose lunch was 5 more than the number of students who chose breakfast.

i.e. $y=5+x$

Now, Total student were 50 and 25 picked dinner the rest picked lunch and breakfast i.e. 25.

So, $x+y=25$

Therefore, the system of linear equations are $y=5+x$ and $x+y=25$

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3 years ago

Answer number 3<br><br><br> quickly i am in a rush

SVEN [57.7K]

Answ34.5

Step-by-step explanation:

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2 years ago

1. Given a regular octagon, find the measures of the angles formed by (a) two consecutive radii and (b) a

Fed [463]

A ) The angle formed by 2 consecutive radii:
Ф= 360° : 8 = 45°
b ) The angle formed by a radius and a side of a polygon:
α = (180° - 45°): 2 = 135° : 2 = 67.5°
Answer:
B ) 45°, 67.5°

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3 years ago