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Pachacha [2.7K]

2 years ago

9

Find the distance between (5, -2) and (7, -2)

1 answer:

Nuetrik [128]2 years ago

7 0

Answer:

The distance is (2, 0)

Step-by-step explanation:

The first number is on the X axis. You move forward two places to get 7. The second number is on the Y axis, and you don't need to move anything so it stays the same. Hence the answer is a distance of two on the X axis.

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A pair of dice is rolled. What is the probability of getting a sum of 6?

emmasim [6.3K]

Answer:

1/6

Step-by-step explanation:

Since you are rolling the die only one time there is only one way of you getting a 6 and that is rolling an actual 6. There are six sides to the die so you take the one 6 out of the the others and there is your probability.

8 0

2 years ago

WANT BRAINLIEST?<br>-4 1/4 - 1 2/5 <br><br>(please show your work all of it)

marishachu [46]

Answer:

-5.65

Step-by-step explanation:

-4 1/4 - 1 2/5 = -5.65

6 0

3 years ago

Find the derivative of y=8ln(sin t+9)

ira [324]

$\bf y=8ln[sin(t+9)]\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=8\cdot \cfrac{cos(t+9)\cdot 1}{sin(t+9)}\implies \cfrac{dy}{dx}=8cot(t+9)$

6 0

2 years ago

Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.

FromTheMoon [43]

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

$\rho = \sqrt{x^{2}+y^{2}+z^{2}}$

$\phi = cos^{-1}\frac{z}{\rho}$

For angle θ:

If x > 0 and y > 0: $\theta = tan^{-1}\frac{y}{x}$ ;

If x < 0: $\theta = \pi + tan^{-1}\frac{y}{x}$ ;
If x > 0 and y < 0: $\theta = 2\pi + tan^{-1}\frac{y}{x}$ ;

Calculating:

a) (4,2,-4)

$\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}$ = 6

$\phi = cos^{-1}(\frac{-4}{6})$

$\phi = cos^{-1}(\frac{-2}{3})$

For θ, choose 1st option:

$\theta = tan^{-1}(\frac{2}{4})$

$\theta = tan^{-1}(\frac{1}{2})$

b) (0,8,15)

$\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}$ = 17

$\phi = cos^{-1}(\frac{15}{17})$

$\theta = tan^{-1}\frac{y}{x}$

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = $\frac{\pi}{2}$

c) (√2,1,1)

$\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}$ = 2

$\phi = cos^{-1}(\frac{1}{2})$

$\phi$ = $\frac{\pi}{3}$

$\theta = tan^{-1}\frac{1}{\sqrt{2} }$

d) (−2√3,−2,3)

$\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}$ = 5

$\phi = cos^{-1}(\frac{3}{5})$

Since x < 0, use 2nd option:

$\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }$

$\theta = \pi + \frac{\pi}{6}$

$\theta = \frac{7\pi}{6}$

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

$r=\sqrt{x^{2}+y^{2}}$

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

$r=\sqrt{4^{2}+2^{2}}$ = $\sqrt{20}$

$\theta = tan^{-1}\frac{1}{2}$

z = -4

b) (0, 8, 15)

$r=\sqrt{0^{2}+8^{2}}$ = 8

$\theta = \frac{\pi}{2}$

z = 15

c) (√2,1,1)

$r=\sqrt{(\sqrt{2} )^{2}+1^{2}}$ = $\sqrt{3}$

$\theta = \frac{\pi}{3}$

z = 1

d) (−2√3,−2,3)

$r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}$ = 4

$\theta = \frac{7\pi}{6}$

z = 3

5 0

3 years ago

What is the 101st term in the sequence 997, 989, 981, ...?

melamori03 [73]

Answer: first option.

Step-by-step explanation:

Find the common difference d of the arithmetic sequence:

$d=a_n-a_{(n-1)}\\d=989-997\\d=-8$

Then the formula for the 101st term is the shown below:

$a_n=a_1+(n-1)d$

Where:

$a_1=997\\d=-8\\n=101$

Substitute values into the formula. Therefore, you obtain:

$a_n=997+(101-1)(-8)=197$

4 0

2 years ago

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