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3 years ago

Given the equation `3x=x+6`

Mathematics

1 answer:

Anettt [7]3 years ago

5 0

Subtract x from both sides of the equation, this will allow only one side to have a variable.

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What is the shape graphed by the function r = 1+ sin theta

IRISSAK [1]

Answer: Is known as a "heart" shape.

Step-by-step explanation:

r = 1 + sin(θ)

Let's do it without a graph, let's use only math and logic:

remember that θ is measured from the x-axis

when θ = 0, we have r = 1 (so we have a radius of 1 over the x-axis)

when θ = pi/2, we have r = 1 + sin(pi/2) = 2

when θ = pi, we have r = 1 + sin(pi) = 1

when θ = 3*pi/2, we have r = 1 + sin(3*pi/2) = 0

First, we have symetry around the y-axis,

now, notice that the value of x in θ = 0, θ = pi and θ = 3*pi/2 is the same. so this is not a circle, this is actually a circle where the bottom part is flatted.

But not actually flat, because between θ = pi and θ = 2pi we are in the negative y-axis, so in this region we have two small bumps that connect in the point (0, 0)

This is a kinda "heart" shape.

3 0

4 years ago

A snail travels 313 ft every hour. How far does the snail travel in 212 hours? Express your answer in simplest form

oksian1 [2.3K]

212 x 313 = 66356
so the snail travels 6656 ft in 212 hours

4 0

3 years ago

Read 2 more answers

If the length of a rectangle is x-2 and its area is 2x3 – 8x2 + 2x+12, it’s width would be what?

hram777 [196]

Width would have to be a quadratic
Use long division to find the other factor of the cubic polynomial P (x).
P (x) factors in case it is reducible over R[x]
if it weren't then P (x) mod R [x] would be a field
otherwise you could use the Eisenstein Criterion.

6 0

3 years ago

The ratio of two numbers is 3 to 7. The sum of the numbers is 150. What are the numbers?

Natalka [10]

45 and 105, you can put the equation as 3x+7x=150. Add them to 10x then divide, x=15 so 3*15=45, and same for the other number.

7 0

3 years ago

Please someone help me to prove this..

Pachacha [2.7K]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the following Sum to Product Identities:

$\sin x+\sin y=2\sin \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\sin x-\sin y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=-2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)$

<u>Proof LHS → RHS</u>

$\text{LHS:}\qquad \qquad \qquad \dfrac{\sin 5-\sin 15+\sin 25 - \sin 35}{\cos 5-\cos 15- \cos 25 + \cos 35}$

$\text{Reqroup:}\qquad \qquad \qquad \dfrac{(\sin 25+\sin 5)-(\sin 35 + \sin 15)}{(\cos 35+\cos 5)-(\cos 25 + \cos 15)}$

$\text{Sum to Product:}\quad \dfrac{2\sin \bigg(\dfrac{25+5}{2}\bigg)\cos \bigg(\dfrac{25-5}{2}\bigg)-2\sin \bigg(\dfrac{35+15}{2}\bigg)\cos \bigg(\dfrac{35-15}{2}\bigg)}{2\cos \bigg(\dfrac{25+15}{2}\bigg)\cos \bigg(\dfrac{25-15}{2}\bigg)-2\cos \bigg(\dfrac{35+5}{2}\bigg)\cos \bigg(\dfrac{35-5}{2}\bigg)}$ $\text{Simplify:}\qquad \qquad \dfrac{2\sin 15\cos 10-2\sin 25\cos 10}{2\cos 20\cos 15-2\cos 20\cos 5}$

$\text{Factor:}\qquad \qquad \dfrac{2\cos 10(\sin 15-\sin 25)}{2\cos 20(\cos 15-\cos 5)}$

$\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}$

$\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10$

LHS = RHS: cot 10 = cot 10 $\checkmark$

8 0

3 years ago