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3 years ago

Is 2/5 greater than or less than 4/5?

Mathematics

2 answers:

belka [17]3 years ago

8 0

It is less because u can count the gap and 4 is only 1 away from 5 while 2 is 3 away from 5 :]

motikmotik3 years ago

3 0

Is less, please mark mine as the brainlest answer!!!

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If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?

Oduvanchick [21]

$\large\underline{\sf{Solution-}}$

Given:

$\rm \longmapsto x = a \sin \alpha \cos \beta$

$\rm \longmapsto y = b \sin \alpha \sin \beta$

$\rm \longmapsto z = c\cos \alpha$

Therefore:

$\rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta$

$\rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta$

$\rm \longmapsto \dfrac{z}{c} = \cos \alpha$

Now:

$\rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} }$

$\rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha$

$\rm = 1$

Therefore:

$\rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1$

5 0

3 years ago

The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Check all that apply.

Bezzdna [24]

Since the coefficient of x^2 is negative, which means that the parabola is facing down. Hence, the vertex is maximum value.
f(-1) = -3(-1)^2 - 3(-1) + 6 = -3(1) - (-3) + 6 = -3 + 3 + 6 = 6
f(-0.5) = -3(-0.5)^2 - 3(-0.5) + 6 = -3(0.25) - (-1.5) + 6 = -0.75 + 1.5 + 6 = 6.75
f(0) = -3(0)^2 - 3(0) + 6 = 0 + 0 + 6 = 6
From the above, the graph stopped increasing at x = -0.5 and started decreasing. Hence, the axis of symmetry is x = -1/2
The domain of all quadatic expression is all real numbers because there is no value of x for which f(x) does not exist.
The range is NOT all real numbers because for instance, there is no value of x for which f(x) = 7.
f(-2) = -3(-2)^2 - 3(-2) + 6 = -3(4) - (-6) + 6 = -12 + 6 + 6 = 0
f(1) = -3(1)^2 - 3(1) + 6 = -3(1) - 3 + 6 = -3 + 3 = 0
Hence, the x-intecepts are at (-2, 0) and (1, 0)
The function is INCREASING from (−∞, 6.75)

6 0

3 years ago

Read 2 more answers

761.8 x 10^-8 Express the number in scientific notation. A) 7.618 x 10^-6 B) 7.618 x 10^-8 C) 7.618 x 10^2 D) 7.618 x 10^6

ludmilkaskok [199]

Answer:

$\huge\boxed{A)\ 7.618\times10^{-6}}$

Step-by-step explanation:

The scientific notation:

$a\cdot10^n$

where

$1\leq a$

We have

$761.8\times10^{-8}$

We need to move the decimal point two places to the left.

$\underbrace{(7.618\times10^2)}_{=761.8}\times10^{-8}=7.618\times(10^2\times10^{-8})$

use

$a^n\cdot a^m=a^{n+m}$

$=7.618\times10^{2+(-8)}=7.618\times10^{-6}$

4 0

3 years ago

What is the quotient [3y+2/3y] / [6y^2+4y/3y+2]

givi [52]

[3y+2/3y] / [6y^2+4y/3y+2]
Steps
First, divide fractions
= (3y + 2)(3y + 2)/3y(6y^2 + 4y)
Then... factor 3y(6y^2 + 4y): 6y^2(3y + 2)
= (3y + 2)(3y + 2)/6y^2(3y + 2)
Then, cancel the common factor: 3y + 2
= 3y + 2/6y^2

6 0

4 years ago

Read 2 more answers

What's the answer this is equivalent fractions

IceJOKER [234]

The answer is 3/4 because if u count it up it equals 36/48 and then u just have to simplify

3 0

3 years ago