The table of values and their graph show above a straight line that passes through the origin. This indicates that the relationship between the two currencies is in direct proportion. Think about what this means in real terms – if you have ten times more dollars than another person, when you both exchange your money, you will still have ten times more money. Notice also that the graph passes through the origin; this makes sense as if you have no dollars you will get no pounds!

We can express these relationships algebraically as well as graphically.

4 0

3 years ago

two airplane fly toward each other from points 900 miles apart, at the rate, per hour, of 300 miles and 250 miles. when will the

mojhsa [17]

They complete a 900-mile distance with their combined speed of (300+250=550) mph
Therefore, they meet after 900m/550mph=18/11h=1.6364h

6 0

3 years ago

Find dy/dx if y =x^3+5x+2/x²-1

stiks02 [169]

<u>Differentiate using the Quotient Rule</u> –

$\qquad$ $\pink{\twoheadrightarrow \sf \dfrac{d}{dx} \bigg[\dfrac{f(x)}{g(x)} \bigg]= \dfrac{ g(x)\:\dfrac{d}{dx}\bigg[f(x)\bigg] -f(x)\dfrac{d}{dx}\:\bigg[g(x)\bigg]}{g(x)^2}}\\$

According to the given question, we have –

f(x) = x^3+5x+2
g(x) = x^2-1

Let's solve it!

$\qquad$ $\green{\twoheadrightarrow \bf \dfrac{d}{dx}\bigg[ \dfrac{x^3+5x+2 }{x^2-1}\bigg]} \\$

$\qquad$ $\twoheadrightarrow \sf \dfrac{(x^2-1) \dfrac{d}{dx}(x^3+5x+2) - ( x^3+5x+2) \dfrac{d}{dx}(x^2-1)}{(x^2-1)^2 }\\$

$\qquad$ $\twoheadrightarrow \sf \dfrac{(x^2-1)(3x^2+5) - ( x^3+5x+2) 2x}{(x^2-1)^2 }\\$

$\qquad$ $\pink{\sf \because \dfrac{d}{dx} x^n = nx^{n-1} }\\$

$\qquad$ $\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-(2x^4+10x^2+4x)}{(x^2-1)^2 }\\$

$\qquad$ $\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-2x^4-10x^2-4x}{(x^2-1)^2 }\\$

$\qquad$ $\green{\twoheadrightarrow \bf \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}\\$

$\qquad$ $\pink{\therefore \bf{\green{\underline{\underline{\dfrac{d}{dx} \dfrac{x^3+5x+2 }{x^2-1}} = \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}}}}\\\\$

7 0

2 years ago

Factor the equation: 25x^2-5xy-5xy^2+y^3-y^2

lianna [129]

Answer:

−5xy^2+y^3+25x^2−5xy−y^2

Step-by-step explanation:

25x^2−5xy−5xy^2+y^3−y^2=

25x^2−5xy−2

———————————-

7 0

3 years ago