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3 years ago

Write an exponential function in the form y=ab^xy=ab^x that goes through points (0, 20) and (3, 1280).

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

5 0

Answer:

y = 20 $4^{x}$

Step-by-step explanation:

Use the points to find the values of a and b

Using (0, 20 ) , then

20 = a $b^{0}$ [ $b^{0}$ = 1 ] , then

20 = a

y = 20 $b^{x}$

Using (3, 1280 ) , then

1280 = 20 b³ ( divide both sides by 20 )

64 = b³ ( take the cube root of both sides )

$\sqrt[3]{64}$ = b , that is

4 = b

Then exponential function is

y = 20. $4^{x}$

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Find the point on the line y = 2x + 3 that is closest to the origin.

ch4aika [34]

1)We have to make a line perpendicular to y=2x+3, passing through the point (0,0).

y=2x+3
m=solpe=2

The slope of the line perpedicular to y=2x+3 is m´
m´=-1/m
m´=-1/2

Point slope form:
y-y₀=m(x-x₀)
(0,0)
m=-1/2

y-0=-1/2(x-0)
y=-x/2

Therefore, the line perpendicular to y=2x+3 is y=-x/2.

2)The point on the line y=2x+3 tha is closest to the origin is the point of intersection of the two lines.

y=2x+3
y=-x/2

We can solve this system of equations by equalization method.
2x+3=-x/2
least common multiple=2
4x+6=-x
4x+x=-6
5x=-6
x=-6/5 (=-1.2)

y=-x/2
y=-(-6/5)/2=6/10=3/5 (=0,6)

Therefore: the point of the line y=2x+3 that is closest to the origin is:
(-1.2 , 0.6)

3 0

3 years ago

Lin and Jada each walk at a steady rate from school to the library. Lin can walk 13 miles in 5 hours, and Jada can walk 25 miles

astra-53 [7]

Answer:

It will take Lin an hour and 25 minutes at her constant speed, and it will take Jada at her constant speed an hour and 30 minutes.

SO, Lin will arrive at 4:25

and Jada will arrive at 4:30

There is a 5 minute difference in time.

Step-by-step explanation:

From the facts given, Lin can walk 13 miles in 5 hours which when you divide means she can walk 2.6 mph (miles per hour), and Jada can walk 2.5 mph.

To get these answers you divide the current speeds into the total distance

For example, in Lin's case...

3.25 (The 3 and 1/4 mile converted to decimal form)

2.6 (Lin's Average speed per hour)

3.25/2.6=1.25

1.25 (1 hour and 25 minutes)

5 0

4 years ago

HELPPP PLZ WHATS THE ANSWER PLZ DONT SEND A FILE PLZ. what is this question going across is going across the y or it going acros

gulaghasi [49]

number 3 going across the x axis

number 5 going across the y axis

4 0

3 years ago

an electrician charges $50 to make a house call and $49 for each hour worked. if you have $200, can u afford a repair that takes

Alexxandr [17]

You would not be able to afford it.
If you use the equation y=mx+b and y= 200, m=49, x=4, and b=50, and you solve the equation that way,
You will find that it will cost $246, which is $46 over your budget.
Hope this helps!

7 0

3 years ago

Currently requiring a little help on this, would not mind any answer <3

trasher [3.6K]

$\bf \sqrt{\cfrac{50x^6y^3}{9x^8}}=\cfrac{5y^c\sqrt{2y}}{dx}\\\\
-------------------------------\\\\
\sqrt{\cfrac{50x^6y^3}{9x^8}}~~
\begin{cases}
50=2\cdot 25\\
\qquad 2\cdot 5^2\\
x^6=x^{3\cdot 2}\\
\qquad (x^3)^2\\
y^3=y^{2+1}\\
\qquad y^2\cdot y\\
9=3^2\\
x^8=x^{4\cdot 2}\\
\qquad (x^4)^2
\end{cases}\implies \cfrac{\sqrt{50x^6y^3}}{\sqrt{9x^8}}\implies \cfrac{\sqrt{2\cdot 5^2(x^3)^2\cdot y^2\cdot y}}{\sqrt{3^2(x^4)^2}}$

$\bf \cfrac{5x^3y\sqrt{2y}}{3x^4}\implies \cfrac{5y\sqrt{2y}}{3x^4x^{-3}}\implies \cfrac{5y\sqrt{2y}}{3x^{4-3}}\implies \cfrac{5y^{\stackrel{\downarrow }{1}}\sqrt{2y}}{\stackrel{\downarrow }{3} x}$

7 0

3 years ago