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s344n2d4d5 [400]
3 years ago
6

100 POINTS PLEASE EXPLAIN AND ADD STEPS. THANK YOU IN ADVANCE

Mathematics
2 answers:
e-lub [12.9K]3 years ago
8 0

Given one to one f(6)=3, f'(6)=5, find tangent line to y=f⁻¹(x) at (3,6)

OK, we know

f⁻¹(3)=6

The inverse function is the reflection in y=x.  So slopes, i.e. the derivative will be the reciprocal.  We know the derivative of f at 6 is 5, so the derivative of f⁻¹  at y=6 is 1/5, which corresponds to x=3.

f⁻¹ ' (3) = 1/5

That slope through (3,6) is the tangent line we seek:

y - 6 = (1/5) (x-3)

That's the tangent line.

y = x/5 + 27/5

Rufina [12.5K]3 years ago
3 0

First, find the inverse function.

Note that an inverse is a reflection; y = x

The derivative given will be the reciprocal and when f is at 6, it equals 5. So, when it is at y = 6 it is at x = 1/5 and corresponds to 3.

f^-1(3) = 1/5

The point (3, 6) is the point in which the slope goes through. We can write all this information in slope-intercept form.

y = 1/5x + 27/5

Best of Luck1

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MrRa [10]

The amount he should sell for one bottle of the fizzy juice to make the 60% profit is 22 Penny.

<h3>Cost of each juice</h3>

Orange :  Lemonade

  3  :  5

After buying 2 liters of orange juice and 3 liters of lemonade, cost of each;

Increase the ratio to form divisible by 2 and 3; (L.C.M of 2 and 3 = 6)

(3 x 6L)  :  (5 x 6L)

18L  :  30L      

total fizzy juice = 18L + 30L = 48 liters

bottle of orange = (18 L ÷ 2 L) = 9 bottles

bottle of lemonade = (30 L ÷ 3L ) = 10 bottles

cost of orange = 9 x £1.20 = £10.8

cost of lemonade = 10 x £1.50 = £150

Total cost = £10.8 +  £150 =  £25.80 =  2580 P

<h3>Total bottles that will make 48 liters fizzy juice</h3>

250 mL = 0.25 L

0.25L(n) = 48 L

n = 48/0.25

n = 192 bottles

<h3>Cost of each bottle in Penny</h3>

cost = 2580 P/192

cost = 13.44 P

<h3>Amount each bottle should be sold to make a profit of 60%</h3>

A = 100%(initial cost) + 60%(initial cost)

A = 160%(initial cost)

A = 1.6(initial cost)

A = 1.6 x 13.44 P

A = 21.5 P ≈ 22 P

Learn more about profit here: brainly.com/question/1078746

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2 years ago
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3 years ago
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I = Prt
Olegator [25]

Answer:

r=3.5\%

Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=5\ years\\ P=\$1,200\\ I=\$210\\r=?

substitute in the formula above

210=1,200(5r)

solve for r

r=210/6,000

r=0.035

convert to percentage (multiply by 100)

r=3.5\%

6 0
3 years ago
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