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2 years ago

What is the equation of the asymptote? f (x) = 3^x-5+1 y=?

Mathematics

1 answer:

Natasha_Volkova [10]2 years ago

4 0

The equation of the asymptote is $y=1$

Explanation:

The given equation is $f(x)=3^{x-5}+1$

We need to determine the horizontal asymptote of the equation.

The given equation is of the exponential function of the form $f(x)=c \cdot n^{a x+b}+k$ and has a horizontal asymptote $y=k$

Hence, from the above equation, the value of k is 1.

Therefore, we have,

$k=1$

Thus, the horizontal asymptote is $y=1$

Therefore, the asymptote of the equation is $y=1$

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Sarah had invested $800 in a savings account that paid 4.2% interest compounded annually. How much money was in the account afte

schepotkina [342]

Answer: $943.11

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

Compound Interest formula is: $A=P(1+r)^t$ where

A is the Accrued amount (total earned)
P is the Principal (amount initially invested)
r is the interest Rate (convert percent to a decimal)
t is the Time (number of years)

It is given that; P = 800 r = 4.2% (0.042) t = 4

A = 800(1 + 0.042)⁴

A = 800(1.042)⁴

A = 943.106 → A = 943.11 (rounded to the nearest penny)

Sarah invested $800 for four years at an interest rate of 4.2% and accrued $943.11

5 0

3 years ago

Scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. The temperature of the gaseous plan

vladimir1956 [14]

Answer:

its 450 k

Step-by-step explanation:

It is given that the temperature of the gaseous planet is linearly related with height of the atmosphere. we can write this in the mathematical equation:

y = m x +c

where y is the temperature values, x is height, m is the slope and c is the y-intercept. we have been given two sets of value in the image, using which we can find the value of slope in y-intercept.

at x = 18.40 km, y = 147.54 K

⇒147.54 = 18.40 m + c

⇒c = 147.54 - 18.40 m ..(1)

at x =78.11 km, y = 567.00 K

⇒567.00 =78.11 m + c ..(2)

Put equation 1 in 2 and solve:

⇒567.00 =78.11 m + 147.54 - 18.40 m

⇒419.46 = 59.71 m

⇒ m =419.46 ÷59.71 = 7.025 K/km

c = 147.54 - 18.40 × 7.025 = 18.28 K

At height, x = 61.5 km the approximate temperature is :

y = 7.025 K/km × 61.5 km + 18.28 K = 450.3 K

Thus, the approximate temperature at altitude 61.5 km is 450 K.

7 0

3 years ago

Please help! :):):);)

AnnZ [28]

Answer:

So 60% of this unknown number is 28

Let this unknown number be n

60/100 × n = 28

0.60 × n = 28

n = 28/0.6

n = 46.7

To the nearest wholw number is 47

So there are 47 votes in total

6 0

3 years ago

diketahui luas permukaan kubus 864 cm2. perbandingan rusuk kubus dan p balok 3 : 4 perbandingan p l dan tinggi 4:3:2 luas permuk

Kryger [21]

S2= 864/6
s = = 12 cm
p = 4/3 x 12 = 16 cm
t = 2/4 x 16 = 8 cm
l= 3/4x 16 = 12 cm

lp= 2 (pl+pt+lt)
= 2 (16 x 12 + 16 x 8 + 12 x8)
= 2 (192+128+96) = 832cm²

3 0

3 years ago

Suppose Y varies directly with X and Y equals 10 when X equals -3 what direct variation equation relates XNY what is the value o

xeze [42]

Answer:

Expression: Y = -10/3 X

Y = 10/3

Step-by-step explanation:

If Y varies directly as X, then;

Y∝X

Y = kX

k is the constant of variation

If Y = 10 and X = -3

10 = -3k

k = -10/3

Substitute k = -10/3 into the expression Y = kX

Y = -10/3 X

This gives the required expression

To get the value of Y when X = -1

Recall that Y = kX

Y = -10/3 (-1)

Y = 10/3

Hence the value of Y is 10/3

8 0

2 years ago