MATHEMATICS COLLEGE

Solve the exponential equation:

Answers

Answer 1

Answer:

Step-by-step explanation:

2⁵ˣ = 8ˣ⁺²

2⁵ˣ = (2³)ˣ⁺²

2⁵ˣ = 2³ˣ⁺⁶

5x = 3x + 6

2x = 6

x = 3

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On a coordinate plane, point M is located at (-5,1) and point N is located at (-5,8)

Answers

Answer:

7 units

Step-by-step explanation:

d=√(x2-x1)² + (y2-y1)²

x1=-5

x2=-5

y1=1

y2=8

d=√(-5--5)² + (8-1)²

d=√0² + 7²

d=√49

d= 7 units

An automobile purchased for 22,000 is worth 2500 after 5 yrs. Assuming that the cars value deprecited steadily from year to year, what was it worth at the end of third year

Answers

Original price = 22000
New price = 2500
Amount depreciated in 5 years = 22000 - 2500
=19500
Amount depreciated in 1 year = 19500/5
= 3900
Worth after 3 years = 22000 - 3(3900)
= 10300

Plzzz help fast I need the answer

Answers

Answer: (The first number are the years and the second are the amount of Komodo's) (0, 0) (1, 4) (2, 20) (3, 100) (4, 500) (5, 2,500)

Step-by-step explanation:

If there are 4 Komodo's in the first year because that's when they moved in, then there would be zero in the 0 year.

If they keep multiplying their population by 5 each year then for every year, you would multiply the existing population of that year by 5

Starting at year 1 which is (1, 4) multiply that by 5 to get 20 and so on to get the function.

I hope this helps!

Jared ate 1/4 of a loaf bread. He cut the rest of loaf into slices. How many slices of bread did he cut?

Answers

Answer: He cut 6 slices of bread.

Step-by-step explanation:

Given : Jared ate $(1)/(4)$ of a loaf of bread.

Then , the reaming portion of the bread will be $1-(1)/(4)=(4-1)/(3)=(3)/(4)$ .

The size of each slice = $(1)/(8)$ of a bread.

N ow , the number of slices he cut the remaining portion = $(3)/(4)/(1)/(8)$

$=(3)/(4)*8=6$

Hence, the number of slices of bread he cut = 6.

3 slices because he ate 1 slice ( 1/4) (2/4) (3/4) (4/4) so 3 slices

Pleeease open the image and hellllp me

Answers

1. Rewrite the expression in terms of logarithms:

$y=x^x=e^(\ln x^x)=e^(x\ln x)$

Then differentiate with the chain rule (I'll use prime notation to save space; that is, the derivative of y is denoted y' )

$y'=e^(x\ln x)(x\ln x)'=x^x(x\ln x)'$

$y'=x^x(x'\ln x+x(\ln x)')$

$y'=x^x\left(\ln x+\frac xx\right)$

$y'=x^x(\ln x+1)$

2. Chain rule:

$y=\ln(\csc(3x))$

$y'=\frac1{\csc(3x)}(\csc(3x))'$

$y'=\sin(3x)\left(-\cot^2(3x)(3x)'\right)$

$y'=-3\sin(3x)\cot^2(3x)$

Since $\cot x=(\cos x)/(\sin x)$ , we can cancel one factor of sine:

$y'=-3(\cos^2(3x))/(\sin(3x))=-3\cos(3x)\cot(3x)$

3. Chain rule:

$y=e^{e^(\sin x)}$

$y'=e^{e^(\sin x)}\left(e^(\sin x)\right)'$

$y'=e^{e^(\sin x)}e^(\sin x)(\sin x)'$

$y'=e^{e^(\sin x)+\sin x}\cos x$

4. If you're like me and don't remember the rule for differentiating logarithms of bases not equal to e, you can use the change-of-base formula first:

$\log_2x=(\ln x)/(\ln2)$