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kifflom [539]
3 years ago
8

In early spring, you buy 6 potted tomato plants for your container garden. The plants contained in 8 inch pots sell for $5 and t

he plants contained in 10 inch pots sell for $8. If you spend $36, how many of each size are you buying?
Mathematics
1 answer:
prohojiy [21]3 years ago
3 0
X - the number of plants in 8 in pots
y - the number of plants in 10 in pots

x+y=6\\
5x+8y=36\\\\
x=6-y\\
5x+8y=36\\
5(6-y)+8y=36\\
30-5y+8y=36\\
3y=6\\
y=2\\\\
x+2=6\\
x=4

4 plants in 8 in pots and 2 in 10 in pots.

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Consider the function g(x) = (x-e)^3e^-(x-e). Find all critical points and points of inflection (x, g(x)) of the function g.
Elden [556K]

Answer:

The answer is "cirtical\  points \ (x,g(x))\equiv  (e,0),(e+3,\frac{27}{e^3})"

Step-by-step explanation:

Given:

g(x) = (x-e)^3e^{-(x-e)}

Find critical points:

g(x) = (x-e)^3e^{(e-x)}

differentiate the value with respect of x:

\to g'(x)= (x-e)^3 \frac{d}{dx}e^{e-r} +e^{e-r}  \frac{d}{dx}(x-e)^3=(x-e)^2 e^{(e-x)} [-x+e+3]

critical points g'(x)=0

\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3

So,

The critical points of (x,g(x))\equiv  (e,0),(e+3,\frac{27}{e^3})

7 0
3 years ago
Thang decided to borrow ​$4000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of
BlackZzzverrR [31]

Answer:

840

Step-by-step explanation:

I=PRT

I =4000 x 0.07 x 3

I=840

3 0
3 years ago
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Raul has 4 identical baseballcards of his favorite player. According to his monthly price guide, the change in value of one of t
MrRissso [65]
0,48 because 4x0.12 is 0.48
5 0
3 years ago
!!!PLEASE HELP ME !!! AND INCLUDE AN EXPLANATION
Ede4ka [16]

Since you have the 42-deg angle and the length of the opposite side, 31, you can use the Law of Sines.


\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}


We will use the law of sines first to find x.

Once we know x, we can find the angle opposite y.

Then we can find y.


\dfrac{31}{\sin 42^\circ} = \dfrac{37}{\sin x}


\sin x = \dfrac{37\sin 42^\circ}{31}


\sin x = 0.798639


x = \sin^{-1} 0.798639 = 53^\circ


Let z = the angle opposite y.


z + 42 + 53 = 180


z = 85

\dfrac{31}{\sin 42^\circ} = \dfrac{y}{\sin 85^\circ}


y = \dfrac{31 \sin 85^\circ}{\sin 42^\circ}


y = 46.2


3 0
3 years ago
Triangle CDE has been rotated 90° in a clockwise direction. Based on the figure, which would be a correct name for the image of
Goryan [66]

Answer:

C'D'E'

Step-by-step explanation:

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3 years ago
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