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bogdanovich [222]
2 years ago
6

From first principle find the derivative of logx​

Mathematics
1 answer:
Archy [21]2 years ago
4 0

Hello!

\large\boxed{\frac{dy}{dx}logx = \frac{1}{xln10}  }

Recall that:

logx can be rewritten as:

log_{10}x

Use the equation for the derivative of a log expression:

\frac{dy}{dx}log_{a}u = \frac{1}{ulna} * u'

Substitute in the values in the expression:

logx = \frac{1}{xln10} * 1 = \frac{1}{xln10}

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A company needs to make at least A company needs to make at least 75,000 bottles 20-oz bottles can made from 1 pound if plastic
strojnjashka [21]

Answer:

By using the recycled plastic the company will save $1050.

Step-by-step explanation:

A company needs to make at least 75,000 bottles.

Now, 20-oz bottles can be made from 1 pound.

Then, 75000-oz bottles can be made from \frac{75000}{20} = 3750 pounds of plastic.

Now, the cost of new plastic is $0.83 per pound.

So, cost of new plastic to make 75000 bottles will be $(3750 × 0.83) = $3112.5.

Again,  the cost of recycled plastic is $0.55 per pound.

So, cost of recycled plastic to make 75000 bottles will be $(3750 × 0.55) = $2062.5.

Therefore, by using the recycled plastic the company will save $(3112.5 - 2062.5) = $1050. (Answer)

3 0
3 years ago
3(x+2)=-5-2(x-3)<br>helps plzs!!!!!.....<br>​
konstantin123 [22]
3x+6=-5-2x-6
3x=-5-2x-6-6
3x+2x=-5-6-6
5x=-17
X=-17/5
X=-3.4
7 0
3 years ago
Please could you find the answers to the questions in the attachment.
Fudgin [204]
(\frac{x1+x2}{2} , \frac{y1+y2}{2})we need 3 equations
1. midpoint equation which is  (\frac{x1+x2}{2} , \frac{y1+y2}{2}) when you have 2 points

2. distance formula which is D= \sqrt{(x2-x1)^{2}+(y2-y1)^{2}}

3. area of trapezoid formula whhic is (b1+b2) times 1/2 times height


so

x is midpoint of B and C
B=11,10
c=19,6
x1=11
y1=10
x2=19
y2=6
midpoint=(\frac{11+19}{2} , \frac{10+6}{2})
midpoint=(\frac{30}{2} , \frac{16}{2})
midpoint= (15,8)

point x=(15,8)



y is midpoint of A and D
A=5,8
D=21,0
x1=5
y1=8
x2=21
y2=0
midpoint=(\frac{5+21}{2} , \frac{8+0}{2})
midpoint=(\frac{26}{2} , \frac{8}{2})
midpoint=(13,4)

Y=(13,4)



legnths of BC and XY
B=(11,10)
C=(19,6)
x1=11
y1=10
x2=19
y2=6
D= \sqrt{(19-11)^{2}+(6-10)^{2}}
D= \sqrt{(8)^{2}+(-4)^{2}}
D= \sqrt{64+16}
D= \sqrt{80}
D= 4 \sqrt{5}
BC=4 \sqrt{5}





X=15,8
Y=(13,4)
x1=15
y1=8
x2=13
y2=4
D= \sqrt{(13-15)^{2}+(4-8)^{2}}
D= \sqrt{(-2)^{2}+(-4)^{2}}
D= \sqrt{4+16}
D= \sqrt{20}
D= 2 \sqrt{5}
XY=2 \sqrt{5}


the thingummy is a trapezoid
we need to find AD and BC and XY
we already know that BC=4 \sqrt{5} and XY=2 \sqrt{5}

AD distance
A=5,8
D=21,0
x1=5
y1=8
x2=21
y2=0
D= \sqrt{(21-5)^{2}+(0-8)^{2}}
D= \sqrt{(16)^{2}+(-8)^{2}}
D= \sqrt{256+64}
D= \sqrt{320}
D= 4 \sqrt{2}
AD=4 \sqrt{2}


so we have
AD=4 \sqrt{2}
BC=4 \sqrt{5} 
XY=2 \sqrt{5}

AD and BC are base1 and base 2
XY=height
so
(b1+b2) times 1/2 times height
(4 \sqrt{2}+4 \sqrt{5}) times 1/2 times 2 \sqrt{5} =
(4 \sqrt{2}+4 \sqrt{5}) times \sqrt{5} [/tex] =
4 \sqrt{10}+4*5=4 \sqrt{10}+20=80 \sqrt{10}=252.982


























X=(15,8)
Y=(13,4)
BC=4 \sqrt{5}
XY=2 \sqrt{5}
Area=80 \sqrt{10} square unit or 252.982 square units







7 0
3 years ago
Which equation best represents a trend line for the scatter plot?
kvasek [131]
Y = (-3/7)x + 4

Looking at the graph, you can see the trend line plotted. And conveniently, there are a couple of points on the trend line that are indicated. Those points being (0,4) and (7,1). The equation of a line in slope intercept form is:y = ax+b

Looking at the points available, the point (0,4) already gives us the y intercept since x is equal to 0. So our equation becomes:
y = ax + 4

Now we need to determine a which is the slope. The slope is the change in y divided by the change in x. So let's do that
(1-4)/(7-0) = -3/7

And now our equation becomes:
y = (-3/7)x + 4

And given formatting issues, the first option available is the correct one.
3 0
3 years ago
Read 2 more answers
If someone could help me figure out #7 ASAP I’d really appreciate it
IceJOKER [234]

Answer: Angle N

Explanation:

For triangle ABC, we refer to the middle angle, Angle B.

For triangle MNP, we refer to its middle angle, Angle N.

Good luck!

8 0
2 years ago
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