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3 years ago

What are the roots of this quadratic equation? 3x^2+10=4x

Mathematics

1 answer:

____ [38]3 years ago

6 0

Step-by-step explanation:

The root of an equation is when x=0.

We need to rewrite this as 3x²-4x+10=0.

The quadratic formula is

(-b+or-sqrt(b²-4ac))/2a

so 4+or-sqrt(16-120)/2a

since the sqrt can no be negative this answer will have imaginary numbers.

(4+2i sqrt(26))6 and (4-2i sqrt(26))6

simplified is

x=(2+i sqrt(26))/3 and x=(2-i sqrt(26))/3

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A lake polluted by bacteria is treated with an antibacterial chemical. Aftertdays, thenumber N of bacteria per milliliter of wat

jeyben [28]

Answer:

N(1)=50 is a minimum

N(15)=4391.7 is a maximum

Step-by-step explanation:

<u>Extrema values of functions </u>

If the first and second derivative of a function f exists, then f'(a)=0 will produce values for a called critical points. If a is a critical point and f''(a) is negative, then x=a is a local maximum, if f''(a) is positive, then x=a is a local minimum.

We are given a function (corrected)

$N(t) = 20(t^2-lnt^2)+ 30$

$N(t) = 20(t^2-2lnt)+ 30$

(a)

First, we take its derivative

$N'(t) = 20(2t-\frac{2}{t})$

Solve N'(t)=0

$20(2t-\frac{2}{t})=0$

Simplifying

$2t^2-2=0$

Solving for t

$t=1\ ,t=-1$

Only t=1 belongs to the valid interval $1\leqslant t\leqslant 15$

Taking the second derivative

$N''(t) = 20(2+\frac{2}{t^2})$

Which is always positive, so t=1 is a minimum

(b)

$N(1)=20(1^2-2ln1)+ 30$

N(1)=50 is a minimum

(c) Since no local maximum can be found, we test for the endpoints. t=1 was already determined as a minimum, we take t=15

(d)

$N(15)=20(15^2-2ln15)+ 30$

N(15)=4391.7 is a maximum

7 0

3 years ago

I need help with this pls

antoniya [11.8K]

I'll explain it simply for you

1st question
Of course you know phythagoras theorm
You even wrote it up there
It states that the sum of the square of the two sides of an equilateral triangle is equal to the square of the hypotenuse
${a}^{2} + {b}^{2} = {c}^{2}$
Where C is the hypotenuse
*NOTE* :
HYPOTENUSE is the greatest side in a triangle!!
And that's where your mistake is!
So you should take the greatest side as C
So in Q3. 7, 24 and 26 are the given numbers
You'll make the smaller two numbers a and b and the greatest number C
Using the Formula you'll solve the left side first which is
${a}^{2} + {b}^{2}$
Then the right side which is
${c}^{2}$

And if both are equal then it is a right triangle otherwise it isn't!
Let
a=7
b=24
c=26

a^2 + b^2
7^2 + 24^2
49 + 576 = 625
GREAT, Now the right side

26^2 = 676
Since they aren't equal it isn't a right angled triangle...

Then let
a=7.5
b=10
c=12.5

7.5^2 + 10^2
= 56.25 + 100
= 156.25

12.5^2 = 156.25

They are EQUAL
Therefore it is a right triangle too

Hopefully I helped

7 0

3 years ago

how many pounds of rock will you need to fill an area 25 ft by 35 ft to a depth of 2 in. If the rock weighs 1050 lb cubic yard?

Eduardwww [97]

The volume of the area is Length x width x height:

25 x 35 x 2/12 = 145.83 cubic feet.

1 cubic foot = 0.037 cubic yards:

145.83 x 0.037 = 5.40 cubic yards.

5.4 cubic yards x 1050 lbs/ cubic yard = 5,665.6 pounds.

Note:

Rounding and conversion may change the answer slightly, but I believe I rounded everything as it should be.

6 0

3 years ago

What would the graph look like

Alex777 [14]

Answer I cant read the thing sorry

Step-by-step explanation:

hoped that hepled:)

6 0

2 years ago

Select all the correct answers.

rusak2 [61]

Answer:

a & c

Step-by-step explanation:

5 0

3 years ago