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3 years ago

Factor 2x4 - 20x2 - 78.

Mathematics

2 answers:

Komok [63]3 years ago

8 0

Answer:

2(x² + 3)(x² - 13)

Step-by-step explanation:

2x⁴ - 20x² - 78

Factor out 2.

2(x⁴ - 10x² - 39)

Find 2 numbers that multiply to get -39 and add to get -10. Those numbers are -13 and 3.

2(x⁴ - 13x² + 3x² - 39)

2(x² + 3)(x² - 13)

Airida [17]3 years ago

7 0

Answer:

2x⁴ - 20x² - 78

To factor the expression look for the LCM of the numbers

LCM of the numbers is 2

Factorize that one out

That's

2( x⁴ - 10x² - 39)

Hope this helps

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A sector of a circle has central angle θ=5π/6 and area 15π ft2. Find the radius of this circle.

Natali [406]

5pi/6 r^2 = 15pi

R^2 = 18

R= 3sqrt(3)

6 0

3 years ago

Please help!! Giving brainliest and extra points!! (Click on photo)

MArishka [77]

Answer:

Step-by-step explanation:

5 0

3 years ago

I think its C, not sure

Alona [7]

Yes; you are correct.
___________________________________________________
The correct answer is:
___________________________________________________
Answer choice: [C]: " x³ − 9x² + 23x − 12 " .
___________________________________________________
Note: (a − b) (c − d + e) = ac − ad + ae − bc + bd − be ;
___________________________________________________
(x − 4) (x² − 5x + 3) =

x * x² = x³ −

x * 5x = 5x² +

x * 3 = 3x −

4 * x² = 4x² −

-4 * 5x = -20x +

-4 * 3 = -12;
________________________________________
 (x − 4) (x² − 5x + 3) =

x³ − 5x² + 3x −4x² − (-20x) + (-12) ;

= x³ − 5x² + 3x −4x² + 20x − 12 ;

= x³ − 5x² − 4x² + 3x + 20x − 12 ;

= x³ − 9x² + 23x − 12 ; which is:
__________________________________________________
Answer choice: [C]: " x³ − 9x² + 23x − 12 " .
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7 0

3 years ago

A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

kkurt [141]

Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

Volume of box, V= $b^2h$

Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

$\implies 3b^2=18$

$b^2=6$

$b=\pm \sqrt{6}$

$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

7 0

3 years ago

Please answer all questions thank you.

Ad libitum [116K]

1) 78.5/pi = 25
radius = 5
The one 5 digits away from that coordinate is (2,-1)

2) This question is area, not perimeter. The width and length has to be added by 4 because of 2 feet on both sides.
9*10 = 90 - 30 = 60

3) 25pi according to pythagorean theorem.

4 0

3 years ago