All categories

3 years ago

Simplify (2√5+3√7)^2

2 answers:

5 0

(2 sq. root 5 + 3 sq. root 7)(2 sq. root 5 + 3 sq. root 7)

4•sq root 25 + 6 sq. root 35 + 6 sq. root 35 + 9 sq. root 49

4 • 5 + 12 sq. root 35 + 9 • 7

20 + 12 sq. root 35 + 63.

I believe this would be the solution.

Anna35 [415]3 years ago

3 0

The answer is: 83 + 12√35

(a + b)² = a² + 2ab + b²

In (2√5 + 3√7)², a = 2√5, b = 3√7

Just substitute a and b:
(a + b)² = a² + 2ab + b² = (2√5)² + 2 * 2√5 * 3√7 + (3√7)² =
= 2²√5² + 2 * 2 * 3 * √5 * √7 + 3²√7² =
= 4 * 5 + 12 * √(5*7) + 9 * 7 =
= 20 + 12 *√35 + 63 =
= 83 + 12√35

You might be interested in

!!!!!!!!!HELP ASAP!!!!!!! WORTH 20 POINTS

Juliette [100K]

F(x)=∛x

The domain will be all real numbers.

Answer: A) all real numbers.

Ej: if x=-8 ⇒∛-8=-2

8 0

3 years ago

Hi! I need help with the attached question in calc. Thank you:)

Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

$\displaystyle V=\pi \int_a^b [R(y)]^2\, dy$

So:

$\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy$

Simplify:

$\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy$

Integrate:

$\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]$

Evaluate (I ignored the 0):

$\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi$

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

$\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi$

We acquire the exact same answer.

8 0

3 years ago

Is this linear or non-linear???

max2010maxim [7]

Answer:

This would be non linear

Step-by-step explanation:

Because a linear is a straight line

this would not equal to a straight line so it is non linear

have a nice day uvu

3 0

3 years ago

Read 2 more answers

A circle has a radius of 10. An arc in circle has a central angle of 72 what is the length of the arc

BARSIC [14]

Answer:

4π

Step-by-step explanation:

-A circle subtends a total angle of 360 ° from its center.

-The length of an arc is directly proportional to the angle it subtends from the circle's center.

#The arc's length can therefore be calculated as:

$C=\pi D=2\pi r\\\\\therefore C=\frac{72\textdegree}{360\textdegree}\times 2\pi \times 10\\\\=4\pi$

Hence, the length of the arc is 4π

5 0

3 years ago

Can you guys please do both with the work please and thank you if you actually do it

salantis [7]

Answer:

7. 29 cm

8. equation: 61 = (x) +(2x -7) +(3x +2); sides 11, 15, 35

Step-by-step explanation:

7. Let w represent the width. The length is 3 less than twice the width, so the length is 2w-3. The perimeter is given by the formula ...

P = 2(L+W)

Substituting the known values, we have ...

90 = 2((2w-3) +w)

45 = 3w -3 . . . . . . . . divide by 2

15 = w - 1 . . . . . . . . . .divide by 3

16 = w . . . . . . . . . . . . add 1

L = 2w -3 = 2(16) -3 = 29

The length of the rectangle is 29 cm.

8. The equation that should be used is the one that relates the side lengths to the perimeter.

P = a + b + c . . . . for sides a, b, c

61 = (x) +(2x -7) +(3x +2)

61 = 6x -5 . . . . . . collect terms

66 = 6x . . . . . . . . add 5

11 = x . . . . . . . . . . divide by 6

Then the side lengths are ...

a = x = 11

b = 2x -7 = 2(11) -7 = 15

c = 3x +2 = 3(11) +2 = 35

_____

Comment on problem 8

You will notice that the side lengths do not satisfy the triangle inequality: the sum of the short sides is not greater than the long side. These side lengths cannot form a triangle. Cute algebra, but bad geometry.

4 0

3 years ago