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Aneli [31]
2 years ago
12

A soup can will have a radius of 4 cm and a

Mathematics
1 answer:
DENIUS [597]2 years ago
5 0

Answer:

<h3>            It's about 365 cm²</h3>

Step-by-step explanation:

2×πr² + 2πr×h =

= 2×π×4² + 2π×4×10.5 =

= 32π + 84π =

= 116π ≈

≈ 364.42 cm²

You might be interested in
-60+x-23=70<br> Need help
LekaFEV [45]

Answer:

x-83=70

x = 70 + 83

x= 153

4 0
3 years ago
Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imagina
dmitriy555 [2]

Step-by-step explanation:

<em>"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"</em>

Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic.  I'll use grouping.

Then, we can either factor or use the quadratic equation to find the remaining two roots.

1. x³ − 7x + 6 = 0; 1

x³ − x − 6x + 6 = 0

x (x² − 1) − 6 (x − 1) = 0

x (x + 1) (x − 1) − 6 (x − 1) = 0

(x² + x − 6) (x − 1) = 0

(x + 3) (x − 2) (x − 1) = 0

The remaining two roots are both real: -3 and +2.

2. x³ − 3x² + 25x + 29 = 0; -1

x³ − 3x² + 25x + 29 = 0

x³ − 3x² − 4x + 29x + 29 = 0

x (x² − 3x − 4) + 29 (x + 1) = 0

x (x − 4) (x + 1) + 29 (x + 1) = 0

(x² − 4x + 29) (x + 1) = 0

x = [ 4 ± √(16 − 4(1)(29)) ] / 2

x = (4 ± 10i) / 2

x = 2 ± 5i

The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.

3. x³ − 4x² − 3x + 18 = 0; 3

x³ − 4x² − 3x + 18 = 0

x³ − 4x² + 3x − 6x + 18 = 0

x (x² − 4x + 3) − 6 (x − 3) = 0

x (x − 1)(x − 3) − 6 (x − 3) = 0

(x² − x − 6) (x − 3) = 0

(x − 3) (x + 2) (x − 3) = 0

The remaining two roots are both real: -2 and +3.

<em>"Find all the zeros of the function"</em>

For quadratics, we can factor using either AC method or quadratic formula.  For cubics, we can use the rational root test to check for possible rational roots.

4. f(x) = x² + 4x − 12

0 = (x + 6) (x − 2)

x = -6 or +2

5. f(x) = x³ − 3x² + x + 5

Possible rational roots: ±1/1, ±5/1

f(-1) = 0

-1 is a root, so use grouping to factor.

f(x) = x³ − 3x² − 4x + 5x + 5

f(x) = x (x² − 3x − 4) + 5 (x + 1)

f(x) = x (x − 4) (x + 1) + 5 (x + 1)

f(x) = (x² − 4x + 5) (x + 1)

x = [ 4 ± √(16 − 4(1)(5)) ] / 2

x = (4 ± 2i) / 2

x = 2 ± i

The three roots are x = -1, x = 2 − i, x = 2 + i.

6. f(x) = x³ − 4x² − 7x + 10

Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1

f(-2) = 0, f(1) = 0, f(5) = 0

The three roots are x = -2, x = 1, and x = 5.

<em>"Write the simplest polynomial function with integral coefficients that has the given zeros."</em>

A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c).  Remember that imaginary roots come in conjugate pairs.

7. -5, -1, 3, 7

f(x) = (x + 5) (x + 1) (x − 3) (x − 7)

f(x) = (x² + 6x + 5) (x² − 10x + 21)

f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)

f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105

f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105

8. 4, 2+3i

If 2 + 3i is a root, then 2 − 3i is also a root.

f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))

f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))

f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))

f(x) = (x − 4) (x² − 4x + 13)

f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)

f(x) = x³ − 4x² + 13x − 4x² + 16x − 52

f(x) = x³ − 8x² + 29x − 52

5 0
3 years ago
What rule would you allow to test weather (x,y) is on line l
n200080 [17]

Answer:

Step-by-step explanation:

If a point (x, y) lies on a straight line, coordinates of the point will satisfy the equation.

Slope of a line passing through two points C(4, 5) and D(8, 10),

m = \frac{y_2-y_1}{x_2-x_1}

m = \frac{10-5}{8-4}

m = \frac{5}{4}

Equation of the line passing through C(4, 5) and slope m = \frac{5}{4}

y - y' = m(x - x')

y - 5 = \frac{5}{4}(x-4)

y = \frac{5}{4}x-5+5

y = \frac{5}{4}x

If point B(4, 0) lies on the line CD,

0 = \frac{5}{4}(4)

0 = 5

Which is not true.

Therefore, point B doesn't lie on line CD.

8 0
3 years ago
What is the quotient of 62 divided by 5? (im in a math quiz ;-;)
Ipatiy [6.2K]

Answer:

the anser is b

12 x 5 = 60

leaves the 2

12.2

B

8 0
2 years ago
Read 2 more answers
Choose the correct simplification of the expression (2x2y6z5)(5x4y5z3).
erastovalidia [21]

Answer:

The correct option is 4.

Step-by-step explanation:

The given expression is

(2x^2y^6z^5)(5x^4y^5z^3)

Simplify the given expression.

(2x^2y^6z^5)\times (5x^4y^5z^3)

(2\times 5)(x^2x^4)(y^6y^5)(z^5z^3)

10x^{2+4}y^{6+5}z^{5+3}                  [\because x^mx^n=x^{m+n}]

10x^6y^{11}z^8

Therefore correct option is 4.

8 0
3 years ago
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