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3 years ago

14

A swimming pool is open for 71/2 hours during the day the pool keeps one lifeguard on duty at a time, and each lifeguards shift

is 11/2 hours long

1 answer:

xxTIMURxx [149]3 years ago

3 0

5 lifeguards are needed during the day

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Find all the zeros of the polynomial function P(x) x^4-4x^3 -5x^2+38x- 30

worty [1.4K]

Answer:

The zeros of the polynomial function are 1, -3, 3+i and 3-i.

Step-by-step explanation:

The given function is

$P(x)=x^4-4x^3-5x^2+38x-30$

We can find a zero of the given function by hit and trial method.

Substitute x=1 in the given function.

$P(1)=(1)^4-4(1)^3-5(1)^2+38(1)-30$

$P(1)=0$

The value of function is 0 at x=1 it means (x-1) is a factor of given function.

Substitute x=-3 in the given function.

$P(-3)=(-3)^4-4(-3)^3-5(-3)^2+38(-3)-30$

$P(-3)=0$

The value of function is 0 at x=-3 it means (x+3) is a factor of given function.

$(x-1)(x+3)=x^2 + 2 x - 3$

Divide the given function by $x^2 + 2 x - 3$ , to get remaining factors.

$\frac{x^4-4x^3-5x^2+38x-30}{x^2 + 2 x - 3}=x^2 - 6 x + 10$

So, the factor form of given function is

$P(x)=(x - 1) (x + 3) (x^2 - 6 x + 10)$

Quadratic formula: If a quadratic equation is $ax^2+bx+c=0$ , then

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using quadratic formula find the zeroes of $x^2 - 6 x + 10$ .

$x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(10)}}{2(1)}$

$x=\frac{6\pm \sqrt{-4}}{2}$

$x=\frac{6\pm 2i}{2}$ $[\because \sqrt{-1}=i]$

$x=3\pm i$

Therefore the zeros of the polynomial function are 1, -3, 3+i and 3-i.

3 0

3 years ago

Brianna paid $350 for a rug. The price of the rug that Bill purchased was 2/5 the price that Brianna paid. How much did Bill pay

lora16 [44]

350 divided by 5= 70
70x2=140
The price of the rugs that Bill purchased is 140 dollars

5 0

4 years ago

R 3.5<br> Mellom hvilke to hele tall ligger kvadratroten til<br> a) 35<br> b) 67<br> c) 93

NikAS [45]

Answer:

a) 5, 6

b) 8, 9

c) 9, 10

Step-by-step explanation:

It is useful to know the squares of small integers:

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

Then the problem becomes one of identifying the perfect squares the given number lies between

a) 25 < 35 < 36 ⇒ 5 < √35 < 6

b) 64 < 67 < 81 ⇒ 8 < √67 < 9

c) 81 < 93 < 100 ⇒ 9 < √93 < 10

7 0

4 years ago

-3c-4=2<br> ---------------

Lilit [14]

Answer:

Solution given:

-3c-4=2

add 4 on both side

-3c-4+4=2+4

-3c=6

divide both side by -3

-3c/-3=6/-3

c=-2

7 0

3 years ago

Read 2 more answers

80 cm of 2m express as percentage

Hunter-Best [27]

Answer:

There are 200 centimetres in 2 metres. Therefore, 80 centimetres is equal to 80/200 x 100 = 40 percent of 2 metres

7 0

2 years ago