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PSYCHO15rus [73]
3 years ago
10

Please help me!! Will get brainliest!

Mathematics
1 answer:
makvit [3.9K]3 years ago
5 0
Completing the square follows the principle of taking a x^{2} +bx+c and converting it into (x+ \frac{b}{2})^2+d where d is the 'correctional number' as I like to call it - i.e. the number that converts the expanded bracket into the +c, since the expanded bracket will give us a x^{2} +b.

In this case, 2/2=1 so we have the first part: (w+1)^2.
Expanding this gives us w^2+2w+1. We need c to be 9, so we can just add 8.
Putting this together:

w^2+2w+9=(w+1)^2+8

Now we can solve it more easily.
Rearranging:
(w+1)^2=-8 \\ w+1= +-\sqrt{-8} = +-\sqrt{8}i=+-2 \sqrt{2}i   \\ \boxed{w=-1+ 2\sqrt{2}i\ or\ -1-2 \sqrt{2}i  }
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The surface area of a given cone is 1,885.7143 square inches. What is the slang height?
kap26 [50]

Answer:

If r >> h, the slang height of the cone is approximately 23.521 inches.

Step-by-step explanation:

The surface area of a cone (A) is given by this formula:

A = \pi \cdot r^{2} + 2\pi\cdot s

Where:

r - Base radius of the cone, measured in inches.

s - Slant height, measured in inches.

In addition, the slant height is calculated by means of the Pythagorean Theorem:

s = \sqrt{r^{2}+h^{2}}

Where h is the altitude of the cone, measured in inches. If r >> h, then:

s \approx r

And:

A = \pi\cdot r^{2} +2\pi\cdot r

Given that A = 1885.7143\,in^{2}, the following second-order polynomial is obtained:

\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2}  = 0

Roots can be found by the Quadratic Formula:

r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}

r_{1,2} \approx -1\,in \pm 24.521\,in

r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in

As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.

3 0
3 years ago
What number is 60 percent of 29
nevsk [136]
60% is 0.60 so you do 0.60 x 29 which = to 17.4
so your answer is 17.40 or 17.4 is 60% of 29
7 0
3 years ago
Given:f(x)=2x+5 and g(x)=
zhannawk [14.2K]

what is the value of g(x)

7 0
3 years ago
Read 2 more answers
How to simplify (2x^4)^5​
Yuliya22 [10]

Answer:

2x^20

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Which graph represents the solution to the system of equations y=3x+2 10x+2y=20
Step2247 [10]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

y=3x+2 ----> equation A

10x+2y=20 ----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

Using a graphing tool

The intersection point is (1,5)

see the attached figure

therefore

The solution of the system is the point (1,5)

7 0
3 years ago
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