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3 years ago

One of the roots of equation x^(2)-(3p-4)x+11p-5=0 is 8. Find the other root. Find the value of p.

Mathematics

2 answers:

aivan3 [116]3 years ago

6 0

Answer:

other root: x = 9

p = 7

Step-by-step explanation:

first, find p:

(8)² - (3p - 4)8 + 11p -5 = 0

64 - (24p - 32) + 11p - 5 = 0 –––––> 64 - 24p + 32 + 11p - 5 = 0

91 - 13p = 0

-13p = -91

p = 7

<u>plug in p to find the polynomial:</u>

x² - (3(7) - 4)x + 11(7) - 5 = 0

x² - (21 - 4)x + 77 - 5 = 0

x² - 17x + 72

<u>find the roots:</u>

we know that 8 is one of the roots, so one factor is (x - 8)

the other number needs to be something that equals -17 when added with -8 and 72 when multiplied by -8

that number is -9

so the poly nomial factors to be: (x-8)(x-9)

so the roots are x = 8 and x = 9

Kisachek [45]3 years ago

6 0

Answer:

p = 7

Step-by-step explanation:

x²-(3p-4)x+11p-5=0 ...(1) Root: 8, x-8 is factor

(x-8) (x- (11p-5)/8) = 0

x² -8x - ((11p-5)/8)*x + (11p-5) = 0

x² - (8 + (11p-5)/8) x + 11p-5 = 0 ----(2)

compare(1) and (2): 3p-4 = 8 + (11p-5)/8

24p - 32 = 64 + 11p - 5

13p = 91

p = 7

check: x²-(3p-4)x+11p-5 = x²- 17x + 72 = (x-8)(x-9)

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A kite flying in the air has a 12 line attached to it. Its line is pulled taut and casts a 9 shadow. Find the height of the kite

alexira [117]

Answer:

8 (7.94)

Step-by-step explanation:

You can think of it as a geometry problem.

What is formed here is a triangle, which sides ate: the line, the line's shadow, and the height from the ground to the kite (here I attach a drawing).

What you need to find is the height. We will call it H.

As the triangle formed is a right one, we can use Pitágoras' theorem. The height H squared plus the squared of the shadow is equal to the squared of the line (the hypotenuse). This is:

H^2 + 9^2 = 12^2

H^2 + 81= 144

H^2 = 63

Applying squared root in both sides

H = √63

H = 7,94

So, the height is approximately 8.