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katen-ka-za [31]
3 years ago
15

The polynomial f(x) leaves a remainder of - 3 and - 7 when divided by (3x - 1) and (x +1) respectively.

Mathematics
1 answer:
olga55 [171]3 years ago
7 0

Step-by-step explanation:

Here, f(x) is the given polynomial.

By remainder Theorem,

When divided by (3x-1),

f(1/3) = -3........(1)

When divided by (x+1),

f(-1) = -7.........(2)

<em>Another</em><em> </em><em>polynomial</em><em> </em><em>is</em><em> </em><em>3</em><em>x</em><em>²</em><em>+</em><em>2</em><em>x</em><em>-</em><em>1</em>

Solving,

3x²+2x-1

= 3x²+3x-x-1

=3x(x+1)-(x+1)

=(3x-1)(x+1)

So

f(x) = (3x-1)(x+1)Qx + (ax+b)

For f(-1),

-7 = -a+b

b= a-7

For f(1/3),

-3 = a/3+b

or, -3 = a/3+a-7

or, 4×3 = 4a

or a = 3

Also, b = 3-7 =-4

Hence, remainder is (3x-4)

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A building is 964 feet tall. Two people are standing on the ground directly west of the building. The
Lina20 [59]

Answer:

The distance from both of them = 1463.925  ft

Step-by-step explanation:

The building is 964 ft tall . 2 people are standing on the ground directly west of the building. The first person looks up at an angle of 62° to the top of the building while the second person did same at an angle of 26°. The distance between them can be computed below.

The illustration forms a right angle triangle . Using the SOHCAHTOA principle let us find the distance of the second person from the building

tan 26° = opposite/adjacent

tan 26° = 964/adjacent

adjacent tan 26° = 964

adjacent = 964/tan 26°

adjacent = 964/0.48773258856

adjacent = 1976.49290328 ft

The distance from the second person to the building = 1976.493 ft

Distance of the first person to the building

tan 62° = opposite/adjacent

tan 62° = 964/adjacent

adjacent tan 62° = 964

adjacent = 964/tan 62°

adjacent = 964/1.88072646535

adjacent = 512.567892122

distance from the first person to the building = 512.568 ft

The distance from both of them =  1976.493 ft - 512.568 ft = 1463.925  ft

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3 years ago
Graph the linear equation.<br><br> x + 4y = - 8
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Answer: See the graph below!

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

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to solve:
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3 years ago
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If 1200 cm^2 of material is available to make a box with a square base and an open top find the largest possible volume of the b
strojnjashka [21]
Surface area of box=1200 cm² 
<span>Volume of box=s²h </span>
<span>s = side of square base </span>
<span>h = height of box </span>
<span>S.A. = s² + 4sh </span>
<span>S.A. = surface area or 1200 cm², s²
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<span>1200 - s² = 4sh </span>
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<span>v(s) = s²((1200 - s²)/(4s)) </span>
<span>v(s) = s(1200 - s²)/4 . </span>
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by derivating
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again derivating
<span>v"(s) = -(3/2)s </span>
<span>v"(-20) = -(3/2)(-20) </span>
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<span>v"(20) = -(3/2)(20) </span>
<span>v"(20) = -30 </span>


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<span>v(s) = 300(20) - (1/4)(20)^3 </span>
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