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KATRIN_1 [288]
3 years ago
15

the polynomial ky^3+3y^2-3 and 2y^3-5y+k when divided by (y-5) leave the same remainder in each case. Find the value of k.

Mathematics
1 answer:
marshall27 [118]3 years ago
3 0

Answer:

k=\frac{153}{124}

Step-by-step explanation:

According to the Remainder Theorem; when P(y) is divided by y-a, the remainder is p(a).

The first polynomial is :

p(y)=ky^3+3y^2-3

When p(y) is divided by y-5, the remainder is

p(5)=k(5)^3+3(5)^2-3

p(5)=125k+75-3

p(5)=125k+72

When the second polynomial:

m(y)= 2y^3-5y+k is divided by y-5.

The remainder is;

m(5)= 2(5)^3-5(5)+k

m(5)= 225+k

The two remainders are equal;

\implies 125k+72=225+k

\implies 125k-k=225-72

\implies 124k=153

k=\frac{153}{124}

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Answer:

  £135.98

Step-by-step explanation:

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5 0
2 years ago
Help Please<br> Find The Surface Area Of The Prism
snow_lady [41]

Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

24 x 2 = 48 cm^2

Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

6 cm x 13 cm = 78 cm^2

Area of another rectangular face:

13 cm x 10 cm = 130 cm^2

Add up all the areas of all faces:

48 + 104 + 78 + 130 = 360

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8 0
2 years ago
Dimitri rode his bike 32 miles yesterday. He rode 12 4/5 miles before lunch and the rest of the distance after lunch. How far di
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Answer: 40 unit²

Step-by-step explanation:

A square pyramid is composed of 1 square and 4 congruent triangles

STEP ONE. Find the area of the square.

A=b²

b=base

A=b²=4²=14

STEP TWO. Find the area of the triangle

A=(1/2)bh

b=base

h=height

A=(1/2)bh

A=(1/2)(4)(3)

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There are 4 congruent triangles, so 6×4=24

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Hope this helps!! :)

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7 0
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