What is the surface area of the figure?

Mathematics

1 answer:

Oliga [24]3 years ago

5 0

Answer:

The total surface area = 582 ft²

Step-by-step explanation:

To find the surface area of it count the number of faces at first

The figure has 8 faces each 2 are equal

1- Two faces with dimensions 4 ft and 15 ft ( base and shaded face)

2- Two faces with dimensions 9 ft and 4 ft

3- Two faces with dimensions 4 ft and 6 ft

4- Two faces with dimensions 15 ft , 9 ft and 6 ft

Area of (1-) = 2(4 × 15) = 120 ft²

Area of (2-) = 2(4 × 9) = 72 ft²

Area of (3-) = 2(4 × 6) = 48 ft²

Area of (4-) = 2[(9 × 9) + (6 × 15)] = 2[81 + 90] = 2 × 171 = 342 ft²

∴ The total surface area = 120 + 72 + 48 + 342 = 582 ft²

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What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

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The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

Solution:

The given expression is $(2 x-3 y)^{10}$

As per binomial theorem, we know,

$(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}$

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now $x^{5}\times y^5$ will be the 6 term where k =5

Now, $\mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}$

So, the coefficient of $x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right$ .

$10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252$