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3 years ago

What's the area of the triangle below?

Mathematics

1 answer:

Nana76 [90]3 years ago

6 0

Area of triangle = 1/2 x base x height =1/2 x 6 x 8 = 24 square metre

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I) Find the first 4 terms in the expansion of

Katyanochek1 [597]

Answer:

(i) $64+192 x^2+240 x^4+160x^6$

(ii) 1072

Step-by-step explanation:

Part (i)

Using Binomial series formula:

$(2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3$

$=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6$

$=64+192 x^2+240 x^4+160x^6$

Part (ii)

$(1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})$

$=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}$

$(2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)$

$=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...$

There is no need to keep expanding since the remaining will include the variable.

Therefore, the term independent of x = 64 - 1152 + 2160 = 1072

6 0

2 years ago

What does h(40) = 1700 mean in terms of the problem?

ipn [44]

Answer:

40 hours of training=h(40)

Monthly Pay=1700

Step-by-step explanation:

For 40 hours of training, you will receive $1700 for the month.

7 0

3 years ago

If a 4 x 16 rectangle has the same area as a square, what is the length of a side of the square?

Licemer1 [7]

Answer:

Option D. 8 units

Step-by-step explanation:

step 1

Find the area of rectangle

The area of rectangle is

$A=(4)(16)=64\ units^2$

step 2

Find the length side of the square with the same area of rectangle

The area of a square is

$A=b^2$

where

b is the length side of the square

we have

$A=64\ units^2$

substitute

$64=b^2$

take the square root both sides

$b=8\ units$

therefore

The length side of the square is 8 units

7 0

3 years ago

What is the value of x? enter your answer in the box.

Mamont248 [21]

Answer:

if 9x8 =72

then 56/8= 7

x=7

8 0

3 years ago

Simplify (4x) · mn · 15 · 2.

Andrej [43]

I think it's 120xmn.

6 0

3 years ago

Read 2 more answers