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2 years ago

Find the area of this semi-circle with radius, r = 66cm. Give your answer rounded to 1 DP.

Mathematics

1 answer:

Darya [45]2 years ago

4 0

Answer:

414.857143

Step-by-step explanation:

r=66

=2*66*22/7

=414.857143

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Two problems here I need solved! I need every step, so please have that with your answers!!

Free_Kalibri [48]

QUESTION 1

We want to solve,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}$

We factor the denominator of the fraction on the right hand side to get,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-4x - 2x+8}.$

This implies
$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x(x-4) - 2(x - 4)}.$

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{(x-4)(x - 2)}$

We multiply through by LCM of
$(x-4)(x - 2)$

$(x - 2) + x(x-4) = 2$

We expand to get,

$x - 2 + {x}^{2} - 4x= 2$

We group like terms and equate everything to zero,

${x}^{2} + x - 4x - 2 - 2 = 0$

We split the middle term,

${x}^{2} + - 3x - 4 = 0$

We factor to get,

${x}^{2} + x - 4x- 4 = 0$

$x(x + 1) - 4(x + 1) = 0$

$(x + 1)(x - 4) = 0$

$x + 1 = 0 \: or \: x - 4 = 0$

$x = - 1 \: or \: x = 4$

But
$x = 4$
is not in the domain of the given equation.

It is an extraneous solution.

$\therefore \: x = - 1$
is the only solution.

QUESTION 2

$\sqrt{x+11} -x=-1$

We add x to both sides,

$\sqrt{x+11} =x-1$

We square both sides,

$x + 11 = (x - 1)^{2}$

We expand to get,

$x + 11 = {x}^{2} - 2x + 1$

This implies,

${x}^{2} - 3x - 10 = 0$

We solve this quadratic equation by factorization,

${x}^{2} - 5x + 2x - 10 = 0$

$x(x - 5) + 2(x - 5) = 0$

$(x + 2)(x - 5) = 0$

$x + 2 = 0 \: or \: x - 5 = 0$

$x = - 2 \: or \: x = 5$

But
$x = - 2$
is an extraneous solution

$\therefore \: x = 5$

7 0

4 years ago

Stanley measured a county park and made a scale drawing. The picnic area, which is 120

algol [13]

Answer:

Step-by-step explanation:

6 0

3 years ago

Helpp answer thiss please

aleksandrvk [35]

The length of the side of the small triangle is 4...the side length of the large triangle is 9 (5+4), not 5. It should be correctly written as 4/6 = 9/x

3 0

3 years ago

Can someone help me with this question please.

ozzi

Answer:

x=88° a=+3 b=4a-3

Step-by-step explanation:

as triangles ADE and BCE are congruent by sss axiom

so correponding angles are equal

i.e<AED = <BEC

and <DAE =90-60

=30°

62°+x+30°=180°

therefore x=88°

5 0

3 years ago

A wedding dress is on sale for $225.00, which is 25% off of its original price. What was the original price of the dress?

Olenka [21]

So if the dress is 25% off, that means you are paying 75% of the original price.

sale price = original price x 0.75
225 = original price x 0.75

divide both sides by 0.75 to isolate original price

225/0.75 = (original price x 0.75)/0.75
300 = original price

7 0

3 years ago

Read 2 more answers

Find the area of this semi-circle with radius, r = 66cm. Give your answer rounded to 1 DP.​

Find the area of this semi-circle with radius, r = 66cm. Give your answer rounded to 1 DP.