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3 years ago

8

What is the missing justification?

2 answers:

vichka [17]3 years ago

8 0

Transitive property:

If a = b, and b = c, then a = c.

Here you are doing it with congruence of angles.

Strictly speaking, the correct reason is not the transitive property of equality since the transitive property applies to equality. In this case, it's a theorem for congruence of angles. Since that theorem is not mentioned, the best answer here is "transitive property."

Vikki [24]3 years ago

4 0

Transitive property is your answer

if ∠A ≅ ∠C, and ∠C ≅ ∠B then, ∠A ≅ ∠B

hope this helps

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Use a Maclaurin series to obtain the Maclaurin series for the given function.

Rama09 [41]

Answer:

$14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}$

Step-by-step explanation:

In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:

$cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}$

So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: $\frac{1}{15}x^{2}$ so for

$cos(\frac{1}{15}x^{2})$

the modified series will look like this:

$cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}$

So we can use some algebra to simplify the series:

$cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}$

which can be rewritten like this:

$cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}$

So finally, we can multiply a 14x to the series so we get:

$14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}$

We can input the x into the series by using power rules so we get:

$14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}$

And that will be our answer.

3 0

3 years ago

Work out the percentage change-decrease £77 by 70%

Dimas [21]

Answer:

£ 23.10

Step-by-step explanation:

100% - 70%

= 30%

If 100% = £ 77

What about 30%

30% × £ 77 ÷ 100%

= £2310 ÷ 100

= £ 23.10

6 0

3 years ago

3kg of meat costs £54<br> Nina buys 2 kg of the meat.<br> Work out how much Nina pays

nadezda [96]

Answer:

£36

Step-by-step explanation:

3kg = 54

÷ 3

1kg = 18

18 × 2 = 36

hope this helps...

5 0

3 years ago

Read 2 more answers

The area of the triangle whose side lengths are 7cm, 24cm and 25cm is ?

Sergio039 [100]

Answer: the area is 84 cm^2

6 0

3 years ago

In the coordinate plane, find the distance between the points using absolute value.

alukav5142 [94]

Answer:

The distance between the two points is 8 units

Step-by-step explanation:

In the given figure

∵ The coordinates of the 2 points are (4, 5) and (4, -3)

∴ x1 = 4 and y1 = 5

∴ x2 = 4 and y2 = -3

∵ Their x-coordinates are equal

→ That means the distance between them is vertical

∴ The length of the vertical distance between two points is

the difference between the y-coordinates of the points

∵ The distance between them = Iy2 - y1I

∵ y1 = 5 and y2 = -3

∴ The distance between them = I-3 - 5I

∴ The distance between them = I-8I

→ Remember absolute value gives always positive values

∴ The distance between them = 8 units

∴ The distance between the two points is 8 units

8 0

3 years ago