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3 years ago

Please help im having trouble with this one

Mathematics

2 answers:

Goryan [66]3 years ago

6 0

Answer:

∠T=22°

Step-by-step explanation:

Given triangle RST with sides 5 cm, 7 cm, 3 cm.

If all sides are given and find the missing angle, we use cosine rule

$CosA=\frac{b^{2}+c^{2} -a^{2}}{2bc}$

Where,

sides are a, b, c and angle A, B, & C are opposite angles respectively.

So,

$CosT=\frac{r^{2}+s^{2} -t^{2}}{2rs}$

$cosT=\frac{25+49-9}{70}$

$cosT=\frac{65}{70} =\frac{13}{14}$

T = 21.79°≈ 22°

That's the final answer.

andrey2020 [161]3 years ago

3 0

Answer:

22 degrees to the nearest degree.

Step-by-step explanation:

Use the Cosine Rule

3^2 = 5^2 + 7^2 - 2*5*7*cos T

9 = 74 - 70 cos T

cos T = (74-9)/ 70

cos T = 65/70

m < T = 21.8 degrees.

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Solve this r/6=5 2/3

myrzilka [38]

First, incorporate the 5 into the 2/3 fraction by multiplying the 5 by the 3 and then adding that quantity by the 2, which now makes the fraction:
17/3
Now set it up with the equation:
r/6 = 17/3
r/6×3 = 17/3×3
r/3 = 17
r/3×3 = 17×3
r = 51

4 0

3 years ago

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Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

I need help on a math problem<br> 48w^3+128w^2+4w-1<br> divided by<br> 4w

raketka [301]

Divide 4w to every term separately.

$\sf\dfrac{48w^3+128w^2+4w-1}{4w}$

$\sf\dfrac{48w^3}{4w}+\dfrac{128w^2}{4w}+\dfrac{4w}{4w}-\dfrac{1}{4w}$

48/4 = 12
w^3/w = w^2
So our first term is 12w^2.

128/4 = 32
w^2/w = w
So our second term is 32w.

4w/4w = 1
Anything divided by itself is 1.

-1/4w, this can't be simplified further, so this is our last term.

So we have:

$\sf 12w^2+32w+1-\dfrac{1}{4w}$

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3 years ago

Light bulbs cost £2.90 each.

s344n2d4d5 [400]

Answer:

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Step-by-step explanation:

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Hope this helps

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3 years ago

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What is the answer of b-6=-14

Nostrana [21]

Answer:

b= -8

Step-by-step explanation:

b-6=-14

add 6 to -14 but its a negative so, you subtract -14 to 6.

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b= -8

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3 years ago