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Reptile [31]
2 years ago
9

3 Solve for x. Round answer to the nearest tenth. X 759 17

Mathematics
1 answer:
QveST [7]2 years ago
7 0

Answer:

x ≈ 4.6

Step-by-step explanation:

Reference angle = 75°

Opposite side to reference angle = 17

Adjacent side = x

Applying TOA:

Tan 75 = opp/adj

Tan 75 = 17/x

Multiply both sides by x

x*Tan 75 = 17

Divide both sides by Tan 75

x = 17/Tan 75

x ≈ 4.6

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2ᵃ = 5ᵇ = 10ⁿ.<br> Show that n = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bab%7D%7Ba%20%2B%20b%7D%20" id="TexFormula1" titl
11Alexandr11 [23.1K]
There are two ways you can go about this: I'll explain both ways.
<span>
</span><span>Solution 1: Using logarithmic properties
</span>The first way is to use logarithmic properties.

We can take the natural logarithm to all three terms to utilise our exponents.

Hence, ln2ᵃ = ln5ᵇ = ln10ⁿ becomes:
aln2 = bln5 = nln10.

What's so neat about ln10 is that it's ln(5·2).
Using our logarithmic rule (log(ab) = log(a) + log(b),
we can rewrite it as aln2 = bln5 = n(ln2 + ln5)

Since it's equal (given to us), we can let it all equal to another variable "c".

So, c = aln2 = bln5 = n(ln2 + ln5) and the reason why we do this, is so that we may find ln2 and ln5 respectively.

c = aln2; ln2 = \frac{c}{a}
c = bln5; ln5 = \frac{c}{b}

Hence, c = n(ln2 + ln5) = n(\frac{c}{a} + \frac{c}{b})
Factorise c outside on the right hand side.

c = cn(\frac{1}{a} + \frac{1}{b})
1 = n(\frac{1}{a} + \frac{1}{b})
\frac{1}{n} = \frac{1}{a} + \frac{1}{b}

\frac{1}{n} = \frac{a + b}{ab}
and thus, n = \frac{ab}{a + b}

<span>Solution 2: Using exponent rules
</span>In this solution, we'll be taking advantage of exponents.

So, let c = 2ᵃ = 5ᵇ = 10ⁿ
Since c = 2ᵃ, 2 = \sqrt[a]{c} = c^{\frac{1}{a}}

Then, 5 = c^{\frac{1}{b}}
and 10 = c^{\frac{1}{n}}

But, 10 = 5·2, so 10 = c^{\frac{1}{b}}·c^{\frac{1}{a}}
∴ c^{\frac{1}{n}} = c^{\frac{1}{b}}·c^{\frac{1}{a}}

\frac{1}{n} = \frac{1}{a} + \frac{1}{b}
and n = \frac{ab}{a + b}
4 0
3 years ago
The temperature was 8°C then the temperature feel 9°C what was the temperature after it fell?
Vladimir79 [104]

Answer:

-1°C

Step-by-step explanation:

8°C - 9°C = -1°C

Hope it helps

4 0
3 years ago
Potatoes are 50p a pound . how much for 24oz​
Tems11 [23]

Answer:

25p

Step-by-step explanation:

IM NOT SURE IF ITS RIGHT BUT THAT WHAT I THINK. HAVE A NICE DAY!

8 0
2 years ago
Read 2 more answers
If \: x + y + z = 0 \: then \: show \: that \: {x}^{3} + {y}^{3 } + {z}^{3} =3xy<br>​
tankabanditka [31]

Answer:

Given

x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y) 3 =(−z) 3

⟹x 3 +y 3 +3x 2y+3xy 2 =−z 3

⟹x 3 +y 3 +3xy(x+y)=−z 3

⟹x 3+y 3+3xy(−z)=−z 3

⟹x 3 +y 3−3xyz=−z 3

⟹x 3 +y 3 +z 3 =3xyz

Step-by-step explanation:

Hope it is helpful.....

8 0
2 years ago
A baseball player makes it to home plate 35% of the time. How many times can he expect to make it home in 850 at bats
choli [55]
850x35% =297.5
=298(cor.to 3 sig.fig.)
5 0
3 years ago
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