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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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The average of 6 ages men is 35 years and the average of four of them is 32. Find the ages of the remaining two men if one is 3

prisoha [69]

Answer:

the first one must be 39.5 and the other 42.5

Step-by-step explanation:

multiply 35 by 6 and subtract 32 x 4 you are left with 82. Divide that by 2 and make the difference 3.

6 0

3 years ago

3. I am collecting baseball cards. My goal before I turn 18 is to have 500 cards. When I tumed 10,

vladimir2022 [97]

Based on the scenario given, the equation to describe the situation will be: c + 125 + 89 = 500 and 286 cards need to be collected.

Number of cards given by grandfather = 125 cards

Number of cards that will be given by father = 89 cards

Therefore, based on the information given, the equation to describe the situation will be:

c + 125 + 89 = 500

Therefore, we can then use the equation to calculate the number of cards that need to be collected. This will be:

c + 125 + 89 = 500

c + 214 = 500

c = 500 - 214

c = 286

Therefore, the person needs to collect 286 cards.

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brainly.com/question/24910157

7 0

2 years ago

1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$