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3 years ago

#1-7 10 points!!!! please help :)

Mathematics

1 answer:

Contact [7]3 years ago

4 0

1. A
2. D
3. C
4. 5n
5. 24 ?
6. 80
7. 5

they may not be right i honestly dont know but hopefully it helps just a little :’)

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Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{cot\theta = \dfrac{cos\theta}{sin\theta}}}}$

$\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}$

$\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}$

$\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}$

$\mathsf{\implies \dfrac{1 - \dfrac{1}{5}}{1 + \dfrac{1}{5}}}$

$\mathsf{\implies \dfrac{\dfrac{5 - 1}{5}}{\dfrac{5 + 1}{5}}}$

$\mathsf{\implies \dfrac{5 - 1}{5 + 1}}$

$\mathsf{\implies \dfrac{4}{6}}$

$\mathsf{\implies \dfrac{2}{3}}$

Hence, option (a) 2/3 is your correct answer.

3 0

2 years ago

\a truck travels at an average of 55 miles per hour once inside city limits the truck decreases it speed by 40 percent what is t

grandymaker [24]

Answer: 33 mph

Step-by-step explanation:

First find out what 40% of 55 is:

= 40% * 55

= 22 mph

This means that the speed reduces by 22 mph inside the city.

The speed inside the city is therefore:

= 55 - 22

= 33 mph

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2 years ago

Royce has $15 with him and spends $12 to buy his favorite comics. He has $3 left, which he deposits in the bank. Which number wi

Sonja [21]

Answer:

C: +3

Step-by-step explanation:

We know this because Royce added money to his bank account, not subtract (b). The other options are just there to confuse you.

I hope this helps!!

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3 years ago

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Evaluate the expression for the given values of the variables.

Studentka2010 [4]

Answer:

Answer of this is... 4...

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2 years ago

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In △ABC, m∠A=52°, c=11, and m∠B=19°. Find a to the nearest tenth.

Ugo [173]

From the problem we have

In △ABC, m∠A=52°, c=11, and m∠B=19°.

Draw the diagram with the help of given information, (see the attached image)

Now using Sine Law in the Triangle ABC, we can write

Now from Triangle ABC , we can write

$\frac{a}{sin52}=\frac{11}{sin109} \\$

Now simplify , we get

$\Rightarrow a=\frac{11}{sin109}*sin52\\ \\ \Rightarrow a=\frac{11}{0.9455}*0.7880\\ \\ \Rightarrow a=9.1676 \approx 9.2\\$

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2 years ago