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adell [148]
3 years ago
5

Given that sin theta = 1/4, 0→theta→π/2, what. what is the exact value of cos 8?​

Mathematics
1 answer:
natali 33 [55]3 years ago
3 0
<h3>Answer: Choice B \frac{\sqrt{15}}{4}</h3>

===========================================================

Work Shown:

Angle theta is between 0 and pi/2, so this angle is in quadrant Q1.

Square both sides of the given equation

\sin \theta = \frac{1}{4}\\\\\sin^2 \theta = \left(\frac{1}{4}\right)^2\\\\\sin^2 \theta = \frac{1}{16}

Then use the pythagorean trig identity to get

\sin^2 \theta + \cos^2 \theta = 1\\\\\cos^2 \theta = 1-\sin^2 \theta\\\\\cos \theta = \sqrt{1-\sin^2 \theta} \ \ \ \text{cosine is positive in Q1}\\\\\cos \theta = \sqrt{1-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16}{16}-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16-1}{16}}\\\\\cos \theta = \sqrt{\frac{15}{16}}\\\\\cos \theta = \frac{\sqrt{15}}{\sqrt{16}}\\\\\cos \theta = \frac{\sqrt{15}}{4}\\\\

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In 1980, the median age of the U.S. population was 30.0; in 2000, the median age was 35.3.
miss Akunina [59]

Answer:

y = 0.265x - 494.7

Step-by-step explanation:

Let median age be represent by 'a' and time be represent by 't'

In 1980, median age is given 30

which means that

a₁ = 30

t₁ = 1980

In 2000, the median age is given 35.3

which means that.

a₂ = 35.3

t₂ = 2000

The slope 'm' of the linear equation can be found by:

m = (a₂ - a₁) /(t₂ - t₁)

m = (35.3 - 30)/(2000-1980)

m = 0.265

General form of linear equation is given by:

y = mx + c

y = 0.265x +c

Substitute point (1980,30) in the equation.

30 = 0.265(1980) + c

c = -494.7

Hence the the linear equation can be written as:

y = mx + c

y = 0.265x - 494.7

4 0
3 years ago
The cheerleader section is on the basketball court. Each row requires a section of floor that is 1 ¾ yards by 3 ⅓ yards. How man
Lady_Fox [76]

Answer:

The area of the floor space is equal to 5.83 sq yards.

Step-by-step explanation:

Given that,

Each row requires a section of floor that is 1 ¾ yards by 3 ⅓ yards.

We need to find how many square yards of floor space are taken up by one row of cheerleaders.

We know that, the area of a rectangle is given by :

A = lb

So,

A=\dfrac{7}{4}\times \dfrac{10}{3}\\\\A=5.83\ yards^2

So, the area of the floor space is equal to 5.83 sq yards.

5 0
3 years ago
Solve step by step solution then only i can do it plxx ​
Anuta_ua [19.1K]

Answer:

<h3><u>Let's</u><u> </u><u>understand the concept</u><u>:</u><u>-</u></h3>

Here angle B is 90°

So \triangle ABC and \triangle ABD Are right angled triangle

So we use Pythagoras thereon for solution

<h3><u>Required Answer</u><u>:</u><u>-</u></h3>
  • First in triangle ABC

perpendicular=p=8cm

Hypontenuse =h =10cm

  • We need to find base=b

According to Pythagoras thereon

{\boxed{\sf b^2=h^2-p^2}}

  • Substitutethe values

\longrightarrow\sf b^2=10^2-p^2

\longrightarrow\sf b={\sqrt {10^2-8^2}}

\longrightarrow\sf b={\sqrt{100-64}}

\longrightarrow\bf b={\sqrt {36}}

\longrightarrow\sf b=6

\therefore\overline{BC}=6cm

  • BD=BC+CD

\longrightarrowBD=9+6

\longrightarrowBD=15cm

  • Now in \triangle ABD

Perpendicular=p=8cm

Base =b=15cm

  • We need to find Hypontenuse =AD(x)

According to Pythagoras thereon

{\boxed {\sf h^2=p^2+b^2}}

  • Substitute the values

\longrightarrow\sf h^2=8^2+15^2

\longrightarrow\sf h={\sqrt {8^2+15^2}}

\longrightarrow\sf h={\sqrt {64+225}}

\longrightarrow\sf h={\sqrt {289}}

\longrightarrow\sf h=17cm

\therefore{\underline{\boxed{\bf x=17cm}}}

3 0
3 years ago
HELP ME FIND SLOPE!! PLZ
Murrr4er [49]

Answer:

Step-by-step

the slope is 1, 1

explanation:

rise over run it is a positive slope btw

5 0
2 years ago
When this 3-digit number is rounded to the nearest hundred, it rounds to 200.  Rounded to the nearest ten, this number rounds to
alisha [4.7K]
199, it rounds to 200 because it's closer to 200 than 100. It is also closer to 200 than to 190. And finally, 1 + 9 + 9 = 19
8 0
3 years ago
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