Find the angular size of a circular object with a 3-inch diameter viewed from a distance of 6 yards.

Mathematics

1 answer:

Rom4ik [11]3 years ago

8 0

Check picture below
thus $\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad thus
\\\\\\
tan(\theta)=\cfrac{3}{6}\implies tan(\theta)=\cfrac{1}{2}
\\\\\\
\theta=tan^{-1}\left( \cfrac{1}{2} \right)$

You might be interested in

Aaron can run 4 miles in 30 minutes. How long does it take him to run one mile

stealth61 [152]

You first divide 30 by 4 to see how long it takes him to run one mile. Then you get 30/4 which simplified is 15/2 minutes

6 0

3 years ago

Read 2 more answers

write a function g whose graph represents a translation 2 units to the right followed by a horizontal stretch by a factor or 2 o

Alenkinab [10]

$\bf f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}\\\\
f(x)=&{{ A}} \left|{{ B }}x+{{ C}} \right|+{{ D}}
\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see,

$\bf f(x)=|x| \implies \begin{array}{lllccll}
f(x)=&1|&1x&+0|&+0\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

so, to shift it to the right by 2 units, simply set C = 2.
to stretch it by 2, set A = 1/2.

the smaller A is, the wider it opens, the larger it is, the more it shrinks.

5 0

3 years ago

Simplify -3x^2-5x^2(4x^3-x^2)2

PSYCHO15rus [73]

Let's simplify step-by-step.

−3x2−5x2(4x3−x2)(2)

Distribute:

=−3x2+−40x5+10x4

Answer:

=−40x5+10x4−3x2

8 0

3 years ago

Please help. I’ll mark you as brainliest if correct!

Ksenya-84 [330]

answer is g(x)=|x+2|-1

5 0

4 years ago

Read 2 more answers

What is the domain of the function f (x) x-5/x^2-9

nikklg [1K]

Means the number you can use
remember we can't divide by zero
domain is x^2-9
set to zero to find values we can't use
x^2-9=0
x^2=9
x=+/-3

domain=all real numbers except -3 and 3

7 0

4 years ago

Read 2 more answers

Find the angular size of a circular object with a 3​-inch diameter viewed from a distance of 6 yards.

Find the angular size of a circular object with a 3-inch diameter viewed from a distance of 6 yards.