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1 year ago

A boy walks 58 feet up a ramp having a 22.5 degree inclination. how high is he standing from the ground?

Mathematics

1 answer:

yKpoI14uk [10]1 year ago

6 0

Boy is 22.5 feet high from the ground

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

The given question can be solved by sin, as value of perpendicular is to be evaluated and height and angle is provided. Let height from the ground be x

sin(22.5°) = x / 58

x = 58sin22.5 = 58(.38258) = 22.5 feet high.

Thus the Boy is 22.5 feet high from the ground.

Learn more about trigonometry here :

brainly.com/question/26719838

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Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4

gtnhenbr [62]

Answer:

Simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

Step-by-step explanation:

We need to simplify the expression $(6^{-2})(3^{-3})(3*6)^4$

Solving:

$(6^{-2})(3^{-3})(3*6)^4$

Applying exponent rule: $a^{-m}=\frac{1}{a^m}$

$=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\$

Factors of $18=2\times 3\times 3=2\times3^2$

Factors of $6=2\times 3$

Replacing terms with factors

$=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\$

Using exponent rule: $(a^m)^n=a^{m\times n}$

$=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}$

Using exponent rule: $a^m.a^n=a^{m+n}$

$=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}$

Now using exponent rule: $\frac{a^m}{a^n}=a^{m-n}$

$=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108$

So, simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

7 0

2 years ago

14(0.89)^x+4.5 =162

lisabon 2012 [21]

$14(0.89)^{x + 4.5} = 162$
$\frac{14(0.89)^{x + 4.5}}{14} = \frac{162}{14}$
$0.89^{x + 4.5} = 11\frac{4}{7}$
$ln(0.89^{x + 4.5}) = ln(11\frac{4}{7})$
$(x + 4.5)ln(0.89) = ln(11\frac{4}{7})$
$\frac{(x + 4.5)ln(0.89)}{ln(0.89)} = \frac{ln(11\frac{4}{7})}{ln(0.89)}$
$x + 4.5 = -2101.14032500$
$x = 2105.64032500$

3 0

3 years ago

13 copies of the small rectangle shown below have been used to make the larger rectangle.

Nikolay [14]

Answer:

4800

Step-by-step explanation:

length = 20mm X 3 = 60mm

width = 20mm X 4 = 80mm

area = length X width = 60 X 80 = 4800 m $m^{2}$

I hope it helps you!

8 0

2 years ago

Identify the property shown .<br><br> 50+0=50

qwelly [4]

The identity property is shown

7 0

3 years ago

How did they get the -5? I got -3

Naya [18.7K]

F(x) = x² - 3x
g(x) = √x - 1

f(g(x))= (√x - 1)² - 3(√x - 1) = (√x - 1)(√x - 1 - 3) =(√x - 1)(√x - 4) =
= √x √x -1*√x -4*√x +4 = x -5√x +4

Answer: x -5√x +4

4 0

2 years ago