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3 years ago

Evaluate each trigonometric equation for θ.

Mathematics

1 answer:

liberstina [14]3 years ago

4 0

Answer:

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

Step-by-step explanation:

Let us revise the trigonometry functions

Sin(x) = opposite/hypotenuse

Cos(x) = adjacent/hypoteouse

Tan(x) = opposite/adjacent

Csc(x) = hypotenuse/opposit

Sec(x) = hypotenues/adjacent

Cot(x) = adjacent/opposite

In the given figure

The opposite side to angle Ф = 8

The adjacent side to angle Ф = 15

Find the hypotenuse using Pythagoras' theorem

$Hypotenuse = \sqrt{8^{2}+15^{2} }$

$Hypotenuse = \sqrt{64+225}$

$Hypotenuse = \sqrt{289}$

$Hypotenuse = 17$

Let us use the rules above to find the trigonometry functions

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

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Alexis wants to make a paperweight at pottery class. He designs a pyramid-like mode l with a base area of 100 square centimeters

olga55 [171]

Answer:

$\frac{3}{2}$ g/cm²

Step-by-step explanation:

First, we need to find the volume of the prism. The volume of a square pyramid is V = Bh/3

B = 100 cm²

h = 6 cm

V = 100 cm² * 6 cm /3

V = 600 cm³ /3

V = 200 cm³

Next, we need to solve for the density based on the desired volume and mass.

m = mass = 300 g

V = volume

density = m/V

density = 300 g / 200 cm³

density = 3/2 g/cm³

The lowest possible density of the material to make the paperweight would be $\frac{3}{2}$ g/cm²

4 0

3 years ago

Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents

Orlov [11]

Step-by-step answer:

The base of the exponential function is 1.29 for 7 days, as in

f(x) = 86*(1.29)^x

The new rate for days can be calculated by dividing x by 7 (where x remains the number of weeks), namely

f(x) = 86*1.29^(x/7)

Using the law of exponents, b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

we simplify by putting b=1.29, a=7 to get

f(x) = 86*(1.29^(1/7))^x

f(x) = 86*(1.037)^x since 1.29^(1/7) evaluates to 1.037

Rounding 1.037 to 1.04 we get a (VERY) approximate function

f(x) = 86 * (1.04^x)

1.04 is very approximate because 1.04^7 is supposed to get back 1.29, but it is actually 1.316, while 1.037^7 gives 1.2896, much closer to 1.29.

7 0

3 years ago

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What is the complete factorization of the polynomial below? x3 + 3x2 + 9x + 27

SVEN [57.7K]

x3+3x2−9x−27=(x−3)(x+3)(x+3)

6 0

3 years ago

Twenty-seven is % of 60 help mee asap

jok3333 [9.3K]

Answer: The answer is: " 45 % " .

________________________________________________

→ " Twenty-seven is 45 % of 60. "

________________________________________________

Step-by-step explanation:

________________________________________________

The question asks:

" 27 is what % {percentage] of 60 " ? ;

________________________

So: " 27 = (n/100) * 60 " ; Solve for "n" ;

________________________________________________

Method 1:

________________________________________________

→ (n/100) * 60 = 27 ;

Divide each side by 60 :

→ [ (n/100) * 60 ] / 60 = 27 /60 ;

to get:

→ (n/100) = 27/60 ;

Now: Cross-factor multiply:

→ 60n = (27)*(100) ;

to get:

→ 60n = 2700 ;

Divide each side by "60" ;

→ 60n = 2700/ 60 ;

to get: n = 45 ;

________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Method 2:

________________________________________________

The question asks:

" 27 is what % {percentage] of 60 " ?

________________________

To solve this problem:

Rephrase this question as:

________________________

" 27 is 60% of what number ? "

→ The answer will be the same!

________________________

→ 27 = (60/100)* n ; Solve for "n" ;

Multiply each side of the equation by "100" ; to eliminate the fraction:

→ 100 * 27 = 100 * [ (60/100)* n ] ;

to get:

→ 2700 = 60n ;

↔ 60n = 2700 ;

Divide Each Side of the equation by "60" ;

→ 60n/60 = 2700 / 60 ;

to get: n = 45 ;

________________________________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Method 2: Variant 1 of 2:

________________________________________________

When we have:

→ 27 = (60/100)* n ; Solve for "n" ;

________________________

Note that: "(60/100) = (60÷ 100) = (6 ÷ 10)" ; since: in "(60/100)" ; the "zero" from the "numerator" cancels out; And: the "last zero" in "100" — from the "denominator" cancels out; since we are dividing "each side" of the fraction by "10" ;

→ "(60÷10) / (600÷10)" = " 6/10 " ;

→ " (6/10)" ; that is; "six-tenths"} ;

→ can be represented by: " 0.6 " ;

→ {by convention; but specifically, here is the explanation} — as follows:

________________________

→ "(6/10)" = " (6 ÷ 10) " ;

Note: When dividing a number by "10" ; we take the original number; and move the decimal point to the left; & then we rewrite that number as the "answer".

Note: When multiplying or dividing by a positive, non-zero integer factor of "10" that has at least 1 (one) "zero" after that particular factor of "10". We can get the answer by taking the original number & moving the decimal point the number of spaces as designated by the number of zeros following the particular [aforementioned factor of "10".].

We move the decimal point to the right if we are multiplying; and to the left if we are dividing. In this case, we are dividing "6" by "10 " :

→ " 6 ÷ 10 = ? " ;

→ " 6. ÷ 10 = ? " ;

We take the: " 6. " ; and move the decimal point "one space backward [i.e. "to the left"]; since we are dividing by "10" ;

→ to get: " .6 " ; & we rewrite this value as "0.6" in a rewritten equation:

________________________

So; we take our equation:

→ 27 = (60/100)*n ; And rewrite—substituting "0.6" for

"(60/100)"— as follows:

________________________

→ 27 = (0.6)n ; ↔ (0.6) n = 27 ;

Multiply each side of the equation by "10" ; to eliminate the decimal:

→ 10 * [ (0.6)n ] = 27 * 10 ;

to get:

→ 6n = 270 ;

Divide each side of the equation by "6" ; to isolate "n" on one side of the equation; & to solve for "n" ;

→ 6n / 6 = 270 / 6 ;

to get: n = 45 ;

________________________________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Method 2 (variant 2 of 2):

________________________________________________

We have the equation: 27 = (60/100)* n ; Solve for "n" ;

________________________

Note: From Method 2 (variant) 1 of 2— see above):

________________________

Note: Refer to the point at which we have:

________________________

→ " { (60÷10) / (600÷10)" = " (6/10) " ; that is; "six-tenths"} ;

________________________

Note that the fraction— "(6/10)" ; can be further simplified:

→ "(6/10)" = "(6÷2) / (10÷2)" = "(3/5)" ;

Now, we can rewrite the equation;

→ We replace "(60/100)" ; with: "(3/5)" :

→ 27 = (3/5)* n ; Solve for "n" ;

↔ (3/5)* n = 27 ;

↔ (3n/5) = 27 ;

Multiply Each Side of the equation by "5" ;

→ 5* (3n/5) = 27 * 5 ;

to get:

→ 3n = 135 ;

Divide Each side of the equation by "3" ; to isolate "n" on one side of the equation; & to solve for "n" ;

→ 3n / 3 = 135 / 3 ;

to get: n = 45 ;

________________________________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

Hope this answer is helpful!

Wishing you the best in your academic endeavors

— and within the "Brainly" community!

________________________________________________

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