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Answer and Step-by-step explanation:

There are three reciprocal trigonometric functions

making a total of six including cosine, sine, and tangent.

→The reciprocal cosine function is secant: sec(Ф)=1/cos(Ф).

→The reciprocal sine function is cosecant, csc(Ф)=1/sin(Ф).

→The reciprocal tangent function is cotangent, expressed two ways: cot(Ф)=1/tan(Ф) or cot(Ф)=cos(Ф)/sin(Ф).

We've already learned the basic trig ratios:

sin(A) = a/c

cos(B) = b/c

tan(C) = a/b

But there are three more ratios to think about:

→Instead of  a/c, we can consider c/a  

​→Instead of  b/c, we can consider c/b  

→Instead of  a/b, we can consider b/a  

These new ratios are the reciprocal trigonometric ratios, and we’re about to learn their names.

The cosecant (csc)

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.

sin(A) = opp / hyp  = a/c

csc(A) = hyp / opp = c/a

The secant (sec)

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

cos(A) = adj/hyp = b/c

sec(A) = hyp/adj = c/b  

The cotangent (cot)

The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.

tan(A) = opp/adj = a/b

cot(A) =adj/opp = b/c

Newton's Law of Cooling:

[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}[/tex]

[tex]T(t) =[/tex] Temperature given at a time

[tex]t =[/tex] Time

[tex]T_{s} =[/tex] Surrounding temperature

[tex]T_{o}=[/tex] Initial temperature

[tex]e =[/tex] Constant (Euler's number) ≈ 2.72

[tex]k =[/tex] Constant

Using this information, find the value of [tex]k[/tex], to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.

First, plug in the given values in the equation and solve for [tex]k[/tex]:

[tex]T(t) =[/tex] 197°, [tex]t =[/tex] 1.5 minutes, [tex]T_{s} =[/tex] 70° and [tex]T_{o}=[/tex] 210°  

[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k[/tex]

[tex]k[/tex] ≈ [tex]0.065[/tex]

Let the temperature of the water cup after [tex]t = 4[/tex] minutes be [tex]T(t) = x[/tex]

Now, let's plug the new time and [tex]k[/tex] constant in the equation and solve for [tex]x[/tex]:

[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\\\\x=70+(210-70})e^{-0.065*4}\\\\x=70+(140})e^{-0.26}, -0.26=-\frac{26}{100}=-\frac{13}{50} \\[/tex]

[tex]x=70+(140})e^{-\frac{13}{50}}\\\\[/tex]

[tex]x=70+(140})e^{\frac{1}{\frac{13}{50}}\\\\\\[/tex]

[tex]x=70+e^{\frac{140}{\frac{13}{50}}\\\\\\[/tex]

[tex]x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\[/tex]

[tex]x = 70 +\frac{140}{1.3} \\x=70+107.947\\[/tex]

[tex]x=177.95[/tex] ≈ [tex]178[/tex]

Temperature of water after 4 minutes is 178°

sorry if there's any misspelling or wrong step but I hope my answer is correct ':3

Answer:

X = 13

Step-by-step explanation:

42 - X = 29

Subtract 42 from each side

42-42 - X = 29-42

-X = -13

Multiply each side by -1

X = 13

Answer:

5 thirteenth ti the nearest tenth Is .6

Answer:

0.4

Step-by-step explanation:

First make it a decimal:

5/13 (divide)

0.38 (round)

So you get 0.4

The measurement is closest to the side length of this counter top in feet is 10.17ft

The formula for calculating the area of a square is expressed as:

area of a square = L^2

where

L is the length of a square

Given the following parameter

A = 103.5ft^2

Substitute

103.5ft^2 = L²

L = √103.5

L = 10.17ft

Hence the measurement is closest to the side length of this counter top in feet is 10.17ft

he measurement is closest to the side length of this counter top in feet is 10.17ft

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11.) 0.5.

12.) 0.25.

13.)1/2,0.49,55%.

14.)2/5,0.6,35%.

15.) To get a whole number from a fraction you have to multiply the fraction by the denominator of the fraction=5/9×9=5.

or you can say that can add 4/9 to 5/9=9/9=1 a whole number also

Answer:

the value of theta i 45°

Answer:

none

Step-by-step explanation:

Answer:

It does not have any solution because 3 is not equal to 8

Answer:

Step-by-step explanation:

Given the step 3 and 4 of the solution Step 3: -6x − 8 < -2 Step 4: -6x < 6

From step 3;

-6x − 8 < -2

Michael got the step 4 by adding 8 to both sides of the inequality as shown;

-6x − 8 + 8 < -2 + 8

-6x < 6 (Step 4)

Since Michael added 8 to both sides of the inequality, the property that justifies the transition from step 3 to step 4 is the addition property of inequality. Addition property is the property that adds an integer to both sides of an inequality without altering the inequality sign and also retaining the inequality equation.

Answer:

[tex]\Huge \boxed{x=6}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex](2^{2x +2}) (2^{3x -7})= 2^{25}[/tex]

When multiplying same bases, add the exponents.

[tex](2^{2x +2+3x -7})= 2^{25}[/tex]

[tex](2^{5x -5})= 2^{25}[/tex]

Cancelling the same bases from both sides.

[tex]5x-5=25[/tex]

Adding 5 to both sides.

[tex]5x=30[/tex]

Dividing both sides by 5.

[tex]x=6[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer: 336+6i

The key to solving this problem is to choose which parts you should solve first.

2i(3-4i)+8(4-5i)(4+5i)​

let's divide this expression to three parts:

2i(3-4i), 8 and (4-5i)(4+5i)​

first let's solve 2i(3-4i):

2i(3-4i) =

2i × 3 + 2i × -4i =

6i - 8i² =

6i + 8

(4-5i)(4+5i)​:

(4-5i)(4+5i)​ =

16 + 20i - 20i -25² =

16 + 25 =

41

8(4-5i)(4+5i)​:

8(4-5i)(4+5i)​ = 8 × 41 = 328

Now let's put back these parts:

2i(3-4i)+8(4-5i)(4+5i)​ =

6i + 8 + 328 =

6i +336 OR 336 +6i

Answer:

[tex](\frac{4}{3},-3)[/tex]

Step-by-step explanation:

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]) is given by the formula:

[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1[/tex]

From the graph, the location of the point is P(2, 5), R(1, -7). Let point Q be (x, y) which divides PR in ratio 2:1. Coordinates of point Q is at:

[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1=\frac{2}{2+1}(1-2)+2=\frac{2}{3}(-1)+2=\frac{4}{3} \\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1=\frac{2}{2+1}(-7-5)+5= \frac{2}{3}(-12)+5=-3[/tex]

Point Q is at [tex](\frac{4}{3},-3)[/tex]

Answer:

PT = 22

Step-by-step explanation:

Given that T is the midpoint of PQ, then

PT = TQ , substitute values

5x + 2 = 7x - 6 ( subtract 5x from both sides )

2 = 2x - 6 ( add 6 to both sides )

8 = 2x ( divide both sides by 2 )

4 = x

Thus

PT = 5x + 2 = 5(4) + 2 = 20 + 2 = 22

Answer:

33 2/6 miles

Step-by-step explanation:

So we know that every 6 inches equals 8 miles. To find one mile, we would divide both sides by 8, so every 6/8 of an inch is 1 mile. if the two cities are 25 in apart on a map, that means that we can first do 6*4:8*4 for the ease of it to get 24 inches and 32 miles. So so far it's already 32 miles. Then we have to calculate the leftover one inch. To find out how many miles one inch is, we can divide both sides by 6, so one inch=8/6 of a mile.

So then we add 32+8/6=33 2/6

Tell me if that works for you

Answer:

yes every natural number is integer

because intezer is collection of positive and negative numbers....

Answer:

Step-by-step explanation:

Hello friend!!!

It's TRUE

Natural numbers are the range of numbers from 1 to infinite.

Integers are made up of positive as well as negative numbers.

Since natural numbers are positive numbers, they are also integers.

Hope this helps

plz mark as brainliest!!!!!

Answer:

[tex]\Huge \boxed{\mathrm{55}}[/tex]

Step-by-step explanation:

[tex]-7x + 6[/tex]

Put x as -7 and evaluate the expression.

[tex]-7(-7)+6 \\\\\\ 49+6 \\\\\\ 55[/tex]

Answer:

You would buy the DVD at Discount DVD.

Step-by-step explanation:

To decide where to buy the DVD, you have to determine the price at each store after the discount is applied.

-Discount DVD: $29.90*0.2=$5.98

$29.90-$5.98=$23.92

-Value Video: $28.60*0.15=$4.29

$28.60-$4.29=$24.31

According to this, you would buy the DVD at Discount DVD because it is where you will get the lower price.

Answer:

-7, -8, -9, -10

Step-by-step explanation:

Is this actually the whole problem? If so, the answer is anything less than -6. z < -6 includes all the numbers less than -6, so that would include -7, -8, -1000, -6.000001, etc.; you get what I mean. This would NOT include -6, though, because z is less than, not equal to, -6.

You can visualize it on a number line. If every value that could possibly equal z had a dot on it, you would see an infinite number of dots starting from -6 and going left to infinity. Like: <-------------o, if o was -6.

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Answer: 72.416

Step-by-step explanation:

Answer:

$1807.94

Step-by-step explanation:

Given that:

Annual income = $43047

Social security (FICA tax) = 4.2% of the gross wages

To find:

Social security paid = ?

Solution:

Social security (FICA tax) is calculated by finding the 4.2% of the Total Gross Annual income.

i.e. for the given value, the social security paid can be calculated as:

4.2% of $43047

[tex]\Rightarrow \dfrac{4.2}{100}\ of \ \$43047\\\Rightarrow \dfrac{42}{1000}\times 43047\\\Rightarrow 0.042\times 43047\\\Rightarrow \bold{\$1807.97}[/tex]

Therefore, the Social Security paid is $1807.94.

Answer:

no, it will always be the same size and image just in a different placement.

Step-by-step explanation:

No, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.

Hence, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.

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Answer:

D) x-3

Step-by-step explanation:

(4x+1)-(3x-4)=

4x-3x+1-4=

x-3

Answer: $39.60

Step-by-step explanation:

Here is the correct question:

Christopher has breakfast at a cafe and the cost of his meal is $36.00 . because of the service he wants to leave a 10% tip.What is his total bill including tip?

His total bill will be the addition of the cost of his meal and the tip. This will be:

= $36.00 + (10% × $36.00)

= $36.00 + $3.6

= $39.60

His total bill including tip is $39.60

Answer:

Expand the left side, group like terms on both sides, and get

(2a)x + 3a = 10x + 15

To be true for all x, equate like terms from both sides and get

2a = 10

3a = 15

Solution: a = 5

You can test the answer.

Step-by-step explanation:

Expand the left side, group like terms on both sides, and get

(2a)x + 3a = 10x + 15

To be true for all x, equate like terms from both sides and get

2a = 10

3a = 15

Solution: a = 5

You can test the answer.

Answer:

The roots are

Step-by-step explanation:

9x² + 54x + 82 = 0

Using the quadratic formula

That's

From the question

a = 9 , b = 54 , c = 82

Substitute the values into the above formula and solve

That's

Separate the real and imaginary parts

That's

We have the final answer as

Hope this helps you

Antarctica , I think

Step-by-step explanation:

Answer:

x = 3 or x = -3

Step-by-step explanation:

Solve for x over the real numbers:

2 x (x + 3) - 6 (x + 3) = 0

Expand out terms of the left hand side:

2 x^2 - 18 = 0

2 x^2 - 18 = 2 (x^2 - 9):

2 (x^2 - 9) = 0

Divide both sides by 2:

x^2 - 9 = 0

x = (0 ± sqrt(0^2 - 4 (-9)))/2 = ( ± sqrt(36))/2:

x = sqrt(36)/2 or x = (-sqrt(36))/2

sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:

x = 6/2 or x = (-6)/2

6/2 = 3:

x = 3 or x = (-6)/2

(-6)/2 = -3:

Answer: x = 3 or x = -3

Answer:

Well make sure your answer is correct. If it’s correct extend your graph.

Step-by-step explanation: