Assume that the terminal side of an angle of t radians passes through the given point. Find sin(t),cos(t), tan(t). (.5,−.8) sin(t)= ____ cos(t)= ____ tan(t)= ____

Answer:

He will pat $94.60.

Step-by-step explanation:

Since you need to add 10% tax to your total, that is ten cents per dollar, and since you are adding it to the $86, you need to do 86 x 1.10, which is 94.60, and there you have it.

we can see that a = 2 and b = 3. Therefore:

A = 2

B = 3

Using the half-angle formula for sine, we have:

sin(π/12) = sqrt[(1 - cos(π/6)) / 2]

We can simplify cos(π/6) using the half-angle formula for cosine as well:

cos(π/6) = sqrt[(1 + cos(π/3)) / 2] = sqrt[(1 + 1/2) / 2] = sqrt(3)/2

Substituting this value into the formula for sin(π/12), we get:

sin(π/12) = sqrt[(1 - sqrt(3)/2) / 2]

Multiplying the numerator and denominator by the conjugate of the numerator, we can simplify the expression:

sin(π/12) = sqrt[(2 - sqrt(3))/4] = 1/2 * sqrt(2 - sqrt(3))

Now we can compare this expression with the given expression:

1/2 * sqrt(a) - sqrt(b) = 1/2 * sqrt(2 - sqrt(3))

what is half-angle formula ?

The half-angle formula is a trigonometric identity that expresses the trigonometric functions of half of an angle in terms of the trigonometric functions of the angle itself.

To learn more about half-angle formula visit:

brainly.com/question/30400810

#SPJ11

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Read more about similar triangles here:https://brainly.com/question/14285697

#SPJ1

Answer:

a2=b2+c2-2bc cos a

Step-by-step explanation:

Answer:

√89 or 9.43 units is the distance between Sophia's house and library

Step-by-step explanation:

H (1 ,1)  ⇒ House

L(6 , 9) ⇒ Library

Leg₁ = OH = 6 - 1 = 5 units

Leg₂ = OL = 9 - 1 = 8 units

            Hypotenuse² = leg₁² + leg₂²

                                   = 5² + 8²

                                    = 25 + 64

                                    = 89

              hypotenuse = √89 units  (radical form)

               hypotenuse = 9.43 units  

Answer:

Step-by-step explanation:

The cost of one ticket will be  £8.20

Explanation

Suppose, the cost of one ticket is  

As the offer says "buy 3 tickets and get a ticket free" , it means they actually need to pay for 3 tickets.

So, the total cost of 3 tickets  

Each of four friends pay £6.15 , so the total amount they pay  

=£6.15*4=£24.60

Thus, the equation will be .....

=3x=24.60

=x=24.60/3=8.20

 So, the cost of one ticket will be  £8.20

Answer:

a B and c because there the shape of the big triangles

The average speed of Usain Bolt is \($10 \frac{5}{12}$\) m/s.

A body's average speed is the mean value of its speed over time. Because the speed of a moving body is not constant and varies over time, an average speed formula is required. Even with varying speed, the values of total time and total distance covered can be used, and we can find a single value to represent the entire motion using the average speed formula.

Usain Bolt set the world record for sprinting 100 meters in approximately 9 \(\frac{3}{5}\)  second.

The formula for average speed is given by:

Speed = Distance/Time

Given Data:

Distance = 100 m

Time = 9 \(\frac{3}{5}\)  

Time = 48/5 sec

Now, Speed = \($\frac{100}{\frac{48}{5}}$\)

Speed = 500/48

Speed = 125/12

Speed = \($10 \frac{5}{12}$\)

As a result, the average speed of Usain Bolt is measured in meters per second is \($10 \frac{5}{12}$\).

To know more about average speed visit:

https://brainly.com/question/27851466

#SPJ9

Answer:

-3 Farenheit change per hour

She didnt divide properly

Step-by-step explanation:

PLZ MARK BRAINLIEST.

Answer:

C

Step-by-step explanation:

The sum of the series [infinity] at n = 1 is equal to 7.

To find the sum of the series [infinity] at n = 1 whose partial sums are given as sn = 7 − 6(0.6)n, we use the given formula :

lim n→∞ sn

So, we need to find the limit of sn as n approaches infinity.

Therefore, we get:

s = lim n→∞ sn= lim n→∞ (7 − 6(0.6)n) = 7 − 6 × lim n→∞ (0.6)n

For the limit, we note that (0.6)n is a geometric series, and its common ratio is r = 0.6.

Therefore, we use the formula to find the limit of the geometric series as n approaches infinity.

Thus, we get:

lim n→∞ (0.6)n= 0 n = ∞

The reason being that 0 < r < 1, then the sum of the infinite series becomes infinite because the terms are continuously getting smaller and smaller but never actually get to 0. Now, plugging in this value to our equation for s, we obtain:

s = 7 − 6 × 0= 7

Therefore, the sum of the series [infinity] at n = 1 whose partial sums are given as sn = 7 − 6(0.6)n is equal to 7.

To learn more about infinite series visit : https://brainly.com/question/26255015

#SPJ11

Answer:

-7/32

Step-by-step explanation:

Multiply,Simplify

Answer:

-1 1/3

Step-by-step explanation:

cross multiply

-3×12=-36

-8×7=-56

simplify

-4/-3

simplify

-1 1/3

Answer:

2

Step-by-step explanation:

slope = rise / run

rise = 20

run = 10

20/10 = 2

Explanation:

Scalene triangle has no side equal. Its angles are also not equal.

The three sides of scalene triangle are all differenet from one another.

Answer:

the answer is b between 6 and 7

Step-by-step explanation:

i say this because the square root of 41 is 6.4031.

6.4031 is in between 6 and 7.

hope this helps :)

Answer:

first quarter

Step-by-step explanation:

Answer: x=-1

Step-by-step explanation: hope this helps!

Answer: Velocity describes motion by indicating how fast an object moves and in what direction. Speed is a magnitude of velocity, which indicates only how fast an object moves. Speed shows how much distance is traversed in a given interval of time:

Step-by-step explanation:

The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

To know more about the right circular cylinder, here

https://brainly.com/question/12762578

#SPJ4

The percentage of the students at the university which are foreign are 25% by conditional probability formula.

According to the question,  10% of all college students are foreign students who also smoke and it is also known that 40% of all foreign college students smoke.

We use the conditional probability formula to solve this question.

Let foreign students be denoted as F

Let students smoking be denoted as S

We know that 10% of all college students are foreign students who also smoke this means

P(F ∩ S) = 0.1

and 40% of all foreign college students smoke which means

P(S/F) = 0.4

So, the percentage of the students at this university who are foreign can be calculated as  

\(P(F) = \frac{0.1}{0.4}\) = 0.25

To know more about probability

https://brainly.com/question/24107596

#SPJ4

Answer:

\(w=4\)

Step-by-step explanation:

So we have the equation:

\(3w+7=19\)

Subtract 7 from both sides:

\(3w=12\)

Divide both sides by 3:

\(w=4\)

So, the value of  w is 4.

And we're done!

The value of w in the equation 3w + 7 = 19 will be 4 .

Given ,

Equation : 3w + 7 = 19

Here,

Solve the equation ,

Take 7 from LHS to RHS ,

3w = 19 - 7

3w = 12

Divide both LHS and RHS by 3

w = 12/3

w = 4

Thus the value of w will be 4 .

Know more about equation ,

https://brainly.com/question/17179940

#SPJ6

By definition, the x-coordinate of the terminal point is equal to cos t and the y-coordinate is equal to sin t. This allows us to easily find the values of sin t and cos t. To find tan t, we use the formula tan t = sin t / cos t, which we can substitute with our previously found values for sin t and cos t.

First need to understand what is meant by the terms "terminal point" and "unit circle". The unit circle is a circle with a radius of 1, centered at the origin of the coordinate plane. The terminal point is the point where the circle intersects with a line that starts at the origin and passes through an angle t measured in radians.
To find sin t and cos t, we need to look at the coordinates of the terminal point. Let's call the x-coordinate of the terminal point x' and the y-coordinate y'. By definition, x' = cos t and y' = sin t. Therefore, sin t = y' and cos t = x'.
To find tan t, we use the formula tan t = sin t / cos t. Substituting in our values for sin t and cos t, we get:
tan t = y' / x'
So, to summarize:
- sin t = y'
- cos t = x'
- tan t = y' / x'
In summary, we can use the unit circle to determine the values of sin t, cos t, and tan t for any angle t measured in radians. The terminal point on the unit circle is the point where the circle intersects with a line passing through the origin at angle t.

To know more about circle visit:

https://brainly.com/question/12930236

#SPJ11

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

More can be learned about supplementary angles at brainly.com/question/2046046

#SPJ1

Answer:

 No

Step-by-step explanation:

You want to know if the set of even integers has the density property.

The density property states that for any two elements of a set, there are additional elements of the set between them.

There are no even integers between any two consecutive even integers, so the set of even integers does not have the density property.

Answer:

please rate as brainliest

The given problem can be solved using the following formulae and procedures: Failure rate is the frequency with which an engineered system or component fails, normally expressed in failures per million hours (FPMH) or in percentage per year.

Failure rate is calculated using the formula FR = Number of failures / Total time Units of Failure rate is percentage per year or failures per million hours.FR(%): Failure rate in percentage per year FR(N): Failure rate in failures per million hours MTBF: Mean Time Between Failures For the given problem, Number of batteries, n = 5

Design life, L = 72 months

Test results = 1 failure at 24 months, 1 failure at 30 months, 1 failure at 48 months, and 1 failure at 60 months. Failure rate is calculated by using the formula: FR = Number of failures / Total time Since all the batteries have different lifespan, calculate the total time for which batteries were used.

Total time, T = 24 + 30 + 48 + 60T

= 162 months

FR = 4 / 162 FR(%):To convert FR from failures per month to percentage per year, use the formula:

FR(%) = (1 - e^(-FR*t)) x 100%

Where, t = 1 year = 12 months

FR(%) = (1 - e^(-FR*t)) x 100%Putting the given values:0.29% is the annual failure rate of the Everstart battery after the given test. Frequency of Failure (FR(N)) is given by:

FR(N) = (Number of failures / Total time) x 10^6FR(N)

= (4 / 162) x 10^6FR(N)

= 24,691.358 failure per million hours.

Mean Time Between Failures (MTBF) can be calculated using the following formula: MTBF = Total time / Number of failures MTBF = 162 / 4

MTBF = 40.5 months

Therefore,FR(%) = 0.29%, FR(N) = 24,691.358 failures per million hours, and MTBF = 40.5 months.

To know more about frequency visit:

https://brainly.com/question/29739263

#SPJ11

Part A

f(0)

that means the value of f(x) for x=0

looking at the table

For x=0 ----> f(x)=4

therefore

f(0)=4

Part B

f(x)=0

looking at the table

f(x)=0 when the value of x=1

therefore

f(1)=0

Part C

f^-1(0)

For f(x)=0 -----> the value of x=1

therefore

f^-1(0)=1

Part D

f^-1(x)=0

looking at the table

For x=0 -----> f(x)=4

therefore

f^-1(4)=0

Answer:

A = Solve 5x2 + 6x + 1 = 0

B= Coefficients are: a = 5, b = 6, c = 1

Quadratic Formula: x =  −b ± √(b2 − 4ac)2a

Put in a, b and c: x =  −6 ± √(62 − 4×5×1)2×5

Solve: x =  −6 ± √(36 − 20)10

 x =  −6 ± √(16)10

 x =  −6 ± 410

 x = −0.2 or −1

Answer: x = −0.2 or x = −1

Step-by-step explanation:

there you go

A person's cardiovascular fitness, age, weight, gender, and the severity of the activity performed may all play a role in how fast a person attains steady-state and fully recovers. When an individual is fit, they tend to have a lower resting heart rate than an unfit person. Furthermore, a fit person's heart rate is less likely to climb to high levels during activity, and their muscles are more efficient, requiring less oxygen to function. Finally, fit people tend to have better cardiovascular health and are more capable of removing waste products from their muscles, allowing for a quicker recovery time.

RQ stands for respiratory quotient and represents the ratio of carbon dioxide produced to oxygen consumed. During exercise, RQ rises because the body is using more carbohydrates than fats to generate energy, which increases carbon dioxide production. During the recovery period, RQ decreases as the body switches back to using fat as its primary energy source and oxygen consumption increases.The graph/plot of RQ as a function of time during rest, physical activity, and recovery phases should show a steady increase during physical activity and a decline during recovery. This variation makes sense because during exercise, the body's demand for energy increases, and RQ increases as a result. Conversely, during recovery, the body switches back to using fat as its primary energy source, resulting in a decrease in RQ.

steady-state: https://brainly.com/question/1900452

#SPJ11