Answer:
It will take about 27.7 years
Step-by-step explanation:
* Lets talk about the compound continuous interest
- Compound continuous interest can be calculated using the formula:
A = P e^rt
• A = the future value of the investment, including interest
• P = the principal investment amount (the initial amount)
• r = the interest rate
• t = the time the money is invested for
- The formula gives you the future value of an investment,
which is compound continuous interest plus the principal.
- If you want to calculate the compound interest only, you need
to deduct the principal from the result.
- So, your formula is:
Compounded interest only = Pe^(rt) - P
* Now lets solve the problem
∵ The invest is $ 1000
∴ P = 1000
∵ The interest rate is 2.5%
∴ r = 2.5/100 = 0.025
- They ask about how long will it take to make double the investment
∴ A = 2 × 1000 = 2000
∵ A = P e^(rt)
∴ 2000 = 1000 (e)^(0.025t) ⇒ divide both sides by 1000
∴ 2000/1000 = e^(0.025t)
∴ 2 = e^(0.025) ⇒ take ln for both sides
∴ ln(2) = ln[e^(0.025t)]
∵ ln(e)^n = n
∴ ln(2) = 0.025t ⇒ divide both sides by 0.025
∴ t = ln(2)/0.025 = 27.7 years
* It will take about 27.7 years
Osmium is a chemical element with a density of 22.6 grams per cubic centimeter. A piece of Osmium has a volume of 15.1 cubic centimeters. What is the mass of the piece of Osmium to the nearest tenth of a gram?
Answer:
341.3 g
Step-by-step explanation:
we know that
The density is equal to the ratio of the mass by the volume
D=m/V
Solve for the mass m
m=D*V
In this problem we have
D=22.6 g/cm³
V=15.1 cm³
substitute in the formula
m=22.6*(15.1)=341.26 g
Round to the nearest tenth of a gram
341.26 g=341.3 g
PLEASE HELP THANK YOU SO MUCH
https://brainly.com/question/11525341
Use the quadratic formula to determine the exact solutions to the equation. 2x^2 + 3x − 7 = 0. (Type 2 separate answers)
Answer:
Step-by-step explanation:
Here the coefficients are a = 2, b = 3 and c = -7.
Thus, the discriminant b²-4ac is 3²-4(2)(-7), or 9 + 56 = 63.
Because the discriminant is positive, we know we have two real, different roots. They are:
-3 ± √63 -3 + 3√7 -3 - 3√7
x = ---------------- = ----------------- and x = -----------------
2(2) 4 4
Nikhil gets paid a 5 percent commission on every pair of shoes that he sells. He earned $1.00 on the last pair of shoes that he sold. The expression that can be used to represent x, the price of the shoes, is What was the price of the shoes?
If 5 equals 1
then 100 will equal 20
the shoes are 20 dollars
Answer:
$20.00 is the correct answer
Step-by-step explanation:
I promise this is correct
Write a rule for the linear function in the graph
Plz help
Answer:
y = -x +4
Step-by-step explanation:
The y-intercept of the line is at +4, so the only viable choice is the last choice.
___
Each of the equations is shown in slope-intercept form:
y = mx + b
where b is the y-intercept, the y-value when x=0. The graph shows that as point (0, 4). So, the equation you're looking for is ...
y = (some x-term) +4
If you want to spend more brain power on the problem, you can compute the slope of the line as ...
m = ∆y/∆x = (1-4)/(3-0) = -3/3 = -1
Now, you know for sure the equation of the line is ...
y = -x +4
Which quotient will be negative?
24 ÷ 6
-35 ÷ 7
-54 ÷ (-6)
3 ÷ (-1)
Answer:
-35/7
3/-1
Step-by-step explanation:
If you divide a positive number by a positive number
the outcome will be positive
If you divide a positive number by a negative number the outcome will be negative
If you divide a negative number by a negative number the outcome will be positive
If you have any questions do not hesitate to ask
:)
3/-1 is also a solution
What are the answers and why?
Answer:
The selected answers are correct.
Step-by-step explanation:
The first step of the 3-step test for continuity is
check to see if the function is defined at the point. Here, the function h(-3) is defined as 5.The second step of the 3-step test for continuity is
check to see if the limit exists at the point. Here, the limit is 2, coming at it either from the left or the right. (log6(36)=2; 16·2^-3=2)The third step is
show the function value is the same as the limit at the point of interest. Here 5 ≠ 2, so there is a discontinuity at x=-3.The heights of all adult males in Croatia are approximately normally distributed with a mean of 180 cm and a standard deviation of 7 cm. How tall must an adult male in Croatia be in order to be the tallest 5% of the males
To be in the tallest 5% of adult males in Croatia, given a mean height of 180 cm and a standard deviation of 7 cm, the required height would be about 191.515 cm.
Explanation:The question is related to the concept of normal distribution in statistics. Given that the heights of all adult males in Croatia are approximately normally distributed with a mean of 180 cm and a standard deviation of 7 cm, we are asked to calculate the height a male would need to be in the tallest 5% of males.
We use the z-score to solve this. The z-score associated with the top 5% of a standard normal distribution is approximately 1.645 (you can find this in a standard z-table or through a statistical calculator).
To find the height associated with this z-score, we use the formula: X = μ + zσ, where X is the measurement we seek, μ is the mean, z is the z-score, and σ is the standard deviation. Substituting the given values, we get:
X = 180 cm + 1.645 * 7 cm
X = approximately 191.515 cm
So, to be in the tallest 5% of males in Croatia, an adult male would have to be about 191.515 cm or taller.
Learn more about Normal Distribution here:https://brainly.com/question/34741155
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An adult male in Croatia must be approximately 190.5 cm tall to be in the tallest 5% of the males.
Explanation:To find out how tall an adult male in Croatia must be in order to be the tallest 5% of the males, we need to find the z-score corresponding to the upper 5% tail of the standard normal distribution.
Using the z-score formula, z = (x - mean) / standard deviation, we can solve for x.
Plugging in the values, we have z = (x - 180) / 7. Now, we can find the z-score corresponding to the upper 5% tail, which is approximately 1.645.
Substituting this value back into the z-score formula, we have 1.645 = (x - 180) / 7. Solving for x, we find that x is approximately 190.5 cm.
Learn more about Finding the height for the tallest 5% of male adults in Croatia here:https://brainly.com/question/31197417
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PLEASE HELP SHOW YOUR WORKING OUT Branliest
Answer:
The equation of this line is therefore y = 2x + 3.
Step-by-step explanation:
this line passes thru the points (0, 3) and (3, 9). As we move from (0, 3) to (3, 9), x increases by 3 and y increases by 6. Thus, the slope of this line is
m = rise / run = 6/3, or m = 2. Inserting the known info (m = 2, x = 0, y = 3) into y = mx + b, we get: 3 = 2(0) + b, so we see that b = 3.
The equation of this line is therefore y = 2x + 3.
how do you solve this proof? help please. thank you! <3
The answer is given in the file attached
angle addition postulate:
m∠B = m∠1 + m∠3
m∠1 = m∠B - m∠3
Richard has $1,089.26 in his checking account at the end of the month. During the month, he withdrew $120, deposited a check for $325, and wrote one check for $425 and one check for $24.10. What was his checking account balance at the beginning of the month?
$845.16
$1,093.36
$1,333.36
$1,490.16
Answer:
The first option is the right answer $ 845.16
Step-by-step explanation:
1.089.26-120=969.26
969.26+325=1.294.26
1.294.26-425=869.26
869.26-24.10= 845.16
Define the following terms. Be sure to write the definitions in your own words and use complete sentences, proper grammar, and spelling.
Mean :
Median:
Mode:
Range:
Outlier:
Answer: Here...
Step-by-step explanation:
Mean: The average of the numbers so add them up then divide by how many numbers you added
Median: The middle number of the numbers in numerical order
Mode: The number that is repeated the most often
Range: The smallest number subtracted from the larger number
Outlier: A data point or observation that is not with the others so basically the odd one out
Hope this helps Brainliest plz
If the circumference of a circle is 36, what is the length of an arc of the circle intercepted by a central angle of 30 degrees?
Answer:330 degrees
Step-by-step explanation: It helps by drawing a picture, hope this helps
Answer: [tex]arc\ length=3[/tex]
Step-by-step explanation:
The formula for calculate the arc lenght is:
[tex]arc\ length=2\pi r(\frac{\theta}{360})[/tex]
Where "r" is the radius and "[tex]\theta[/tex]" is the central angle of the arc in degrees.
The formula used to find the circumference of a circle is:
[tex]C=2\pi r[/tex]
Where "r" is the radius.
Then, we can observe that the formula for calculate the arc lenght can be rewritten in this form:
[tex]arc\ length=C(\frac{\theta}{360})[/tex]
Where "C" is the circumference of the circle.
Finally we need to substitute the central angle and the circumference into [tex]arc\ length=C(\frac{\theta}{360})[/tex]. Then the result is this:
[tex]arc\ length=36(\frac{30\°}{360})=3[/tex]
A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism.
The company wants to use the package that has the least amount of wasted space. The company should choose
a.)the prism because it has approximately 11.6 in.3 less wasted space than the cylinder.
b.)the prism because it has approximately 14.1 in.3 less wasted space than the cylinder.
c.)the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
d.)the cylinder because it has approximately 14.1 in.3 less wasted space than the prism.
Answer:
Option c.) the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
Step-by-step explanation:
step 1
Find the volume of one ball
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]V=\frac{4}{3}(3.14)(1.5)^{3}=14.13\ in^{3}[/tex]
therefore
The volume of two balls is
[tex](2)*14.13=28.26\ in^{3}[/tex]
step 2
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]h=1.5*4=6\ in[/tex]
substitute
[tex]V=(3.14)(1.5)^{2}(6)=42.39\ in^{3}[/tex]
therefore
The wasted space with the cylinder is equal to
[tex]42.39\ in^{3}-28.26\ in^{3}=14.13\ in^{3}[/tex]
step 3
Find the volume of the square prism
The volume of the square prism is equal to
[tex]V=b^{2}h[/tex]
we have
[tex]b=1.5*2=3\ in[/tex]
[tex]h=1.5*4=6\ in[/tex]
substitute
[tex]V=(3)^{2}(6)=54\ in^{3}[/tex]
therefore
The wasted space with the prism is equal to
[tex]54\ in^{3}-28.26\ in^{3}=25.74\ in^{3}[/tex]
step 4
Find the difference of the wasted space
[tex]25.74\ in^{3}-14.13\ in^{3}=11.61\ in^{3}[/tex]
Answer:
C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
Step-by-step explanation:
if you find the volumes of both shapes and subtract the volumes of the two balls and then subtract the two remaining values you get a difference of 11.6 inches. This makes the cylinder smaller and therefore uses less space.
Pleeeeeease help. !! !!!!!
Answer:
259.8 cm²
Step-by-step explanation:
A regular hexagon can be cut into 6 equilateral triangles and an equilateral triangle can be divided into two 30°- 60°- 90° triangles
Note that the apothem (5[tex]\sqrt{3}[/tex]) divides the triangle into two equilateral triangles, thus
The apothem is the long leg (the x[tex]\sqrt{3}[/tex]) side of a 30- 60- 90 triangle, so
x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex] ⇒ x = 5
Thus the side length of the hexagon = 2 × 5 = 10
and the perimeter = 6 × 10 = 60
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
= 0.5 × 60 × 5[tex]\sqrt{3}[/tex] = 150[tex]\sqrt{3}[/tex] ≈ 259.8 cm²
If you were to draw three different parallelograms each base of 6 units and a height of 4 units how would the areas compare
Answer:
They are all the same.
Step-by-step explanation:
The area of a parallelogram is computed by multiplying the base length by the height. All of these parallelograms will have an area of ...
A = (6 units)(4 units) = 24 units²
You can draw any number of parallelograms with these dimensions, and they will all have the same area.
Write the complex number in the form a + bi.
3(cos 60° + i sin 60°)
Answer:
The complex number in the form of a + b i is 3/2 + i √3/2
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = 3(cos 60° + i sin 60°)
∴ r = 3 and Ф = 60°
∵ cos 60° = 1/2
∵ sin 60 = √3/2
- Substitute these values in z
∴ z = 3(1/2 + i √3/2) ⇒ open the bracket
∴ z = 3/2 + i √3/2
* The complex number in the form of a + b i is 3/2 + i √3/2
Answer:
3/2 + (3sqrt(3))/2 i
Step-by-step explanation:
On the unit circle cosine and sine 60 degrees can be found in the first quadrant. With the correct measures. Once located, (1/2, sqrt(3)/2), multiply those numbers by 3. Don't forget to include i.
3(1/2 + sqrt(3)/2 * i)
= 3/2 + (3sqrt(3))/2 i
This is a quadrilateral that contains two pairs of parallel sides. What is this quadrilateral?
Answer
A quadrilateral with one pair of parallel sides is a trapezoid. If it has two pairs of parallel sides it is a parallelogram, but parallelograms are also trapezoids in the same way that dogs are also mammals. A parallelogram has two pairs of congruent sides.
What is the length of a diagonal of a cube with a side length of 10 cm? 200 cm 210cm 300 cm 320cm
Answer:
The length of the diagonal of the cube = √(3 × 10²) = √300 cm
Step-by-step explanation:
* Lets revise the properties of the cube
- It has six equal faces all of them are squares
- It has 12 vertices
- The diagonal of the cube is the line joining two vertices in opposite
faces (look to the attached figure)
- To find the length of the diagonal do that:
# Find the diagonal of the base using Pythagoras theorem
∵ The length of the side of the cube is L
∵ The base is a square
∴ The length of the diagonal d = √(L² + L²) = √(2L²)
- Now use the diagonal of the base and a side of a side face to find the
diagonal of the cube by Pythagoras theorem
∵ d = √(2L²)
∵ The length of the side of the square = L
∴ The length of the diagonal of the cube = √[d² + L²]
∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root
∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)
* Now lets solve the problem
∵ The length of the side of the square = 10 cm
∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm
- Note: you can find the length of the diagonal of any cube using
this rule Diagonal = √(3L²)
Answer:
its c on endeguity
Step-by-step explanation:
Identify the volume and surface area of the sphere in terms of π. HELP PLEASE!!
Answer:
First choice V = 18,432π m^3; S = 2,304π m^2
Step-by-step explanation:
Start with the two formulas:
Volume of a circle:
[tex] V = \dfrac{4}{3} \pi r^3 [/tex]
Surface area of a circle:
[tex] S = 4 \pi r^2 [/tex]
Now use r = 24 m in each formula.
Volume:
[tex] V = \dfrac{4}{3} \pi (24~m)^3 [/tex]
[tex] V = \dfrac{4}{3} \pi (13,824~m^3) [/tex]
[tex] V = 18,432\pi~m^3 [/tex]
Surface area:
[tex] S = 4 \pi r^2 [/tex]
[tex] S = 4 \pi (24~m)^2 [/tex]
[tex] S = 4 \pi (576~m^2) [/tex]
[tex] S = 2,304\pi ~m^2 [/tex]
Answer: First choice V = 18,432π m^3; S = 2,304π m^2
Correct Option 2: The volume of the sphere is 972π cm³ and its surface area is 324π cm²
To determine the volume and surface area of a sphere, we use the formulas:
Volume: V = (4/3)πr³Surface Area: S = 4πr²Given the radius (r) of the sphere is 9 centimeters:
Volume: V = (4/3)π(9)³ = (4/3)π(729) = 972π cm³Surface Area: S = 4π(9)² = 4π(81) = 324π cm²Hence, the volume of the sphere is 972π cm³ and the surface area is 324π cm².
Use technology or a z-score table to answer the question.
The lengths of green beans for sale at a supermarket are normally distributed with a mean of 11.2 centimeters and a standard deviation of 2.1 centimeters. Consider a bag of 150 green beans.
How many green beans will be 13 centimeters or shorter?
Answer:
121
Step-by-step explanation:
First, we find the z-score for 13 cm:
z = (x - μ) / σ
z = (13 - 11.2) / 2.1
z = 0.86
Next, we use a calculator or a z-score table to find P(x<0.857).
P(x<0.86) = 0.8051
So the number of green beans in a bag of 150 less than or equal to 13 cm is:
0.8051 * 150
121
The number of green beans that is 13 centimeters or shorter will be 121. Then the correct option is C.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The z-score is given as,
z = (13 - 11.2) / 2.1
z = 1.8 / 2.1
z = 0.587
The number of green beans that is 13 centimeters or shorter will be given as,
⇒ 150 x P(z ≤ 0.587)
⇒ 150 x 0.8023
⇒ 121
Thus, the correct option is C.
More about the z-score link is given below.
https://brainly.com/question/15016913
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The mechanics at Giuseppe’s Auto House specialize in changing fuel injection units and transmissions. Last week, they changed 5 fuel injection units and 10 transmissions and billed 70 hours. This week, they changed 8 fuel injection units and 8 transmissions and billed 64 hours. Let x represent the number of hours to change a fuel injection unit and y represent the number of hours to change a transmission.
What is the solution to the system that represents this scenario?
(5, 8)
(2, 6)
(4, 14)
(7, 8)
Answer:
The solution is (2,6)
Step-by-step explanation:
Let
x-----> the number of hours to change a fuel injection unit
y-----> the number of hours to change a transmission
we know that
5x+10y=70 -----> equation A
8x+8y=64 -----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (2,6)
see the attached figure
Help please ..............
Answer:
x = 437.3 ft
Step-by-step explanation:
The angle at the top of the triangle = 90° - 29° = 61°
Using the sine ratio in the right triangle
sin61° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{500}[/tex]
Multiply both sides by 500
500 × sin61° = x, hence
x ≈ 437.3
COS(29) = X/500ft
500 COS(29) = X
X = 437,31 ft
There are 3.76 × 1022 atoms in 1 gram of oxygen. How many atoms are there in 700 grams of oxygen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
Final answer:
To find the number of atoms in 700 grams of oxygen, multiply the number of atoms in 1 gram (3.76 × [tex]10^2^2[/tex]) by 700 to get 2.63 × [tex]10^2^5[/tex] atoms, expressed in scientific notation.
Explanation:
To calculate the number of atoms in 700 grams of oxygen, you can use the number of atoms in 1 gram as a conversion factor:
Number of atoms in 1 gram of oxygen = 3.76 × [tex]10^2^2[/tex] atomsMultiply this by the mass of oxygen: 3.76 × [tex]10^2^2[/tex] atoms/g × 700 gThis equals 2.632 × [tex]10^2^5[/tex]atoms of oxygen, which is the number of atoms in 700 grams of oxygen.When multiplying, you multiply the numbers (3.76 × 700) and add the exponents for 10 (22 remains constant because the base is ten and we're dealing with grams of oxygen).
The final calculation gives 2.63 × [tex]10^2^5[/tex] atoms of oxygen, with the answer rounded to two decimal places as instructed and written in scientific notation.
Please help me please
Answer:
1.44π m²
Step-by-step explanation:
The area (A) of the circle is calculated as
A = πr² ← r is the radius
here the diameter is 2.4 and the radius is half the diameter, thus
r = 1.2, so
A = π × 1.2² = 1.44π m²
Charlie can invest $8,000 at 8.5% interest for 15 days. How much interest will he earn on his investment if the interest is compounded daily?
Answer:
$27.99 interest.
Step-by-step explanation:
Use the formula for Compound interest = P(1 + r/n)^t . Here n = 365 (number of days in a year), r = annual rate as a decimal and t = the number of days, P = 8000.
Amount after 15 days = 8,000(1 + 0.085/365)^15
= $8027.99.
Final answer:
Charlie will earn interest on his $8,000 investment at an 8.5% annual rate, compounded daily, for 15 days. The interest can be calculated using the formula for compound interest and will likely result in slightly more interest earned than if it was calculated using simple interest.
Explanation:
Charlie can invest $8,000 at 8.5% interest for 15 days. To calculate the interest earned with daily compounding, we use the formula A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount ($8,000), r is the annual interest rate (8.5%), n is the number of times that interest is compounded per year (365, since it's daily), and t is the time the money is invested in years (15/365, because here t is 15 days).
By substituting the values into the formula we get: A = $8,000(1 + 0.085/365)365*(15/365). After computing this, we find the new amount that Charlie will have after the 15 days are over. The interest earned is then found by subtracting the principal ($8,000) from this new amount.
Note that compound interest, especially when compounded frequently, can lead to greater earnings than simple interest. This difference is more pronounced with larger amounts and over longer periods, as shown by the reference provided where compound interest for a $100 investment over three years was $0.76 more than with simple interest.
Car A went 60 km in 3/4 hour while a car B went 80 km in 4/5 hour. Which car was faster? How many times faster?
Answer:
Car A went 60 km in 3/4 hour, mean 60: 3/4=80 km per hour.
Car B went 80km in 4/5 hour, mean 80;4/5= 100km per hour.
So Car B went faster than Car A and faster than 20 km. That will be help.
Step-by-step explanation:
Answer: Car B was 1 1/4 times faster
Step-by-step explanation:
Car A went 60 km in 3/4 hour
1 divided by 3/4=4/3 (the inverse of 3/4 is 4/3)
60/1*4/3=80
Car A=80
Car B went 80 km in 4/5 hour
1 divided by 4/5=5/4
80/1*5/4=100
Car B=100
100 divided by 80 is 1 1/4
Hope This helps :P
What is the term a_5?
Answer:
34Step-by-step explanation:
[tex]\text{We have the recursive form of sequence:}\\\\a_1=50\\a_n=a_{n-1}+(-4)=a_{n-1}-4\\\\a_2=a_{2-1}-4=a_1-4\to a_2=50-4=46\\a_3=a_{3-1}-4=a_2-4\to a_3=46-4=42\\a_4=a_{4-1}-4=a_3-4\to a_4=42-4=38\\a_5=a_{5-1}-4=a_4-4\to a_5=38-4=34[/tex]
PLEASE HELP ASAP 50 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Since; There are two pre-images for -2
It cannot be a linear Function.
And if we were to plot a graph...
A vertical line would cross At Three point
So; It has to be a cubic function.
Hope it helps...
Regards;
Leukonov/Olegion.
guys im actually begging please.
Answer:
sin 2Ф = -24/25
Step-by-step explanation:
* Lets revise the trigonometry functions in the four quadrants
# First quadrant the measure of all angles is between 0° and 90°
∴ All the angles are acute
∴ All the trigonometry functions of any angle are positive
# Second quadrant the measure of all angles is between 90° and 180°
∴ All the angles are obtuse
∴ The value of sin of any angle is positive (cos and tan are negative)
# Third quadrant the measure of all angles is between 180° and 270°
∴ All the angles are reflex
∴ The value of tan of any angle is positive (sin and cos are negative)
# Fourth quadrant the measure of all angles is between 270° and 360°
∴ All the angles are reflex
∴ The value of cos any angle is positive ( sin and tan are negative)
* We will need to revise two identity to solve the question
# sin²Ф + cos²Ф = 1
# sin 2Ф = 2 sinФ cosФ
* Now lets solve the question
∵ cosФ = 3/5
∵ Ф is in the fourth quadrant
∴ The value of sinФ is negative
∵ sin²Ф + cos²Ф = 1
∴ sin²Ф + (3/5)² = 1
∴ sin²Ф + 9/25 = 1 ⇒ subtract 9/25 from both sides
∴ sin²Ф = 16/25 ⇒ take √ for both sides
∴ sinФ = ± 4/5
- We will chose the value -4/5 because Ф is in the fourth quadrant
∴ sinФ = -4/5
∵ sin 2Ф = 2 sinФ cosФ
∵ sinФ = -4/5 and cosФ = 3/5
∴ sin 2Ф = 2 (-4/5) (3/5) = -24/25