1. Draw a right triangle with sides 2,2√3, and 4 units. Label all angle measures and sides. Using the side relationships from the figure, show that the following trigonometric identities hold true for either one of the non-right angles:
a. tan 0=sin 0/cos O
b.) sin^2(0)+cos^2(0)=1
where 0 represents whichever angle you choose
FYI...all of the 0 have a line through them
THank you because I don't understand this at all.
Answers
we know that
in a right triangle ABC
sin ∅=opposite side angle ∅/hypotenuse
cos ∅=adjacent side angle ∅/hypotenuse
tan ∅=opposite side angle ∅/adjacent side angle ∅
in this problem
opposite side angle ∅=2 units
adjacent side angle ∅=2√3 units
hypotenuse=4 units
so
sin ∅=2/4----> 1/2
cos ∅=2√3/4----> √3/2
tan ∅=2/2√3----> 1/√3----> √3/3
Part a) show that the following trigonometric identities hold true for either one of the non-right angles:
tan ∅=sin ∅/cos ∅
sin ∅=1/2
cos ∅=√3/2
tan ∅=(1/2)/(√3/2)--> (1/2)*2/√3---> 1/√3--->1/√3*(√3/√3)---> √3/3--> is ok
Part b) show that the following trigonometric identities hold true for either one of the non-right angles:
sin² ∅+cos² ∅=1
sin ∅=1/2
cos ∅=√3/2
so
(1/2)²+(√3/2)²=1------> 1/4+3/4----> 4/4----> 1=1----> is ok
Related Questions
a rectangle box is twice as long as it is wide. the height of the box is 3 feet less than the width. if the box is x feet wide, what polynominal represents its volume in cubic feet
Answers
The length is twice the width, so is 2x.
The height is 3 less than the width, so is x-3.
The volume is (length)*(width)*(height), so is (2x)(x)(x -3). Eliminating parentheses, the volume in cubic feet is represented by the polynomial ...
2x³ -6x²
One 16-ounce bottle of an energy drink has an average of 400 mg of caffeine with a standard deviation of 20 mg. What is the probability that the average caffeine in a sample of 25 bottles is no more than 395 milligrams?
Answers
a company observes the lifespan of 560 lightbulbs and finds that their data follows a normal distribution. what is the approximate number of light bulbs that fall within two standard deviations from the mean?
Answers
According to the empirical rule, 95% of the values lie within 2 standard deviations of the mean.
Total number of bulbs = n = 560
95% of n = 0.95 x 560 = 532
This means, 532 bulbs will lie within 2 standard deviations from the mean
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 8 inches. How far did Chubby run? Give your answer in terms of pi. (prize is 99 points)
Answers
=======================================
Explanation:
The formula to find the circumference of a circle is
C = pi*d
where
C = distance around the circle (aka circumference)
pi = 3.14 approximately
d = diameter
We know that the diameter of the wheel is d = 8, so
C = pi*d
C = pi*8
C = 8pi
is the circumference of the wheel
One full rotation will have the wheel cover a distance of 8pi inches. Imagine that wet paint is on the outer surface of the wheel. If the wheel is rolled out in a straight line, then the wet paint would cover a linear distance of 8pi inches along the flat ground. This is one full rotation, so 100 rotations covers 100*8pi = 800pi inches
Note: if we use pi = 3.14 as the approximation, then the hamster ran approximately 800*pi = 800*3.14 = 2512 inches if the wheel could move
Answer:
6280
Step-by-step explanation:
It's 6280
Caleb bought a car for $6,900. He agreed on a five-year loan at a 5.4% interest rate. Calculate what Caleb's monthly payments will be.
Answers
To calculate Caleb's monthly car payments, use the loan amortization formula that deals with compound interest, not simple interest. Input the loan amount of $6,900, the monthly interest rate (annual rate of 5.4% divided by 12), and the total number of payments (5 years times 12 payments per year) into the formula to find the monthly payment.
Explanation:Caleb's car loan scenario comes under financial mathematics, specifically, it deals with loan amortization using the concept of compound interest. Since the car loan spans multiple years, compound interest is the accurate model to use, not simple interest. As opposed to simple interest which only accrues on the original amount or principal, compound interest accrues on the principal and all interest previously added.
The formula to calculate the monthly payment, P, on a loan is given by, where PV represents t
[tex]P = [r*PV] / [1 - (1 + r)^-n][/tex]he present value or the amount of loan, which is $6,900 in this case; r is the monthly interest rate which can be calculated as annual interest rate divided by 12, translating to 0.054/12 in this case; and n is the total number of payments (i.e., 5 years of payments with 12 payments per year, hence, 5*12).
To calculate the monthly payment, plug these values into the formula which should give you the monthly payment amount that Caleb needs to pay for his car loan.
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A round table top has a diameter of 2.6 meters.What is its surface area
Answers
To find the area of a circle you use the equation
[tex] \pi r^{2} [/tex]
r is radius which is half the diameter
r = 2.6 / 2
r = 1.3
Put in the values you know
[tex] \pi 1.3^{2} [/tex]
Square the number
[tex]1.69 \pi = 5.31[/tex]
The answer is [tex]1.69 \pi [/tex] or ≈5.31
Hope this helps!
remmber that [tex]A=\pi r^2[/tex] where r=radius and A is area and pi is pi or about 3.14159265
so if diameter is 2.6, ah, tricky, they give you dameter
rmemeber that d/2=r so 2.6/2=d/2=r=1.3
so
[tex]A=\pi r^2[/tex]
[tex]A=\pi (1.3)^2[/tex]
using your calculator
[tex]A=5.309 m^2[/tex]
the surface area is [tex]5.309 m^2[/tex]
If the train that Megan is riding covers 80 miles in 2 hours, how fast is the train traveling?
Answers
To find this, you divide both 80 and 2 by 2 to find how many miles in a single hour the train travels. Thus giving you 40 miles in an hour (40 mph) as a ginal answer.
I hope this helps!
Final answer:
The average speed of the train Megan is traveling on is 40 miles per hour. It's obtained by dividing the total distance of 80 miles by the total time of 2 hours.
Explanation:
To find the average speed of the train that Megan is riding, which covers 80 miles in 2 hours, we will use the formula for average speed, which is total distance divided by total time. The train travels 40 miles one way and 40 miles back, totaling 80 miles.
Here is the step-by-step calculation:
Calculate the total distance the train travels: 40 miles one way + 40 miles back = 80 miles.
Calculate the total time of the journey: 2 hours.
Divide the total distance by the total time to find the average speed: 80 miles / 2 hours = 40 miles per hour.
This means the average speed of the train is 40 miles per hour.
Suppose f(x)=x^2-2. Find the graph of f(5x).
Answers
It is asked to find the graph of f (5x)
So where the x goes we must now place "5x"
In this way the function is as shown below:
f (5x) = (5x)² -2
f (5x) = 25x² -2
The graph of this function is shown in the attached image.
What is the length of AA' , rounded to the nearest hundredth? Type a numerical answer is the space provided. Do not type spaces in your answer
Answers
Coordinates of A' are (5,2)
We can find the distance from A to A' using the distance formula:
[tex]AA'= \sqrt{(5-0)^{2}+ (2-0)^{2} } \\ \\ AA'= \sqrt{25+4} \\ \\ AA'= \sqrt{29} \\ \\ AA'=5.39 [/tex]
Thus, rounded to nearest hundredth, AA' is equal to 5.39
Daisy is cooking pasta. The recipe says she needs 480 grams of pasta for 4 people. How many kilograms will she need for 14?
Answers
Rule of three:
Pasta People
(kilograms)
0.48 → 4
x ← 14
x=(14 * 0.48)/4
x=1.68
Answer: She will need 1.68 kilograms of pasta for 14 people
Answer:
1.68 kilo grams are required for 14 people.
Step-by-step explanation:
First of all the answer is required in kilo grams and the data given is in grams.
Lets convert the given value to kilo grams;
480 grams = 0.48 kilo grams
If 0.48 kilo grams are required to cater 4 people then how many kilo grams are required to cater 14 people?
⇒[tex]\frac{0.48}{4} *14[/tex] kilo grams
1.68 kilo grams.
which word best describe 8(2x+4)
Answers
~~~~~~~~~~~~~~~~~~
8*2 is 16
Then 8*4 is 32.
Answer is 16x+32
Distribution it should be used 8(2x+4).
-Charlie
A coefficient is a number that is in front of a variable. Examples of this are 6 in 6x, 100 in 100s, and 45 in 45h. Thus making 8 the coefficient of the problem.
There are also no like terms (like 4 and 6 or 5x and 9x), there is no inequality sign (greater than, less than, etc), and there are no constant variables (like 2 and 7 in the equation " 2x - 2 = 7).
I hope this helps!
need help please.I forgot this.
Answers
6. (-20×50)×-29 = -1000×-29 = 29,000
7. (5×10)×18 = 50×18 = 900
8. 400 + (60 + 98) = 400 +158 = 558
9. 3×(20×5) = 3×100 = 300
10. (18 + 9) +91 = 27 +91 = 118
What is the annual rate of productivity advance implied by moore's law? (assume linear growth from the base.) instructions: enter your response rounded to the nearest whole number. %?
Answers
Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousandth.
Answers
[tex]\log_358=\dfrac{\log_458}{\log_43}\approx\dfrac{2.929}{0.792}\approx3.698[/tex]
-7y to the third (4y + y - 3)
Answers
So if we have the equation: -7y^3(4y + y - 3), we're essentially distributing "-7y^3" to everything of what's in the parenthesis. When you distribute -7y^3, know that you add exponents but you multiply the numbers. After simplifying you get:
-28y^4 - 7y^4 + 21y^3
**We can still simplify this expression because there are still like terms:
-35y^4 +21y^3
Hope this helps!
May
The total cost of a prescription is $119.25. Mr. Jones's co-insurance plan requires him to contribute 15 percent of the cost. What's Mr. Jones's out-of-pocket cost for this prescription?
Answers
To find Mr. Jones's out-of-pocket cost for his prescription, calculate 15% of the total cost of $119.25, resulting in $17.89 after rounding.
Explanation:The question asks us to calculate Mr. Jones's out-of-pocket cost for his prescription if his co-insurance plan requires him to pay 15% of the total cost. The total cost of the prescription is $119.25.
To find out Mr. Jones's out-of-pocket expense, we calculate 15% of $119.25:
Out-of-pocket cost = 15% of total cost
= 0.15 × $119.25
= $17.8875
So, Mr. Jones's out-of-pocket cost will be $17.8875, which we can round to $17.89 for practical purposes.
hey can you please help me posted picture of question
Answers
If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.
The discriminant can be calculated as:
Disc = b² - 4ac
For the given equation:
Disc = 9 - 4(2)(1) =1
Since the value of discriminant is positive, the function will have two distinct roots.
So, the answer to this question is option B
find the unit price rounded to the nearest cent: $12.35 for 11 lb
Answers
All you have to do is divide $12.35 / 11 = 1.12
Hope this Helps!!
unit price = $1.1
Explanation:
We are given that 11 lb cost $12.35. To know how much does 1 lb cost (unit price), all you have to do is cross multiplication as follows:
11 lb .......................> 12.35
1 lb .........................> ??
unit price = (1*12.35) / 11 = $1.122 which is approximately $1.1 (to the nearest cent)
Hope this helps :)
Factor completely the following quadratic expression 16x^2-25y^2
Answers
[tex](4x)^2-(5y)^2[/tex]
[tex](4x+5y)(4x-5y)[/tex]
Answer:
(4x+5y)(4x-5y)
Step-by-step explanation:
it is correct i got it right
What is one possible solution for the triangle below?
Answers
Answer:
The correct answer is C, i can promise you that
Step-by-step explanation:
the only one with Angle Z as 94.6 degrees.
One possible solution for the triangle below is:
Option D:
YZ = 95.4
∠X = 26.7°
∠Z = 85.3°
How use law of sines and cosines?If only one of these is missing, the law of cosines can be used.
3 sides and 1 angle. So if the known properties of a triangle are SSS (side-side-side) or SAS (side-angle-side), then this law applies.
If you want the ratio of the sine of an angle and its inverse to be equal, you can use the law of sine. This can be used if the triangle's known properties are ASA (angle-side-angle) or SAS.
Using Law of sine:
40/sin 68 = 43/sin Z
sin Z = (43/40) * sin 68
sin Z = 0.9967
Z = sin⁻¹0.9967
Z = 85.3°
The only option with the correct value of angle Z is Option D with:
YZ = 95.4
∠X = 26.7°
∠Z = 85.3°
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What type of conic section is the following equation? 4x2 + y2 = 36
Answers
The signs of the terms are both positive, so it is a circle or an ellipse.
The coefficients of the terms are different, so it is not a circle, it is an ELLIPSE.
Answer:
Ellipse
Step-by-step explanation:
The signs of the terms are both positive, so it is either a circle or an ellipse.
The coefficients of the terms are different, so it can not be a circle.
Therefore it is an Ellipse.
What is the median of the data set represented by the dot plot? A number line with line with two dots above the number 10, one dot above the number 12, one dot above the number 13, one dot above the number 14, one dot above the number 15, one dot above the number 18, and two dots above the number 19.
Answers
The median of the data set is 14.
Answer:
The median of the data set is 14.
If P(A or B)equals=0.60.6, P(A)equals=0.40.4, and P(A and B)equals=0.350.35, find P(B).
Answers
Answer:
P(B) = 0.55 .
Step-by-step explanation:
We are given that P(A or B) = 0.6 , P(A) = 0.4 , and P(A and B) = 0.35 .
As we know that;
P(A or B) = P(A) + P(B) - P(A and B)
0.6 = 0.4 + P(B) - 0.35
P(B) = 0.35 + 0.6 - 0.4 = 0.55
Therefore, P(B) = 0.55 .
What is the length of the hypotenuse of the triangle?
sides 7cm and 3cm
A. sqrt 20cm
B. sqrt 23cm
C. sqrt 40cm
D. sqrt 58cm
Answers
7² + 3² = c²
49 + 9 = c²
49 + 9 = 58
58 = c²
Sqrt of 58 = 7.6 cm
So the answer is D) Sqrt 58 cm.
Hope this Helps!!
The length of the hypotenuse of the triangle is √58 cm (Option D).
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle:
Side a = 7 cm (one of the legs)
Side b = 3 cm (the other leg)
Side c = ? (the hypotenuse)
The Pythagorean theorem is:
[tex]c^2 = a^2 + b^2[/tex]
Substitute the given values:
[tex]c^2 = 7^2 + 3^2\\\\c^2 = 49 + 9\\\\c^2 = 58[/tex]
Now, we can find the square root of both sides to solve for c:
c = √58 cm
So, the length of the hypotenuse of the triangle is √58 cm.
The correct answer is: D. √58 cm
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HI :) I NEED HELP PLEASE BEFORE 12 AM
Answers
In a woodworking you are planing boards to make shelves. The planer is set to remove 1/16 inch from a board on each pass the board makes through the planer. If a board starts out at 3/4 inch thick, how many times will you need to send it through the planer to get it down to 5/8 inch?
Answers
Initial thickness = 3/4 in
Final thickness = 5/8 in
If x is the number of passes,
The material removed = (1/16)x in.
Therefore,
3/4 - (1/16)x = 5/8
3/4 - x/16 = 5/8
x/16 = 3/4 - 5/8 = 1/8
x = 16*1/8 = 2
Therefore, the board will be passed through the plane twice.
simplify completely 3x^2+21x-54 over x^2+3x-54
Answers
Answer: 3(x-2) / x-6
Step-by-step explanation: find gcf..
[tex] \sqrt[3]{ 3x + 1 - 4 = - 6} [/tex]
Answers
In case of [tex] \sqrt[3]{3x+1-4} =sqrt[3][-6][/tex] --> (by multiplying the power by 3)
[tex] 3x+1-4 = -6[/tex]
[tex] 3x -3 = -6 [/tex] ---> by adding 3 for the both sides
[tex] 3x = -3 [/tex] ---> by dividing both sides by 3
[tex] x = -1 [/tex]
in case of [tex] \sqrt[3]{3x+1-4} = -6[/tex] ----> we will repeat the first step again
therefore,
[tex] 3x + 1 -4 = (-6)^{3} = -216 [/tex]
[tex] 3x -3 = -216 [/tex] ----> by adding both sides by 3
[tex] 3x = -213 [/tex] ----> by dividing both sides by 3
[tex] x = \frac{-213}{3} = -71 [/tex]
then x = -71
I hope that helps ;)
A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square centimeters. A dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?
To the nearest whole percent, the probability is
A) 18
B) 25
C) 35
D) 50
Answers
Hope this helps!!
Answer: B) 25
Step-by-step explanation:
Given: A rectangular dartboard has an area of 648 square centimeters.
The triangular part of the dartboard has an area of 162 square centimeters.
If a dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, the probability (in percent) that it lands inside the triangle will be :
[tex]\dfrac{162}{648}\times100=25\%[/tex]
Hence, the probability that it lands inside the triangle = 25%.
PLEASE PLEASE HELP WITH THIS
Answers
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]
We can infer from our picture that [tex]BC=m[/tex]. Also we can find the length of AC by adding AD and CD:
[tex]AC=AD+CD[/tex]
[tex]AC=11+7[/tex]
[tex]AC=18[/tex]
Lets replace the values in our proportion:
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]
[tex] \frac{18}{m} = \frac{m}{7} [/tex]
Solving for [tex]m[/tex]:
[tex]m^2=(18)(7)[/tex]
[tex]m^2=126[/tex]
[tex]m= \sqrt{126} [/tex]
We can conclude that the correct answer is: D [tex] \sqrt{126} [/tex]