Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
Writing a equation of a circle centers at the origin
ANSWER
[tex]x^2+y^2=100[/tex]EXPLANATION
The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = the center of the circle
r = radius of the circle (i.e. distance from any point on its circumference to the center of the circle)
The center of the circle is the origin, that is:
[tex](h,k)=(0,0)[/tex]To find the radius, apply the formula for distance between two points:
[tex]r=\sqrt[]{(x_1-h)^2+(y_1-k)^2_{}}[/tex]where (x1, y1) is the point the circle passes through
Hence, the radius is:
[tex]\begin{gathered} r=\sqrt[]{(0-0)^2+(-10-0)^2}=\sqrt[]{0+(-10)^2} \\ r=\sqrt[]{100} \\ r=10 \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(10)^2 \\ \Rightarrow x^2+y^2=100 \end{gathered}[/tex]Find the derivativef(x) = 1 / (x - 2)
ANSWER
[tex]\frac{df}{dx}=-\frac{1}{(x-2)^2}[/tex]EXPLANATION
We want to find the derivative of the given function:
[tex]f(x)=\frac{1}{x-2}[/tex]First, we have to rewrite the function as follows:
[tex]f(x)=(x-2)^{-1}[/tex]Next, make the following substitution:
[tex]a=x-2[/tex]The function now becomes:
[tex]f(x)=a^{-1}[/tex]Apply the chain rule of differentiation:
[tex]\frac{df}{dx}=\frac{df}{da}\cdot\frac{da}{dx}[/tex]Therefore, we have that:
[tex]\frac{df}{da}=-1\cdot a^{-1-1}=-a^{-2}[/tex]and:
[tex]\frac{da}{dx}=1[/tex]Therefore, the differentiation of the function is:
[tex]\begin{gathered} \frac{df}{dx}=-a^{-2}\cdot1 \\ \Rightarrow\frac{df}{dx}=-(x-2)^{-2}\cdot1 \\ \frac{df}{dx}=-\frac{1}{(x-2)^2} \end{gathered}[/tex]The expression secθ - ((tan^2)(θ)/(sec)(θ)) simplifies to what expression?−tan θ−cot θcos θsec θ
Given the expression
[tex]sec(\theta)-\frac{tan^2(\theta)}{sec(\theta)}[/tex]express in sen and cos terms
[tex]\frac{1}{cos(\theta)}-\frac{\frac{sin^2(\theta)}{cos^2(\theta)}}{\frac{1}{cos(\theta)}}[/tex][tex]\frac{1}{cos(\theta)}-\frac{sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{1-sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{cos^2(\theta)}{cos^(\theta)}[/tex][tex]cos^(\theta[/tex]then the correct answer is option C
Cos (angle)
Which statement describes how the reasonable domain
compares to the mathematical domain?
A statement which best describes how the reasonable domain compares to the mathematical domain is that: C. the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of any graph comprises all the input numerical values or numbers which are primarily shown on the x-axis.
Next, we would evaluate the function which represents the perimeter of this rectangle by substituting the value of 2 as follows:
f(w) = 6w – 8
f(2) = 6(2) – 8
f(2) = 12 – 8
f(2) = 4.
For the length of this rectangle, we have:
Length = 2w - 4
Length = 2(2) - 4
Length = 4 - 4
Length = 0
Therefore, the width of this rectangle must be real numbers that are greater than 2.
Read more on domain here: brainly.com/question/17003159
#SPJ1
Complete Question:
A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can be expressed with the function f(w) = 6w – 8, where w is the width of the rectangle in centimeters.
Which statement describes how the reasonable domain compares to the mathematical domain?
Both the mathematical and reasonable domains include only positive real numbers.
Both the mathematical and reasonable domains include only positive whole numbers.
The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
The mathematical domain includes all real numbers, while the reasonable domain includes only whole numbers greater than 2.
What is the measure of the unknown angle? (2 points)120°2100009240
To find the angle measure "n", we proceed as follows:
Step 1: Recall that the sum of angles at a point is 360 degrees, as below:
[tex]\begin{gathered} the\text{ sum of angles at a point = 360 degrees} \\ n+120\text{ = 360} \\ n=360\text{ - 120} \\ n=240^o \\ \end{gathered}[/tex]Therefore, the meas
Consider the complex number 2 = V17 (cos(104°) + i sin(104°)).Plot z in the complex plane below.If necessary, round the point's coordinates to the nearest integer.Im5+4+3+2+1 +ReA+-5+-4-3-2-112345-1+-2-3 +-4+-5 +
Recall that to plot a point in the complex plane we have to know its real part and its imaginary part.
The real part of the given number is
[tex]\sqrt[]{17}\cos 104^{\circ},[/tex]and its imaginary part is
[tex]\sqrt[]{17}\sin 104^{\circ}.[/tex]Simplifying the above expressions, and rounding to the nearest integer we get that:
[tex]\begin{gathered} \operatorname{Re}(z)=-1, \\ \operatorname{Im}(z)=4. \end{gathered}[/tex]Therefore, the point has coordinates (-1,4).
Answer:
Question 7(Multiple Choice Worth 3 points)(05.04 LC)triangle PQR with side p across from angle P, side q across from angle Q, and side r across from angle RIf ∠R measures 18°, q equals 9.5, and p equals 6.0, then which length can be found using the Law of Cosines? p q RQ PQ
Answer
PQ
Explanation
It must be PQ because we have the measure of the other two sides and the angle opposite it.
find the minimum value of the function f(x)=2x2-22x+68 to the nearest hundredth
Minimum value of the function
[tex]f(x)=2x^2-22x+68[/tex]To calculate the minimum value we will use the derivative.
[tex]\begin{gathered} f^{\prime}(x)=4x-22 \\ 4x-22=0 \\ 4x=22 \\ x=\frac{22}{4} \\ x=5.5 \end{gathered}[/tex]The answer would be 5.5
used to figure for exercises two through nine period determine whether each pair of lines are parallel or perpendicular. right yes or no
2. q and v are parallel. YES
3. r and s are parallel. NO
4. r and t are parallel. NO
5. s and u are parallel. YES
6. q and s are perpendicular. NO
7. q and v are perpendicular. NO
8. r and s are perpendicular. YES
9. t and v are perpendicular. YES
Find the values of the variables in the parallelogram. The diagram is not drawn to scale. (Image is attached below)thank you in advance :)
For this problem, we are given a parallelogram with a diagonal drawn, inside it there are markings for a few angles. We need to determine the unknown angles.
Opposite sides of a parallelogram are parallel, this means we can treat the diagonal as a transversal line that crosses two parallel lines. Since this is the case, the angles 33º and xº are alternate interior angles and have the same length:
[tex]x=33º[/tex]The opposite angles in a parallelogram are congruent, therefore:
[tex]z=109º[/tex]The sum of internal angles is 360º, therefore we have:
[tex]\begin{gathered} 2\cdot109+2\cdot(x+y)=360\\ \\ 218+66+2y=360\\ \\ 284+2y=360\\ \\ 2y=360-284\\ \\ 2y=76\\ \\ y=38 \end{gathered}[/tex]The value of x is 33º, the value of y is 38º and the value of z is 109º.
Evaluate 1312e 4 Sov? 3x²x3 dx (Type an exact answer.)
We have to solve the integral:
[tex]\int ^4_03x^2e^{x3}dx[/tex]We will apply a variable substitution in order to simplify the solution. We have a hint when we see that the derivative of x^3 is 3x^2, that is part of the factors.
[tex]\begin{gathered} u=x^3\Rightarrow du=(3x^2)dx \\ x=0\Rightarrow u=0^3=0 \\ x=4\Rightarrow u=4^3=64 \end{gathered}[/tex]Then, we can write:
[tex]\int ^4_03x^2e^{x3}dx=\int ^4_0e^{x3}(3x^2)dx=\int ^{64}_0e^udu[/tex]Then, we have a simpler integral to solve:
[tex]\int ^{64}_0e^udu=e^u+C=e^{64}-e^0=e^{64}-1[/tex]The exact solution is e^64-1.
A car is traveling at a speed of 70 kilometers per hour. What is the car's speed in miles per hour? How many miles will the car travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
What is the car's speed in miles per hour?
Let's make a conversion:
[tex]\frac{70\operatorname{km}}{h}\times\frac{1mi}{1.6\operatorname{km}}=\frac{43.75mi}{h}[/tex]How many miles will the car travel in 5 hours?
1h---------------------->43.75mi
5h---------------------> x mi
[tex]\begin{gathered} \frac{1}{5}=\frac{43.75}{x} \\ x=5\times43.75 \\ x=218.75mi \end{gathered}[/tex]six teachers share 4 packs of paper equally.how much paper does each teacher get
Six teachers share 4 packs of paper
Each teacher gets
[tex]\frac{4}{6}=\frac{2}{3}\text{ = 4 sixths of a pack, option C}[/tex]The answer is option C
3a^2 -3a - 36. solving quadratic by factoring. factor each expression. be sure to check for greatest common factor first.
we have the expression
[tex]3a^2-3a-36[/tex]step 1
Factor 3
[tex]3(a^2-a-12)[/tex]step 2
equate to zero
[tex]3(a^2-a-12)=0[/tex]step 3
Solve
[tex](a^2-a-12)=0[/tex][tex]\begin{gathered} a^2-a=12 \\ (a^2-a+\frac{1}{4}-\frac{1}{4})=12 \\ (a^2-a+\frac{1}{4})=12+\frac{1}{4} \\ (a^2-a+\frac{1}{4})=\frac{49}{4} \end{gathered}[/tex]Rewrite as perfect squares
[tex](a-\frac{1}{2})^2=\frac{49}{4}[/tex]take the square root on both sides
[tex]\begin{gathered} a-\frac{1}{2}=\pm\frac{7}{2} \\ a=\frac{1}{2}\pm\frac{7}{2} \end{gathered}[/tex]the values of a are
a=4 and a=-3
therefore
[tex]3(a^2-a-12)=3(a-4)(a+3)[/tex]Ariana is going to invest $62,000 and leave it in an account for 20 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Ariana to end up with $233,000?
The rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.
What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/f))ⁿ ;
where A = amount that the depositor will receive
P = initial amount that the depositor has invested
R = rate of interest offered to the depositor
f = frequency of compounding offered per year
n = number of years.
Given, Amount that Ariana wants to end up receiving = A = $233,00
Principal amount that Ariana can invest = P = $62,000
Frequency of compounding offered per year = f = 1
Number of years = 20
Let the rate of interest offered to the depositor be = R
Following the formula established in the literature, we have:
233000 = 62000(1 + R)²⁰ ⇒ 3.76 = (1 + R)²⁰ ⇒ 1.07 = 1 + R ⇒ R = 0.07%
Thus, the rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.
To learn more about compound interest, tap on the link below:
https://brainly.com/question/24924853
#SPJ9
A small radio transmitter broadcasts in a 60 mile radius. If you drive along a straight line from a city 75 miles north of the transmitter to a second city 76 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answer:
Explanation:
We start by having a diagrammatic representation as follows:
This data is from a sample. Calculate the mean, standard deviation, and variance. Suggestion: usetechnology. Round answers to two decimal places.х23.542.131.116.321.132.144.813.529.9Mean?Standard deviation?Variance?Ooops - now you discover that the data was actually from a population! So now you must give thepopulation standard deviationPopulation Standard Deviation?
The formula to find the mean of a data set is:
[tex]\begin{gathered} \bar{x}=\frac{\text{Sum of all the items}}{\text{ Number of items}} \\ \text{ Where }\bar{\text{x}}\text{ is the mean of a sample} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} \bar{x}=\frac{23.5+42.1+31.1+16.3+21.1+32.1+44.8+13.5+29.9}{9} \\ \bar{x}=\frac{254.4}{9} \\ \bar{x}=28.27 \end{gathered}[/tex]Therefore, the mean of the given data set rounded to two decimal places is 28.27.
Standard deviationThe sample standard deviation formula is:
[tex]\begin{gathered} s=\sqrt[]{\frac{\sum ^n_{i\mathop=1}(x_i-\bar{x})^2}{n-1}} \\ \text{ Where} \\ \text{ n is the number of data points} \\ x_i\text{ is each of the values of the data} \\ \bar{x}\text{ is the mean of the data set} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} s=\sqrt[]{\frac{(23.5-28.27)^2+(42.1-28.27)^2+(31.1-28.27)^2+(16.13-28.27)^2+(21.1-28.27)^2+(32.1-28.27)^2+(44.8-28.27)^2+(13.5-28.27)^2+(29.9-28.27)^2}{8}} \\ s=\sqrt[]{\frac{(-4.77)^2+(13.83)^2+(2.83)^2+(-11.97)^2+(-7.17)^2+(3.83)^2+(16.53)^2+(-14.77)^2+(1.63)^2}{8}} \\ s=\sqrt[]{\frac{22.72+191.36+8.03+143.2+51.36+14.69+273.35+218.05+2.67}{8}} \\ s=\sqrt[]{\frac{925.44}{8}} \\ s=\sqrt[]{115.68} \\ s=10.76 \end{gathered}[/tex]Therefore, the sample standard deviation of the given dataset rounded to two decimal places is 10.76.
VarianceThe standard deviation is the square root of the variance. Thus, the formula to find the variance of a sample is,
[tex]s^2=\frac{\sum^n_{i\mathop{=}1}(x_i-\bar{x})^2}{n-1}[/tex]So, in this case, we have:
[tex]s^2=115.68[/tex]Therefore, the sample variance of the given dataset rounded to two decimal places is 115.68.
PopulationStandard deviationThe population standard deviation formula is:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{\sum ^n_{i\mathop{=}1}(x_i-\bar{x})^2}{N}} \\ \text{Where} \\ \sigma\text{ is the population standard deviation} \\ x_i\text{ is each of the values of the data} \\ N\text{ is the number of data points} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} s=\sqrt[]{\frac{(23.5-28.27)^2+(42.1-28.27)^2+(31.1-28.27)^2+(16.13-28.27)^2+(21.1-28.27)^2+(32.1-28.27)^2+(44.8-28.27)^2+(13.5-28.27)^2+(29.9-28.27)^2}{9}} \\ s=\sqrt[]{\frac{(-4.77)^2+(13.83)^2+(2.83)^2+(-11.97)^2+(-7.17)^2+(3.83)^2+(16.53)^2+(-14.77)^2+(1.63)^2}{9}} \\ s=\sqrt[]{\frac{22.72+191.36+8.03+143.2+51.36+14.69+273.35+218.05+2.67}{9}} \\ s=\sqrt[]{\frac{925.44}{9}} \\ s=\sqrt[]{102.83} \\ s=10.14 \end{gathered}[/tex]Therefore, the population standard deviation of the given dataset rounded to two decimal places is 10.14.
The formula, = / + , converts temperatures between Celsius and Fahrenheit degrees. What is the temperature in degrees Celsius that is equivalent to 14 degrees FahrenheitA) -10B) -9 C) -8D) -7
Hello there. To answer this question, we need to plug in the value given by the question and solve for C, the temperature in Celsius.
We want to find the equivalent temperature in Celsius to 14 degrees Fahrenheit.
Knowing that F = 9/5C + 32, making F = 14 lead us to:
14 = 9/5C + 32
Subtract 32 on both sides of the equation
9/5C = -18
Multiply both sides of the equation by a factor of 5/9, in order to get:
C = 5/9 (-18) = -10.
This is the equivalent temperature we were looking for.
You deposit $6000 in an account earning 6% interest compounded continuously. How much will you have in the account in 10 years?
Solution
Step 1:
Write the compounded interest continuously formula.
[tex]\text{A = Pe}^{rt}[/tex]Step 2:
Given data
P = $6000
r = 6% = 0.06
t = 10 years
Step 3:
Substitute in the formula
[tex]\begin{gathered} A\text{ = Pe}^{rt} \\ A\text{ = 6000 }\times\text{ 2.7183}^{10\times0.06} \\ A\text{ = 6000 }\times\text{ 2.7183}^{0.6} \\ A\text{ = 6000 }\times\text{ 1.822126} \\ A\text{ = \$10932.76} \end{gathered}[/tex]Final answer
A = $10933 ( nearest whole number)
VIP at (-2,7) dropped her pass and moved to the right on a slope of -9. Where can you catch up to her to return her VIP pass? I know the answer is (-1 ,-2) my question is how do you solve to get the answer?
we are told that VIP is located at (-2,7) and then she drops her pass. Then she moves on a slope of -9. To determine where you can catch up, we simply analyze what would be the next position by incrementing x by 1.
In this case, we are told that the slope is -9.
Recall that given points (a,b) and (c,d) the slope of the line that joins this points is given by
[tex]m=\frac{d-b}{c-a}=\frac{b-d}{a-c}[/tex]Lets call the next point (-1,y) . So using this, we have
[tex]\text{ -9=}\frac{y\text{ - 7}}{\text{ -1 -(-2)}}=\frac{y\text{ -7}}{2\text{ -1}}=y\text{ -7}[/tex]So, by adding 7 on both sides, we get
[tex]y\text{ = -9+7 = -2}[/tex]So, the next position, following a slope of -9 and starting at (-2,7) is (-1,-2)
In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 11,000 students participated in the poll, how many chose green?Orange 13%Pink 7%Blue 10%Red 24%Purple 10%Green 36%
Total of 11,000 students
Green 36%
how many chose green?
Chose green = 11000 * 36/100 = 3960
36% of 11,000 is 3960
Answer:
3,960 students chose green
In the following diagram, we know that line AB is congruent to line BC and angle 1 is congruent to angle 2. Which of the three theorems (ASA, SAS, or SSS) would be used to justify that triangle ABC congruent triangle CDA?
The theorem that justifies why triangle ABC is congruent to triangle CDA is the: SAS.
What is the SAS Theorem?The SAS theorem states that if we can show that two triangles have a pair of corresponding congruent included angles, and two pairs of corresponding sides that are also congruent to each other, then we can prove that both triangles are congruent to each other.
The triangles, ABC and CDA have:
Two pair of corresponding sides that are congruent to each other, which are AB ≅ BC, and AC ≅ CA.
A pair of corresponding included angles, which is angle 1 ≅ angle 2.
Based on the above known information, we can conclude that triangle ABC is congruent to triangle CDA by SAS theorem.
Learn more about the SAS on:
https://brainly.com/question/14252518
#SPJ1
What is the solution to the equation below? Round your answer to two decimal places.ex = 5.9A.x = 124.50B.x = 1.77C.x = 365.04D.x = 0.77
We have the next given equation:
[tex]e^x=5.9[/tex]Now, we can solve for x using the exponent's properties:
Add both sides ln:
[tex]\ln e^x=\ln5.9[/tex]With the ln we can take down the exponent and simplify ln*e = 1.
Hence,
[tex]\begin{gathered} x=\ln(5.9) \\ x=1.77 \end{gathered}[/tex]Hence, the correct answer is option B.
the points E,F,G and H all lie on the same line segment, in that order, such that ratio of EG:FG:GH is equal to 4:1:5. If EH=10, find EG
You have that the ratio of EG:FG:GH = 4:1:5.
Moreover, segment EH = 10.
In order to find EG you consider the following ratios:
EG/FG = 4/1
FG/GH = 1/5
Furthermore, EH = EG + FG + GH
Solve the following system of equations by graphing. Graph the system below and enter the solution set as an ordered pair in the form (x,y).if there are no solutions enter none and inter all if there are infinite solutions X + 2y = 3 2x + 4y =12
System of equations:
[tex]x+2y=3[/tex][tex]2x+4y=12[/tex]To solve the system by graphing, we have to remember that the point in which both graphs meet is the solution of the system.
• Graph of both equations:
As we can see, there is no point in which both meet. Then, this system has no solution.
Answer: none
A rectangular room is twice as long as it is wide, and its perimeter is 60 meters. Find the dimensions of the
room.
The length is __
meters and the width is __
meters.
Answer: 20, 10
Step-by-step explanation:
Let the width be w. Then, the length is 2w. Substituting into the formula for the perimeter of a rectangle,
[tex]2(w+2w)=60\\\\w+2w=30\\\\3w=30\\\\w=10\\\\\implies 2w=2(10)=20[/tex]
Find the simple interest. Principal Time in Months Rate 1 $11.800 21% 4 The simple interest is $ (Round to the nearest cent.)
we use the formula
Where Cn is the final amount= co the initial amount, n the number of months and i the rate dividing between 100
transform the mixed number
[tex]2\frac{1}{4}=2.25[/tex]now, replace
[tex]\begin{gathered} Cn=11,800(1+(4)\times(\frac{2.25}{100})) \\ \\ Cn=11,800(1.09) \\ \\ Cn=12862 \end{gathered}[/tex]the solution is 12,862
Which graphed matches the equation y+6= 3/4 (x+4)?
To start, it is important to find the slope intercept form of the equation
[tex]\begin{gathered} y+6=\frac{3}{4}(x+4) \\ y+6=\frac{3}{4}x+3 \\ y=\frac{3}{4}x+3-6 \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]Once we have the slope intercept form we know that the y intercept is -3 and the slope is positive, it means the line is increasing
The graph will look like this
helpppppppppppppppppppppppppppppp
skill issue hahahahahhaahahhahaha
Factor the given polynomial by finding the greatest common monomial Factor 6x^3y+9xy^3
Answer:
(3xy)(2x² + 3y²)
Step-by-step explanation:
Hello!
The greatest common factor for the coefficients is 3, as both terms have a coefficient with the greatest factor of 3.
The greatest common factor for the x-terms is x, as both terms has x to a minimum of the first power.
The greatest common factor for the y terms is y as both terms has y to a minimum of the first power.
Factor out 3xy:6x³y + 9xy³3xy(2x²) + 3xy(3y²)(3xy)(2x² + 3y²)The factored form is (3xy)(2x² + 3y²).
