Answers
Given:
We are required to prove:
[tex]\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ = sin}\theta[/tex]From the left-hand side:
[tex]\begin{gathered} =\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ } \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin\theta}{\cos\theta}\text{ + }\frac{\cos \theta}{\sin \theta}} \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin ^2\theta+cos^2\theta}{\sin \theta\cos \theta}} \\ \end{gathered}[/tex]From standard trigonometric identity, we have:
[tex]\sin ^2\theta+cos^2\theta\text{ = 1}[/tex]Substituting we have:
[tex]\begin{gathered} =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{1}{\sin \theta\cos \theta}} \\ =\text{ }\frac{\sin \theta\cos \theta}{\cos \theta} \\ =\text{ sin }\theta\text{ (Right-hand side)} \end{gathered}[/tex]Related Questions
Problem Solving: Fraction Division For exercises 1 and 2, write three problem situations for each division 56÷1/3 and 6/1/2÷1/2/3
Answers
56÷1/3
We have to model a problem where the solution is 56÷1/3.
So, we take something that is 56 and we have to divide it by 1/3rd.
So, we can say:
George had 56 large cakes.
Giving 1/3rd of each cake to each person is enough.
If George used all of the cake, how many person could he feed?
Find equation of line containing the given points (4,3) and (8,0) Write equation in slope-intercept form
Answers
SOLUTION
Write out the given point
[tex]\begin{gathered} (4,3) \\ \text{and } \\ (8,0) \end{gathered}[/tex]The equation of the line passing through the point above will be obtain by following the steps
Step1: Obtain the slope of the line
[tex]\begin{gathered} \text{slope,m}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Hence } \\ x_1=4,x_2=8 \\ y_1=3,y_2=0 \end{gathered}[/tex]Substituting the values we have
[tex]\begin{gathered} \text{slope,m}=\frac{0-3}{8-4}=-\frac{3}{4} \\ \text{Hence } \\ m=-\frac{3}{4} \end{gathered}[/tex]Step 2: Obtain the y- intercept
The y-intercept is the point where the graph touch the y, axis
[tex]\begin{gathered} \text{slope, m=-3/4} \\ y=6 \\ y-intercept=6 \end{gathered}[/tex]Steps 3; use the slope intercept rule
[tex]\begin{gathered} y=mx+b \\ \text{Where m=-3/4,b=y-intercept} \\ \text{Then } \\ y=-\frac{3}{4}x+6 \end{gathered}[/tex]Hence
The equation in slope intercept form is
y = - 3/4 x + 6
What is the starting value of the exponential function below?
Answers
The starting value of an exponential function is the value that it takes when x=1.
In this case, we can see that y=3 when x=1.
Then, the starting value is equal to 3.
What is the slope of the line that passes through the points (2,8) and (12, 20)? Write your answer in simplest form.
Answers
EXPLANATION
The slope of a line, is given by the next expression:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x_1,y_1) = (2,8) and (x_2,y_2)=(12,20)
Plugging in the values into the expression:
[tex]Slope=\frac{20-8}{12-2}[/tex]Subtracting numbers:
[tex]Slope=\frac{12}{10}[/tex]Simplifying:
[tex]Slope=\frac{6}{5}[/tex]In conclusion, the solution is 6/5
under normal conditions, 1.5 feet of snow will melt into 2 inches of water. after a recent snowstorm, there were 4 feet if snow. how many inches of water will there be when the snow MELTS? express your answer as a fraction reduced to lowest terms or decimal rounded correctly to two decimals places. Do not include units with this answer.
Answers
If 1.5 feet of snow melts into 2 inches of water, this implies that:
[tex]undefined[/tex]Answer to the question
Answers
If A=(-7,8,1) and B(8,7,7), find ||AB||. Round to 3 decimal places
Answers
Given,
A= (-7, 8, 1).
B= (8, 7, 7)
The value of ||AB|| is,
[tex]\begin{gathered} \mleft\Vert AB\text{ }\mleft\Vert\text{ = }A.B\mright?\mright? \\ \end{gathered}[/tex]The value of A.B is ,
[tex]\begin{gathered} A\mathrm{}B=(-7.8+8.7+1.7) \\ AB=(-56+56+7) \\ AB=7 \end{gathered}[/tex]Hence, the value is 7.
5. (20 x 5 + 10) - (8 × 8 - 4)=
a. 58
b. 50
c. 40
Answers
Answer:
b. 50
Step-by-step explanation:
20 x 5 + 10 = 110
8 × 8 - 4 = 60
110 - 60 = 50
Answer:
b. 50
Step-by-step explanation:
(20x5+10)- (8x8-4)
(100+10) - (64-4)
110 - 60
equals 50
In class, we determined that 11 peoplewould fit comfortably in a 5 ft by 5 ftsquare. How many square feet wouldeach person require?
Answers
We have to first determine the area of the square. The area of a square can be represented as follows
[tex]\begin{gathered} \text{Area of square = L}^2 \\ L\text{ = 5 ft} \\ \text{Area of square = 5}^2 \\ \text{Area of a square = 25 ft}^2 \end{gathered}[/tex]The number of each square feet each person will requre can be calculated as follows
[tex]\begin{gathered} numbers\text{ of each square ft each person require = 25/11} \\ numbers\text{ of each square ft each person require = }2.27272727273ft^2 \\ numbers\text{ of each square ft each person require }\approx\text{ }2.27ft^2 \end{gathered}[/tex]You bought your first car for $3,000 and make payments of $150 each month. Letting B represent the balance (what still needs to be paid), which function rule represents how much money is still owed (the balance) after m months?
Answers
The function rule represents how much money is still owed is B = 3000 - 150m
What is a function?A function is used to show the relationship between the data given. This can be illustrated with the variables.
Here, the person bought the first car for $3,000 and make payments of $150 each month.
Let B represent the balance.
The function to illustrate this will be:
B = 3000 - 150(m)
B = 3000 - 150m
where B = balance
m = number of months
Learn more about functions on:
brainly.com/question/25638609
#SPJ1
I will give brainliest. By the way, two people need to answer for someone to give brainliest.
For the direct variation equation y=223x, what is the constant of proportionality?
A: 2
B: 2 2/3
C: 2/3
D: 3
The equation y=7x gives the relationship between the number of road projects, x, and the number of weeks it takes a crew of workers to complete all the projects, y. What is the constant of proportionality? What does it mean in this context?
A: The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete 1 road project.
B: The constant of proportionality is 7. It takes the crew of workers 7 days to complete all of their road projects.
C: The constant of proportionality is 7. It takes the crew of workers 7 days to complete 1 road project.
D: The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete all of their road projects.
Write a direct variation equation to find the number of miles a jet travels in 3 hours if it is flying at a rate of 600 mph.
A: 600 = 3x
B: 3 = 600x
C: y = 600/3
D: y = 600 x 3
Jamal earns $125,000 a year as a systems analyst. He wants to know how much he will earn if he continues at the same rate of pay for 7 years. Which equation will help him find this amount?
A: x = 125,000/5
B:125,000 = 7x
C:125,000 = 7/x
D: y = 125,000 x 7
Answers
Answer: I think B and for the second one I think C
Step-by-step explanation: The constant of proportionality is 7. It takes the crew of workers 7 days to complete 1 road project. That means they have to take at least 7 days which is correct.
A satellite dish is the shape of a paraboloid. The dish is 42 inches wide, and 10 inches
deep. How many inches should the receiver be located from the vertex for optimal
reception? (round to the nearest thousandth)
Answers
The receiver is situated 44.24 inches from the vertex, is the correct response.
Define parabola.Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here. A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Observe the illustration below. It depicts the paraboloid's vertical cross-section through its axis of symmetry.
Make the origin of the parabola the vertex.
Then, it has the equation y = bx².
The parabola crosses via (21,10), therefore
10 = b(21²)
= 0.0226
because
Its equation is y =0.0226²
For best reception, the receiver should be positioned at the paraboloid's focus point.
The focus has a y-coordinate of
a = 1/(4b)
= 1/0.0226
= 44.24 in
The receiver is situated 44.24 inches from the vertex, is the correct response.
To learn more about parabola, visit:
https://brainly.com/question/21685473
#SPJ13
The table below shows the probability distribution of students in a highschool with 1500 students. What is the expected value for the ageof arandomly chosen student?Age131415161718Probability.0.010.250.300.280.150.01A. 15.28B. 15.64C. 15.34D. 15.36
Answers
Solution
We are required to determine the expected value of the given distribution
The formula for expected value is shown below
Thus,
[tex]\begin{gathered} Expected\text{ value =13\lparen0.01\rparen+14\lparen0.25\rparen+15\lparen0.30\rparen+16\lparen0.28\rparen+17\lparen0.15\rparen+18\lparen0.01\rparen} \\ = \end{gathered}[/tex][tex]=0.13+3.5+4.5+4.48+2.55+0.18[/tex][tex]=15.34[/tex]The correct option is C
Consider the following expression 9x+4y + 1 Select all of the true statements below 1 is a constant. 9x and 1 are like terms. 9x is a factor, 9x + 4y + 1 is written as a sum of three terms. ( 9x is a coefficient. None of these are true.
Answers
ANSWER:
1st option: 1 is a constant
4th option: 9x + 4y + 1 written as a sum of three terms
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]9x+4y+1[/tex]From the following equation we can say the following:
• The only constant term is 1
,• None of the terms are similar
,• There are a total of 3 terms
,• The coefficients are 9 and 4
,• The factors are 9, 4, 1, x and y
From the above we can affirm that the true statements are:
• 1 is a constant
• 9x + 4y + 1 written as a sum of three terms
Writing and evaluating a function modeling continuous exponential growth or decay given doubling time or half-life
Answers
We were given the following details:
Half-life = 11 minutes
Initial amount = 598.8 grams
[tex]\begin{gathered} y=a_0e^{kt} \\ where\colon \\ y=amount \\ a_0=Initial\text{ }Amount \\ e=euler^{\prime}s\text{ }constant \\ k=decay\text{ }constant \\ t=time \end{gathered}[/tex]a)
We have the exact formula to be:
[tex]undefined[/tex]What is the value of w?14w +12 = 180
Answers
A population of bacteria grows according to function p(t) = p. 1.42^t, where t is measured in hours. If the initial population size was1,000 cells, approximately how long will it take the population to exceed 10,000 cells? Round your answer to the nearest tenth.
Answers
Given the function p(t) and the initial condition, we have the following:
[tex]\begin{gathered} p(t)=p_0\cdot1.42^t \\ p(0)=1000 \\ \Rightarrow p(0)=p_0\cdot1.42^0=1000 \\ \Rightarrow p_0\cdot1=1000 \\ p_0=1000 \end{gathered}[/tex]Therefore, the function p(t) is defined like this:
[tex]p(t)=1000\cdot1.42^t[/tex]Now, since we want to know the time it will take the population to exceed 10,000 cells, we have to solve for t using this information like this:
[tex]\begin{gathered} p(t)=1000\cdot1.42^t=10000 \\ \Rightarrow1.42^t=\frac{10000}{1000}=10 \\ \Rightarrow1.42^t=10 \end{gathered}[/tex]Applying natural logarithm in both sides of the equation we get:
[tex]\begin{gathered} 1.42^t=10 \\ \Rightarrow\ln (1.42^t)=\ln (10) \\ \Rightarrow t\cdot\ln (1.42)=\ln (10) \\ \Rightarrow t=\frac{ln(10)}{\ln (1.42)}=6.56 \end{gathered}[/tex]Therefore, it will take the population 6.56 hours to exceed 10,000 cells
Let f(x)=3x-2. What is f^-1 (x) ?
Answers
Given the function:
f(x) = 3x - 2
Let's find the inverse of the function f⁻¹(x).
To find the inverse of the function, apply the following steps:
• Step 1.
Rewrite y for f(x)
[tex]y=3x-2[/tex]• Step 2.
Interchange the x and y variables:
[tex]x=3y-2[/tex]• Step 3.
Solve for y.
Add 2 to both sides:
[tex]\begin{gathered} x+2=3y-2+2 \\ \\ x+2=3y \end{gathered}[/tex]• Step 4.
Divide all terms by 3:
[tex]undefined[/tex]
Maxim has been offered positions by two car companies. The first company pays a salary of $12000 plus a commission of $800 for each car sold. The second pays a salary of $15600 plus a commission of $600 for each car sold. How many cars would need to be sold to make the total pay the same?
Answers
To make the total pay the same, 18 cars would need to be sold
Explanation:Let the number of cars sold be x
The first company pays a salary of $12000 plus a commission of $800 for each car sold
Total pay for the first company = 12000 + 800x
The second pays a salary of $15600 plus a commission of $600 for each car sold
Total pay for the second company = 15600 + 600x
If the total pay is the same:
12000 + 800x = 15600 + 600x
800x - 600x = 15600 - 12000
200x = 3600
x = 3600/200
x = 18
To make the total pay the same, 18 cars would need to be sold
Hello I need help with the following question. 8. Use the given graph of the function f to find the domain and range(−6,6)8 The domain of f is(Type a compound inequality.)The range of f is(Type a compound inequality.)
Answers
We are to use the given graph in the question to find the domain and range
From the graph,
The lowest value of x plotted is x = -14
The highest value of x plotted is x = 12
The loowest value of y is y= -4
The highest value of y is y = 6
Hence, the domain is
[tex]-14\leq x\leq12[/tex]While the range is
[tex]-4\leq y\leq6[/tex]Terry invested $2,200 in the stock market for 2 years. If the investment earned 12%, how muchmoney did Terry earn in 2 years?
Answers
We will have that $2200 represent the 100%, then how much money does 12% represent.
In order to solve for the ammount of money we multiply the invested ammount ($2200) times the percentage we want to know (12%) and divide it by 100%, that is:
[tex]m=\frac{2200\cdot12}{100}\Rightarrow m=264[/tex]Here we can see, he earned $264 in those 2 years.
Aunt Eloise’s house is always 20°C. She has just made a fresh cup of tea (tea is made with boiling water and water boils at 100°C) five minutes after she made the tea her mad scientist nephew came in, stuck a thermometer in the cup and announced that the tea was now only 70°C. She had gotten involved with her book and forgot to have even a sip of her tea. Now she won’t drink it because it isn’t piping hot anymore.Write and equation that models this problem and use it to predict the temperature of the tea 20 minutes after it was taken off the stove.
Answers
Given:
a.) She has just made a fresh cup of tea (tea is made with boiling water and water boils at 100°C)
b.) Five minutes after she made the tea her mad scientist nephew came in, stuck a thermometer in the cup, and announced that the tea was now only 70°C.
c.)
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 enter all if there are infinite solutions.X - y = 0X + y = - 4
Answers
EXPLANATION
Since we have the system of equations:
(1) x - y = 0
(2) x + y = -4
Isolating x in (1):
x = y
Plugging in x=y into (2):
y + y = -4
Adding like terms:
2y = -4
Dividing both sides by 2:
y = -4/2
Simplifying:
y = -2
Plugging in y=-2 into (1):
x - (-2) = 0
Removing the parentheses:
x + 2 = 0
Subtracting -2 to both sides:
x = -2
The solution of the system of equations is (-2, -2)
Representing the graph:
A store charges $140 for every 10 bags of fertilizer a farmer buys. a. Complete the table. Graph the values. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840 b. How much would a farmer pay for 50 bags of fertilizer? Explain. a. Complete the table. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840
Answers
Question:
Solution
a) If for every 10 bags the store charges $140 then
1. for 10x2 = 20 bags the store charges 2x$140 = 280.
2. for 10x3 = 30 bags the store charges 3x$140 = 420.
3. for 10x4 = 40 bags the store charges 4x$140 = 560
4. for 10x6 = 60 bags the store charges 6x$140 = 840
b) According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
c)
According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
What is 1/3 of the sum of 45 and a number is 16 Translated to algebraic equation
Answers
the statement given 1/3 of the sum of 45 and a number is 16
[tex]\frac{1}{3}(45+x)=16[/tex]In order to find the value of x, w
Bert opened a savings account 4 years ago the account earns 13%interest compounded monthly if the current balance is 1,000.00 how much did he deposit initially
Answers
To answer this question we need to remember the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where r is the interest rate, n is the number of times it is compounded in a given time t.
In this case we know that A=1,000, r=0.13, n=12 and t=13. Plugging this values in the formula and solving for P we have:
[tex]\begin{gathered} 1000=P(1+\frac{0.13}{12})^{12\cdot4} \\ P=\frac{1000}{(1+\frac{0.13}{12})^{12\cdot4}} \\ P=596.19 \end{gathered}[/tex]Therefore, the initial deposit was $596.19
D. What is the change in temperature when the thermometer readingmoves from the first temperature to the second temperature? Write anequation for each part.1. 20°F to +10°F2. 20°F to 10°F3. 20°F to 10°F4. 10°F to +20°F
Answers
Given
What is the change in temperature when the thermometer reading
moves from the first temperature to the second temperature? Write an
equation for each part.
Solutiion
Please help me with this question I have a test next week and I really have to study this is 11th grade algebra 2
Answers
ANSWER:
(a)
(b) P(x < 4) = 0.29
(c) P(x= 6) = 0.17
(d) P(x ≥ 5) = 0.34
STEP-BY-STEP EXPLANATION:
The probability in each case would be the specific amount divided by the total amount, therefore, we calculate the total amount and the probability in each case, like this:
[tex]\begin{gathered} 5+10+2+9+33+12+15+3+1\:=\:90 \\ \\ P(0)=\frac{5}{90}=0.06 \\ \\ P(1)=\frac{10}{90}=0.11 \\ \\ P(2)=\frac{2}{90}=0.02 \\ \\ P(3)=\frac{9}{90}=0.1 \\ \\ P(4)=\frac{33}{90}=0.37 \\ \\ P(5)=\frac{12}{90}=0.13 \\ \\ P(6)=\frac{15}{90}=0.17 \\ \\ P(7)=\frac{3}{90}=0.03 \\ \\ P(8)=\frac{1}{90}=0.01 \end{gathered}[/tex]Therefore, the table would look like this:
With this we calculate the probability in each case:
[tex]\begin{gathered} P\left(x<4\right)=P\left(x=0\right)+P\left(x=1\right)+P\left(x=2\right)+P\left(x=3\right)=0.06+0.11+0.02+0.10=0.29 \\ \\ P(x=6)=0.17 \\ \\ P(x\ge5)=P\left(x=5\right)+P\left(x=6\right)+P\left(x=7\right)+P\left(x=8\right)=0.13+0.17+0.03+0.01=0.34 \end{gathered}[/tex]59.25 ÷ 0.75 = 1.06 × 7.3 =on chart. will send image
Answers
For the division, notice that we can multiply both numbers by 100, to get the following:
[tex]\begin{gathered} 59.25\cdot100=5925 \\ 0.75\cdot100=75 \end{gathered}[/tex]then, we can make the long division:
therefore, the result of 59.25 ÷ 0.75 is 79
For the multiplication, we can write the following:
notice that since both factors have 2 digits and 1 digit each after the decimal point, the final result will have 3 digits after the decimal point,
Therefore, the result of 1.06 × 7.3 is 7.738
find the surface area of the cone in terms of pi. SA=__ cm squared. simply
Answers
Given the figure of a cone.
As shown, the slant height = s = 23 cm
And the diameter of the base = d = 18 cm
So, the radius = r = 0.5d = 9 cm
The surface area of the cone will be calculated using the following formula:
[tex]SA=\pi rs+\pi r^2[/tex]Substitute s = 23, and r = 9, writing the surface area in terms of π
[tex]SA=π(18)(23)+π(9)^2=414π+81π=495π[/tex]So, the answer will be:
The surface area of the cone = 495π cm²
