A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t. The point P is (√10/10 , -3√10/10) sin t=cos t= tan t=csc t=sec t=cot t=
Answers
Given
Graph
Procedure
Point P
[tex]P=(\frac{\sqrt[]{10}}{10},-\frac{3\sqrt[]{10}}{10})[/tex]Let's calculate the swept angle
[tex]\begin{gathered} \sin \theta=\frac{\frac{3\sqrt[]{10}}{10}}{1} \\ \sin \theta=\frac{3\sqrt[]{10}}{10} \\ \theta=\sin ^{-1}(\frac{3\sqrt[]{10}}{10}) \\ \theta=71.56\text{ \degree} \end{gathered}[/tex]Now the angle swept by t is
[tex]\begin{gathered} t=360-\theta \\ t=288.44\text{ \degree} \end{gathered}[/tex][tex]\begin{gathered} \sin (288.44)=-0.948 \\ \cos (288.44)=0.3163 \\ \tan (288.44)=-2.999 \\ \end{gathered}[/tex][tex]\begin{gathered} \csc (288.44)=-1.054 \\ \sec (288.44)=3.1614 \\ \cot (288.44)=-0.333 \end{gathered}[/tex]Related Questions
The temperature is currently 30 degrees if the temperature drops 2 degrees every hour for the next 4 hours, what temperature will it be
Answers
Given:
The temperature is currently 30 degrees
The temperature drops 2 degree every hour
So,
After the next 4 hours, the temperature drop = 2 * 4 = 8 degree
so,
The temperature after the next 4 hours = 30 - 8 = 22 degree
Find the supplementary angle for 59° 00'17 "
Answers
The supplementary angle is an angle x that adding to 59° 00'17 " give as 180°
So, x can be calculated as:
x + 59° 00'17 " = 180°
x = 180° - 59° 00'17 "
First, we need to write 180° as 179° 59' 60", so the subtraction is equal to:
So the supplementary angle is 120° 59' 43"
Answer: 120° 59' 43"
dliswer the question.Three vertices of a square are shown on the grid.y54+32+.11012345XWhat are the coordinates of the missing vertex? Enter the answer in the boxes.
Answers
The coordinate = (1, 5)
Explanation:The 3 vertices given:
(4, 2), (1,2), (4, 5)
Since the shape is a square, it means the length of all sides will be the same
Distance between (4, 2) and (4, 5) is the same
From (4, 2) to (4, 5), there are 3 lines in between them
Distance between (1, 2) and the 4th vertices will also be the same
from (1, 2) to the 4th vertice, there will also be 3 lines in between
Now counting the three lines upward on the graph from the same line as x =1,
on the y axis from 2, we would get y = 5
So the x coorcinate will remain the same but the y cordinate moves 3 units upward.
The missing vertex is x = 1, y = 5
The coordinate = (1, 5)
If we put the point on the graph, we would see the diatance are the same for the 4 sides of the square
I need to know the answer to this question please
Answers
First, order the dataset from least to greatest, as shown below
[tex]354,356,368,372,374,378,378,381,388,399,412,419[/tex]We will make a stem-and-leaf plot using stem units equal to 100; therefore, round the number above to the nearest tens
[tex]350,360,370,370,370,380,380,380,390,400,410,420[/tex]Then, use the first digits as stems and the second ones as leaves, obtaining the plot below,
Some information is lost in the process; therefore, another alternative is to use steam units equal to 10, obtaining the stem-and-leaf plot below
This version keeps all the information provided by the question.
Both plots are valid.Simplify1 19 х1 181 x. (2 points)O x+9909X +9O *+99x9xX+9
Answers
So, we're going to simplify:
[tex]\frac{\frac{1}{9}-\frac{1}{x}}{\frac{1}{81}-\frac{1}{x^2}}[/tex]For this, we could sum the fractions in the numerator, and the denominator, first:
[tex]\frac{\frac{1}{9}-\frac{1}{x}}{\frac{1}{81}-\frac{1}{x^2}}=\frac{\frac{x-9}{9x}}{\frac{x^2-81}{81x^2}}[/tex]We could rewrite the previous fraction as:
[tex]\frac{\frac{1}{9}-\frac{1}{x}}{\frac{1}{81}-\frac{1}{x^2}}=\frac{\frac{x-9}{9x}}{\frac{x^2-81}{81x^2}}=\frac{81x^2(x-9)}{9x(x^2-81)}=\frac{9x(x-9)}{x^2-81}=\frac{9x(x-9)}{(x+9)(x-9)}[/tex]And, finally:
[tex]\frac{9x(x-9)}{(x+9)(x-9)}=\frac{9x}{x+9}[/tex]Find the product. (6p + 6) (4p - 4)
Answers
We will have the following:
[tex]\begin{gathered} (6p+6)(4p-4)=24p^2-24p+24p-24 \\ \\ =24p^2-24 \end{gathered}[/tex]What property is demonstrated below:9 + -9 = 0
Answers
Answer
The inverse property of addition.
Explanation
The inverse property of addition states that adding a number and it's opposite, called the additive inverse, will produce a sum of zero.
Additive inverse of any number is simply multiplying the number by -1.
So, 9 + -9 = 0 indicates the inverse property of addition.
Hope this Helps!!!
Rewrite 20 oz as ____ lb ____ oz, using 1 pound = 16 ounces. You don’t need to use the unit-fraction method.
Answers
Step 1: Write the unit conversion
1 pound = 16 ounces
which means
1 lb = 16 oz
Step 2: Apply the conversion rate
If 16 oz = 1 lb
Then let 20 oz be represented by y
As shown in the diagram above, y will be obtained by cross multiplying
[tex]y\text{ =}\frac{20\text{ x 1}}{16}\text{ =}\frac{20}{16}=\frac{5}{4}\text{ = 1.25 pounds}[/tex]Answer is
20 0z is 1.25 lb
What is the x-value between 2tt and 4tt corresponding to a y-value of -1
Answers
We are given the equation;
[tex]y=\sin x[/tex]Where we have
[tex]\begin{gathered} \sin \frac{\pi}{2}=1 \\ \text{AND} \\ \sin -(\frac{\pi}{2})=-1 \end{gathered}[/tex]We can add 2pi and 4pi to -(pi/2);
[tex]\begin{gathered} 2\pi+(-\frac{\pi}{2}) \\ =\frac{4\pi-\pi}{2} \\ =\frac{3\pi}{2} \\ \text{Also;} \\ 4\pi+(-\frac{\pi}{2}) \\ =\frac{8\pi-\pi}{2} \\ =\frac{7\pi}{2} \end{gathered}[/tex]In other words;
[tex]\sin (\frac{3\pi}{2})=\sin (\frac{7\pi}{2})=-1[/tex]Therefore;
[tex]\frac{7\pi}{2}\text{ lies between 2}\pi\text{ and 4}\pi[/tex]ANSWER:
[tex]\frac{7\pi}{2}[/tex]Paul makes bars of soap to sell.He pays $47 for supplies. If he sells 77 bars of soap for $3 each. what is his revenue?
Answers
The cost of the supplies = $47
And the number of sells bars of soap = 77
The cost of each one = $3
So, the cost of all bars = 77 * 3 = 231
So, the revenue = 231 - 47 = 184
So, the answer is : his revenue = $184
The circumference of a circle is 20π. What is the area of the circle?A. 20πB. 10πC. 100πD. 400π
Answers
The circumference of a circle is 20π. What is the area of the circle?
A. 20π
B. 10π
C. 100π
D. 400π
Remember that
The circumference is equal to
[tex]C=2\pi r[/tex]we have
C=20pi
substitute the given value and solve for r
so
[tex]\begin{gathered} 20\pi=2\pi r \\ r=10\text{ units} \end{gathered}[/tex]Find the Area
[tex]A=\pi\cdot r^2[/tex]substitute
[tex]\begin{gathered} A=\pi\cdot10^2 \\ A=100\pi\text{ unit2} \end{gathered}[/tex]therefore
the answer is option CYou are offered a job that pays $50,000 during the first year, with an annual increase of 10% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.1 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.
Answers
Given:
Initial Salary = $50000
Rate of increase = 10%
Let's find the amount you can earn in the fourth year.
To find the amount in the fourth year, apply the exponential growth formula:
[tex]f(t)=a(b)^t[/tex]Where:
a = 50000
b = 1.1
t is the number of years = 4
Plug in values into the equation and solve:
[tex]\begin{gathered} f(4)=50000(1.1)^4 \\ \\ f(4)=50000(1.4641) \\ \\ f(4)=73205 \end{gathered}[/tex]Therefore, the amount you can expect in yoyr fourth year on the job is $73205
ANSWER:
$73205
At Winnie's restaurant, one serving of chicken soup is 1 and 1/2 cups. The chef makes 48 cups of soup each night. How many servings of chicken soup are in 48 cups? Explain how you know.
Answers
We want to find how many times 1 1/2 cups fits in to 48 cups. In other words, we need to divide 48 by 1 1/2.
To make easier, let's convert 1 1/2 in to a proper fraction:
[tex]1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2}[/tex]Now we want to divide 48 by 3/2. Remember that divide by a fraction is the same as multiply by the inverse:
[tex]48\div\frac{3}{2}=48\cdot\frac{2}{3}[/tex]Now solve:
[tex]\frac{48\cdot2}{3}=\frac{96}{3}=32[/tex]Thus, the amount of serving with 48 cups is 32.
a piece of blue yarn is 8 2/10 yards long. a piece of pink yarn is 6 times as long as the blue. what is the total length of the blue and pink yarn?
Answers
The blue yarn is
[tex]8\frac{2}{10}\text{ yars long}[/tex]And the pink yarn is 6 times as long.
Step 1. Simplify the number given for the yards of blue yarn.
We have a mixed number:
[tex]8\frac{2}{10}[/tex]But to simplify the operations, we can simplify 2/10 by dividing both numbers by 2:
[tex]\frac{2}{10}=\frac{1}{5}[/tex]So the length of the blue yarn is:
[tex]8\frac{1}{5}\text{ yards}[/tex]Step 2. Find the length of the pink yarn.
The pink yarn is 6 times as long as the blue one. Thus, to find the length of the pink yarn, we multiply the length of the blue yarn by 6:
[tex]6\times8\frac{1}{5}[/tex]We can expand this operation by multiplying 6 times 8, and 6 times 1/5:
[tex]6\times8\frac{1}{5}=6\times8+6\times\frac{1}{5}[/tex]This gives the following result:
[tex]=48+\frac{6}{5}[/tex]Which can be expressed as a mixed number:
[tex]48\frac{6}{5}\text{ yards}[/tex]That is the length of the pink yarn.
Step 3. Now we need to find the total length:
[tex]\text{Total length = length blue + length pink}[/tex]So we have that:
[tex]\text{total length=8}\frac{1}{5}+48\frac{6}{5}[/tex]we add the whole numbers:
8+48=56
and the fractions:
1/5 + 6/5 =7/5
And the result is:
[tex]56\frac{7}{5}[/tex]But we can still simplify the result, because:
[tex]\frac{7}{5}=1\frac{2}{5}[/tex]So the final result is:
[tex]56\frac{7}{5}=56+1\frac{2}{5}=57\frac{2}{5}[/tex]Answer:
[tex]57\frac{2}{5}\text{ yards}[/tex]10. The perimeter of the square and the equilateral triangle are equal. Which of the following is NOT a true statement about the figures? 10 a. The value of x is 4.5. b. The perimeter of each figure is 36 units. 2x 3x – 1.5 c. Each side length of the square measures 6 units. d. Each side length of the triangle measures 12 units.
Answers
We have the perimeter of the square and the triangle is equal, then:
[tex]4\cdot(2x)=3\cdot(3x-1.5)[/tex][tex]8x=9x-4.5\Rightarrow9x-8x=4.5\Rightarrow x=4.5[/tex]The perimeter of the square is:
[tex]8x=8\cdot4.5=36[/tex]The perimeter of the triangle is:
[tex]9\cdot(4.5)-4.5=36[/tex]Each side of the triangle is:
[tex]3\cdot(4.5)-1.5=12[/tex]Each side of the square is:
[tex]2\cdot4.5=9[/tex]The only statement that is not true is, therefore, option C. Each side length of the square is 9 units (not 6 units).
What is the five number summary for the data set? 1, 4, 6, 7, 8, 10, 12, 13, 14, 16,19, 22, 23, 27, 30, 31, 31, 33, 34, 36, 41, 42, 47
Answers
Answer:
Explanation:
Given the data set:
[tex]1,4,6,7,8,10,12,13,14,16,19,22,23,27,30,31,31,33,34,36,41,42,47[/tex]The data set contains 23 items where:
• The minimum number = 1
,• The maximum number = 47
Next, the median number (the number in the middle will be the 12th item):
[tex]1,4,6,7,8,10,12,13,14,16,19,\boxed{22},23,27,30,31,31,33,34,36,41,42,47[/tex]• The median = 22
The lower quartile will be the number in the middle of the first half.
[tex]1,4,6,7,8,\boxed{\textcolor{red}{10}},12,13,14,16,19,\boxed{22},23,27,30,31,31,33,34,36,41,42,47[/tex]• The lower quartile, Q1 = 10
Similarly, the upper quartile will be the number in the middle of the second half.
[tex]1,4,6,7,8,\boxed{\textcolor{red}{10}},12,13,14,16,19,\boxed{22},23,27,30,31,31,\boxed{\textcolor{red}{33}},34,36,41,42,47[/tex]• The upper quartile, Q3= 33
Therefore, the five-number summary is: 1,10,22,33,47 where
• Minimum: 1
,• Lower Quartile = 10
,• Median = 22
,• Upper Quartile = 33
,• Maximum = 47
alan mixes 1 1/4 cuos of milk with a can of condensed soup. he makes a hotel of 2 3/8 cups of soup how many cups of comdensed soup were made in a can?3 5/81 1/21 1/81 5/8
Answers
ANSWER
Option C
[tex]1\frac{1}{8}[/tex]STEP BY STEP EXPLANATION
Step 1:
[tex]1\frac{1}{4}\text{ + x = 2}\frac{3}{8}[/tex]Step 2
where would the zeros be plotted on this graph of the function f(x)=(x-1)(x-7)
Answers
If we have a polynomial written in the form:
[tex]f(x)=(x-x_1)(x-x_2)...(x-x_n)[/tex]Then,
[tex]x_1,x_2,...,x_n[/tex]are x values of the zeros of the polinomial. In this case:
[tex]f(x)=(x-1)(x-7)[/tex]Thus, x = 1 and x = 7 are zeros of the function.
Since in the zeros the y coordinate is y = 0, then:
Zeros:
(1, 0)
(7, 0)
Thus, in the graph:
rental car companycharges$23.50 aday,plus $0.30 per mile if a customer can spend $70 how many miles can he drive in one day
Answers
Total cost per day = $23.5
Money customer can spend = $70
Remaining money with the customer after he paid $23.5 = 70 - 23.5 = $46.5
Cost of mile per hour = $0.30
Number of miles = 46.5/0.3
= 155 miles
Final answer
155 miles
What is the value of the boat after 5 years?
Answers
Answer:
Explanation:
Given:
Initial Value, a= $23,000
Depreciation rate=18% or 0.18
Time in years, x = 5 years
To find the equation, we use the formula:
[tex]\begin{gathered} y=ab^x \\ \text{where:} \\ a=\text{ initial value} \\ b=(1-r)\text{ } \\ x=\text{time} \end{gathered}[/tex]We plug in what we know.
[tex]\begin{gathered} y=ab^x \\ y=23,000(1-0.18)^x \\ y=23000(0.82)^x \\ \text{Plug in 5 into x} \\ y=23,000(0.82)^5 \\ y=8527.02 \end{gathered}[/tex]Therefore, the boat would be worth $8527.02 after 5 years.
What is the volume of a sugar cube that measures 1 centimeter on each side? *4 points
Answers
we have that
the volume of the cube is equal to
V=b^3
we have
b=1 cm
so
V=(1)^3=1 cm3
volume is 1 cubic centimetersA circular plaque of diameter 6cm is cut from a square piece of metal with side length 6cm.What percentage of the metal is wasted?
Answers
Given a square piece of metal of side length 6cm
If a circular plaque of diameter 6cm is cut from the metal piece, the area wasted is the shaded area in the diagram below:
Total Area of the Metal Piece = 6 x 6 = 36 square cm
Area of the Circular Plaque
[tex]\begin{gathered} =\pi\times3^2 \\ =9\pi\; cm^2 \end{gathered}[/tex]Therefore:
Area of the Shaded Portion=Area of Metal Piece-Area of circular Plaque
[tex]=(36-9\pi)cm^2[/tex]The percentage of metal that was wasted will then be:
[tex]\begin{gathered} =\frac{\text{Area of the Shaded Portion}}{\text{Area of the Metal Piece}}\times100 \\ =\frac{\text{3}6-9\pi}{\text{3}6}\times100 \\ =\frac{\text{3}6-9(3.14)}{\text{3}6}\times100 \\ =\frac{\text{7}.74}{\text{3}6}\times100 \\ =21.5\% \end{gathered}[/tex]The percentage of metal that is wasted is approximately 21.5%.
Translate this phrase into an algebraic expression 63 decreased by twice a number use the variable n to represent the unknown number
Answers
We need to translate the word problem to an algebraic expression:
First, we have 63 decreased, where the word decreased in this kind of problem refers to subtraction.
Now, twice a number refers to the multiplication of a number by 2.
We need to use n for the unknown number, Then, we can write it as 2n.
Hence, the whole expression can be written as 63 -2n.
Write log3729= 6in exponential form.
Answers
Answer::
[tex]3^6=729[/tex]Explanation:
Given the logarithmic form below:
[tex]\log_3729=6[/tex]To write the equation in exponential form:
• Make the base of the logarithm the base of the exponent.
,• Make the number on the right of the logarithm the index.
That is:
Therefore, the exponential form is:
[tex]3^6=729[/tex]Trinity spent $147.22 over 8.5 months on treats for her pets. If she spent the same amount of money each month, how much money did Trinity spend per month on treats for her pets?
Answers
The total money spent by Trinity on treats for her pets over 8.5 months is $147.22, then amount of money Trinity spent on her pets every month equally is $17.32.
As given in the question,
Total money spent by Trinity on treats for her pets = $147.22
Number of months $147.22 spent over pets treatment = 8.5 months
Amount of money spent by Trinity on her pets treatment every month equally is given by :
8.5 months = $147.22
To get the value of per month divide both the side by 8.5 we get,
( 8.5 /8.5 ) month = $(147.22 / 8.5)
⇒ 1 month = $ 17.32
Therefore, the total money spent by Trinity on treats for her pets over 8.5 months is $147.22, then amount of money Trinity spent on her pets every month equally is $17.32.
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what property tax is due on a home assessed at 210,000 if the tax rate is 4.23 per $100
Answers
Given,
You have to pay $4.23 per $100 of the assessed value of your asset.
That is:
4.23/100 = 0.0423
That is 4.23%.
To find the property tax, you multiply the tax rate (4.23% = 0.0423) with the assessed value of the property (210,000). Hence,
[tex]0.0423\cdot210,000=\$8883[/tex]Answer$8,883
Factoring a quadratic with leading coefficient greater than 1
3n^2+5n+2=0
Answers
The algebraic factor is the multiplication term that can be common to the whole equation thus the factorization form of 3n²+5n+2=0 will be (n + 1)(3n + 2) = 0.
What is an algebraic factor?An algebraic factor is the multiplication of two algebraic terms.
The root of the quadratic equation formed by the algebraic factor is always real.
That term could be in form of summation multiplication or in subtraction.
As per the given quadratic equation,
3n²+5n+2=0
Let's 5n = 2n + 3n
3n²+ (3n + 2n) + 2 = 0
3n² + 3n + 2n + 2 = 0
(3n² + 3n) + (2n + 2) = 0
3n(n + 1) + 2(n + 1) = 0
(n + 1 )(3n + 2) = 0
Hence "The algebraic factor is the multiplication term that can be common to the whole equation thus the factorization form of 3n²+5n+2=0 will be (n + 1)(3n + 2) = 0".
For more about the algebraic factor,
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find the area of the square pictured above
Answers
Please upload the picture associated with the problem.
If Event A is "the card is black" and Event B is "the card is a king," demonstrate the equation holds true.
Answers
Event A = the card is black
Event B = the card is a king
For the equation to hold true:
[tex]\begin{gathered} P(A\text{ and B) = }P(A|B)\times P(B) \\ P(\text{card is black and a king) = P(}card\text{ is black|card is king)}\times\text{ P(card is king)} \end{gathered}[/tex][tex]\begin{gathered} \text{There are 4 kings in a deck} \\ P(A|B)\text{ = }\frac{1}{4} \\ P(B)=\text{ }\frac{4}{52} \\ P(A\text{ and B) = }\frac{1}{4}\times\frac{4}{52}\text{ = }\frac{1}{52} \end{gathered}[/tex][tex]\begin{gathered} \text{There are 26 blacks in a deck} \\ P(B|A)\text{ = }\frac{1}{26} \\ P(A)=\text{ }\frac{26}{52} \\ P(A\text{ and B) = }\frac{1}{26}\times\frac{26}{52}\text{ = }\frac{1}{52} \end{gathered}[/tex][tex]\begin{gathered} \text{Hence, the equation holds true:} \\ \text{for }P(A\text{ and B) = }P(A|B)\times P(B) \\ \frac{1}{52}=\frac{1}{4}\times\frac{4}{52} \\ \end{gathered}[/tex]Question 14, pre calc, I am at work so please finish question so when I get home I can review it, thanks!
Answers
SOLUTION
Given the question in the image, the following are the solution steps to get the discontinuity of the function
Step 1: Write the given function
[tex]f(x)=\frac{2x^2+3x-5}{\left(x-1\right)\left(x+5\right)}[/tex]Step 2: Define discontinuity of a function
A function has a removable discontinuity at x=a if
[tex]\begin{gathered} \lim _{x\to a}(f(x))\text{ exi}sts\text{ and is finite} \\ \end{gathered}[/tex]f(x) has step discontinuity if one-sided limits exist and finite but not equal.
f(x) has infinite discontinuity if one or both of the one-sided limits don't exist or are infinite
Step 3: State the infinite discontinuity and the removable discontinuity
To get the removable discontinuity
[tex]\begin{gathered} x-1=0 \\ x=0+1 \\ x=1 \end{gathered}[/tex]To get the infinite discontinuity
[tex]\begin{gathered} x+5=0 \\ x=0-5 \\ x=-5 \end{gathered}[/tex]Hence, the discontinuity is removable at x=1 and infinite at x=-5
Option D