Answer:
[tex]sec(\theta) \times cosec(\theta) = \dfrac{tan^2 (\theta)+ 1}{tan (\theta)} = tan (\theta)+ \dfrac{1}{tan (\theta)} = p + \dfrac{1}{p}[/tex]
Step-by-step explanation:
The given trigonometric relations are
tan(θ) = p
sec(θ)×cosec(θ) = p + 1/p
We note that, when tan(θ) = p, we have;
p + 1/p = tan(θ) + 1/(tan(θ)) = (tan²(θ) + 1)/tan(θ)
By trigonometric ratios, we have;
tan²(θ) + 1 = sec²(θ) =1/cos²(θ) which gives;
(tan²(θ) + 1)/tan(θ) = 1/cos²(θ) × 1/tan(θ) = cos(θ)/sin(θ)×1/cos²(θ)
[tex]\dfrac{1}{cos^2(\theta)} \times \dfrac{cos (\theta)}{sin( \theta)} = \dfrac{1}{cos(\theta)} \times \dfrac{1}{sin( \theta)} = sec(\theta) \times cosec(\theta)[/tex]
Therefore;
[tex]If \ tan (\theta) = p \ then \ sec(\theta) \times cosec(\theta) = p + \dfrac{1}{p}[/tex]
Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?
Answer:
here is your answer
Answer:hey guys just saying its 1/52
Step-by-step explanation:
Write the equation of the circumference that meets the condition: Center on the line: x -4y = 1 And it passes through the points A (3,7) and B (5,5)
Answer:
(x + 3)² + (y + 1)² = 100
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center of the circle and r is the radius.
The center is on the line x − 4y = 1, so:
h − 4k = 1
h = 1 + 4k
(x − 1 − 4k)² + (y − k)² = r²
Two points on the line are (3, 7) and (5, 5), so:
(3 − 1 − 4k)² + (7 − k)² = r²
(5 − 1 − 4k)² + (5 − k)² = r²
Set the equations equal:
(3 − 1 − 4k)² + (7 − k)² = (5 − 1 − 4k)² + (5 − k)²
(2 − 4k)² + (7 − k)² = (4 − 4k)² + (5 − k)²
4 − 16k + 16k² + 49 − 14k + k² = 16 − 32k + 16k² + 25 − 10k + k²
4 − 16k + 49 − 14k = 16 − 32k + 25 − 10k
53 − 30k = 41 − 42k
12k = -12
k = -1
h = 1 + 4k
h = -3
(3 − 1 − 4k)² + (7 − k)² = r²
(3 − 1 + 4)² + (7 + 1)² = r²
6² + 8² = r²
r = 10
Therefore, the equation of the circle is:
(x + 3)² + (y + 1)² = 10²
WILL GIVE BRAINLEST ANSWER IF ANSWERED IN THE NEXT 24 HRS Express the complex number in trigonometric form. -5i
Answer:
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Step-by-step explanation:
If a complex number is z=a+ib, then the trigonometric form of complex number is
[tex]z=r(\cos \theta +i\sin \theta)[/tex]
where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].
The given complex number is -5i.
It can be rewritten as
[tex]z=0-5i[/tex]
Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.
[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]
[tex]\tan \theta=\dfrac{-5}{0}[/tex]
[tex]\tan \theta=\infty[/tex]
[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex] [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]
[tex]\theta=\dfrac{3\pi}{2}[/tex]
So, the trigonometric form is
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Answer:
in degrees the answer is 5 (cos 270 + i sin 270)
in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))
Step-by-step explanation:
The owner of a music store gathered data from several schools about the number of students in their concert and marching bands. The scatter plot shows the data she gathered and the line of best fit
Answer:
25 students
Step-by-step explanation:
What we need to do here is to do some tracing. We simply need to go to the point on the concert band where we have the value 35.
After sighting this value, we then make a tracing to the line of best fit. Then from this line of best fit, we trace the point on the matching band that correlated with the value 35.
If properly traced, we would arrive at a value of 25 on the marching band
What the answer question
Answer:
TW = 3.18 yd (Approx)
Step-by-step explanation:
Given:
TV = 6 yd
∠TYW = 32°
∠TWV = 90°
Find:
TW
Computation:
Using trigonometry application.
TW / TV = Sin 32°
TW / 6 = 0.53
TW = 3.18 yd (Approx)
Mrs.joshi bought a saree for Rs 1750.she sold it at a profit of 4%.what would be her profit or loss percent ?
Answer: Rs 1820
Step-by-step explanation:
This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750. Thus, simply do 1.04*1750 to get 1820.
Hope it helps <3
Does the table represent a function? Why or why not?
4
5
NWNWOX
5
7
9
A. No, because one x-value corresponds to two different y-values.
O B. Yes, because every xvalue corresponds to exactly one y value.
O C. No, because two of the y-values are the same.
O D. Yes, because there is the same number of x-values as y-values.
Answer:
Let's put the chart into ordered pairs:
(x, y)
(2,1)
(3,4)
(3,3)
(4,2)
(5,5)
In bold, we see that there are two y-values at x=3. This means that this relation fails the vertical line test (two points on the same verticle line). This is not a function.
The answer options may be mis-written.
The answer is no, because one x value corresponds to more than one y-value.
In which quadrant or on which axis do each of the points (2, 3 ), ( 5, -6 ), ( 2,0 ) , ( -5, 2 ), (-2,-4), (0,-2).
from the above picture
2,3 = 1 quadrant
5,-6 = 4 quadrant
2,0 = on x axis
-5,2 = 2 quadrant
-2,-4 =3 quadrant
0,-2 = on y axis
The equal sides of isosceles triangle are 10 cm and perimeter is 28 cm. The area of this triangle is?
Answer:
A=24 CM²
Step-by-step explanation:
10 x 2 + x=28
20+x=28
x=8
a=b x h/2
a=6 x 8 / 2
a=24CM²
36 моля колкото по бързо може формулата е (X÷2)÷(x×3)=305,4
Answer:
Step-by-step explanation:
The quotient of two numbers is 305.4. Find the quotient if the divisor decreases 2 times and the divisor increases 3 times
x/y = 305.4
3x/(y/2) = 6x/y = 6*305.4 = 1832.4
Note that the question will be deleted soon because it is posted in a language other than English.
Обратите внимание, что вопрос будет удален в ближайшее время, потому что он размещен на языке, отличном от английского.
On a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20). Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.
Answer:
(10, 17)
Step-by-step explanation:
It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.
Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)
From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.
y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.
The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.
x: 4+6 = 10
y: 8+9=17
The fruit market is at point (10,17)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates
[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]
[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]
Tia is at P(4, 8) and Lei is at Q(12, 20).
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1
So,
[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]
Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.
Learn more about graph here:
brainly.com/question/16608196
#SPJ5
C(n)=4/9(-3)^n-1. WHATS THE 3rd TERM? Please help I can’t get this done
Answer:
Third term=4
Step-by-step explanation:
Given:
C(n)=4/9(-3)^n-1
Find the third term
Let n=3
Substitute n=3 into the equation
C(n)=4/9(-3)^n-1
C(3)=4/9(-3)^3-1
Step 1: evaluate the power 3-1
C(3) = 4/9(-3)^2
Step 2: evaluate (-3)^2
C(3) = 4/9(9)
It can be rewritten as
C(3) = 4/9*9
9 numerator will strike 9 denominator out leaving 4
C(3)=4
Therefore, the third term=4
C(3)=4
ASAP! Please help me with this question!
Answer:
24 cm
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
2304 pi = 4/3 pi r^3
Divide each side by pi
2304 = 4/3 r^3
Multiply each side 3/4
2304 * 3/4 = 4/3 r^3 * 3/4
1728 = r^3
Take the cube root of each side
1728 ^ 1/3 = r^3 ^ 1/3
12 = r
We want the diameter
d = 2*r
d = 2*12
d = 24
Answer:
24 centimeters
Step-by-step explanation:
A basketball is a sphere. The volume of a sphere can be found using the following formula:
V= 4/3 π r^3
We know that the volume is 2304 π cm^3, therefore we can substitute 2304π in for V.
2304π = 4/3 π r^3
We want to find out what r is. Therefore, we must get r by itself. First, divide both sides by pi.
2304π/π=4/3πr^3/π
2304π/π=4/3r^3
2304=4/3r^3
Next, divide both sides by 4/3, or multiply by the reciprocal of 4/3. The reciprocal of 4/3 is 3/4 (flip the numerator and denominator).
2304*3/4=4/3r^3*3/4
2304*3/4=r^3
1728=r^3
Now, take the cube root of both sides.
∛1728=∛r^3
∛1728=r
12=r
r= 12 cm
The radius is 12 centimeters, but the question asks us to find the diameter. The diameter is twice the radius.
d= 2r
d= 2* 12 cm
d= 24 cm
The diameter of the basketball is 24 centimeters.
Each day that a Redbox movie is kept past its due date, a $1.50 fee is charged at midnight.
What is the ordered pair it a movie is kept for 5 days?
Let x represents the number of days that a movie is late and y represents the total fee
Answer:
(5, 7.5)
Step-by-step explanation:
Each day the movie is late adds $1.50 for late fees.Then, after 5 days of past due, the total late fee would be: 5 * $1.50 = $7.50
Then the coordinate pair representing this would be: (5, 7.5)
Find the angle θ between the two sides of a triangle whose lengths are 5cm and 4cm , if its area is 5cm²
[tex] \Delta = \frac 1 2 a b \sin C[/tex]
[tex]\Delta=5, \quad a=5, \quad b=4[/tex]
[tex]\sin C = \dfrac{2 \Delta}{ab} = \dfrac{2 (5)}{5(4) } = \dfrac 1 2[/tex]
[tex]C=30^\circ \textrm{ or } C=150^\circ[/tex]
Answer: two possibilities, θ=30° or 150°
Urgent help I need it right now!!!!
Answer:
[tex]\boxed{\sf 30 \ bean \ cans}[/tex]
Step-by-step explanation:
The ratio of bean cans to corn cans is 6 : 7
Given that Corn cans = 35
Let the bean can be x
So,
The proportion for it will be:
6 : 7 = x : 35
Product of Means = Product of Extremes
7 * x = 6 * 35
7x = 210
Dividing both sides by 7
x = 30
So, 30 bean cans have to be put on the table to hold the needed ratio
On the coordinate plane below, Point P, is located at (2,-3) and point Q is located at (-4,4). Find the distance between points, P and Q
Answer:
[tex]d = \sqrt{85}[/tex] or d ≈ 9.22
Step-by-step explanation:
Distance formula:
[tex]d = \sqrt{(2 - (-4))^2 + (-3- 4)^2} \\d = \sqrt{36+ 49}\\d = \sqrt{85} \\[/tex]
which ordered pair has a solution to the system of inequalities. y>2x and y>3
Answer:
We have the system:
y > 2*x
y > 3
Now, let's find the limits:
taking y > 3, we can see the limit y = 3.
Now we replace it in the first inequality:
3 > 2*x
3/2 > x.
Then we have that:
y > 3
x < 3/2
Those two inequalities define our system.
So any ordered pair where x is smaller than 3/2 and y is larger than 3, is a solution.
or example:
(1, 3.5) is a solution.
Answer:
(1,5)
Step-by-step explanation:
the other options make the system of equations wrong..
The temperature in Chicago when the plane left was 22°F. When the plane arrived in Atlanta it was 46°F. What was the difference in temperature?
Answer:
24
Step-by-step explanation:
46 - 22 = 24
Can anyone plz help me? with this math question?
Answer:
it May be SAS postulate
Evaluate the expression. Assume that all the angles are in Quadrant I. (cos (arctan √3/7))
Answer:
0.971
Step-by-step explanation:
Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.
From the expression given
(cos (arctan √3/7)), we need to get the expression in parenthesis first.
Let y = (cos (arctan √3/7))
If u = arctan √3/7
Then y = cos(u) .... 1
Let's get the value of u first
u = arctan √3/7
u = arctan(0.2474)
u = 13.896°
Substituting u = 13.896° into equation 1, we will have;
y = cos(u)
y = cos13.896°
y = 0.971.
Hence the expression (cos(arctan√3/7)) is equivalent to 0.971
Answer:
y = 0.971.
Step-by-step explanation:
Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.
From the expression given
(cos (arctan √3/7)), we need to get the expression in parenthesis first.
Let y = (cos (arctan √3/7))
If u = arctan √3/7
Then y = cos(u) .... 1
Let's get the value of u first
u = arctan √3/7
u = arctan(0.2474)
u = 13.896°
Substituting u = 13.896° into equation 1, we will have;
y = cos(u)
y = cos13.896°
y = 0.971.
Please answer this question now in two minutes
Answer:
d is 5 units
Step-by-step explanation:
Use pi=3.14. Round to the nearest hundredth
Answer:
9.42
pi x radius x radius x (height / 3) = volume
1 x 1 = 1 and 9/3 = 3
pi x 1 x 3 = volume
pi x 3 = volume
3.14 x 3 = 9.42
Hope this helps
Step-by-step explanation:
the mapping diagram shows a function S(x).
Which mapping diagram shows the inverse of S(x)?
Answer:
Again the domain consists of the pre-images and the range the images.
When we are looking for the f(x) we just look at the number it is pointing to in the range (when we have a diagram), and when we are looking for x when f(x)=y we look at the number that has a line pointed to y.
So the f(4)=
f(x)=4 when x is 8
An economist is studying the linear relationship between the selling price p, of a
mobile phone and the number of persons buying the phone x. The table of values
illustrates her findings. Write the equation that represents the relationship between the
number of persons buying the phone and the price of the phone.
Answer:
The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60
Step-by-step explanation:
The given data are as follows
x, p($)
10, 52.5
25, 41.25
40, 30
60, 15
We note that a plot of the given points give a straight line graph indicating a linear relationship
The rate of change of p($) with x is given by slope, m in the following relation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Which gives;
[tex]Slope, \, m =\dfrac{41.25-52.5}{25-10} = \dfrac{30-41.25}{40-25} = \dfrac{15-30}{40-60} =-0.75[/tex]
Therefore, to write the equation in slope and intercept form, we have;
From the first point with coordinates (52.5, 10), we have
y - 52.5 = -0.75×(x - 10)
y = -0.75·x + 7.5 + 52.5 = -0.75·x + 60
The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60.
Expand. Your answer should be a polynomial in standard form. (6x+1)(1-3x)
Answer:
3x-18x^2+1
Step-by-step explanation:
(6x+1)(1-3x)
6x-18x^2+1-3x
6x-3x-18x^2+1
3x-18x^2+1
Hope this helps :)
Answer:
[tex]-18x^2+3x+1[/tex]
Step-by-step explanation:
[tex]6x *1=6x\\6x*-3x=-18x^2\\1*1=1\\1*-3x=-3x\\[/tex]
Add all the like terms
[tex]-9x^2+3x+1[/tex]
Rearrange the following formula to solve for p: wa+3p=q
Answer:
wa + 3p = q
3p = q - wa -- Subtract wa
p = (q - wa) / 3 -- Divide by 3
Answer:
[tex] \boxed{\sf p = \frac{1}{3} (p - wa)} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: p: \\ \sf \implies wa + 3p = q \\ \\ \sf Subtract \: wa \: from \: both \: sides: \\ \sf 3p = q - wa \\ \\ \sf Divide \: both \: sides \: by \: 3: \\ \sf \implies p = \frac{1}{3} (q- wa)[/tex]
Simplify the following v^4*v^5*v
Answer:
v^10
Step-by-step explanation:
For this, we need to understand one important rule of exponents. For powers of like bases, you add the exponents when they are being multiplied. With this in mind let's continue.
In this problem, the base is v, each multiplied with different powers. So:
v^4 * v^5 * v = v^(4+5+1) = v^10
So the solution will be v^10.
An additional example would be 2^2 * 2^3.
For this we know it would be 2^2 * 2^3 = 2^(2+3) = 2^5 = 32.
We can verify by simply doing 2 * 2 * 2 * 2 * 2 = 32. Note both are 32, and this example shows the usefulness of exponent rules.
Hope this helps. Cheers.
Answer:
v10
Step-by-step explanation:
v^4*v^5*v=v^10
add exponents when multiplying since we have exponents 4,5, and 1
4+5+1=10
Find the ordered pair $(s,t)$ that satisfieFor a certain value of $k,$ the system \begin{align*} 3a + 4b &= 7,\\ 6a + 4b &= k- 4b \end{align*}has infinitely many solutions $(a,b).$ What is $k$?s the system \begin{align*} \dfrac{s}{2} + 5t &= 3,\\ 3t - 6s &= 9. \end{align*}
Answer:
Step-by-step explanation:
The circle below is centered at the point (-3,4) and had a radius of 3. What is it equation? ( top answers gets )
Answer:
( x+3) ^2 + ( y-4) ^2 = 9
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2
Where ( h,k) is the center and r is the radius
( x--3) ^2 + ( y-4) ^2 = 3^2
( x+3) ^2 + ( y-4) ^2 = 9