The statement that is true about the given circle equation is:
Option A: The circle is centered at (−6, 3) and has a radius of 11.
How to find the equation of a circle?The standard form for finding the equation of a circle is given by the expression:
(x - h)² + (y - k)² = r²
where:
(h, k) represents the coordinates of the center of circle
r represents the radius of the circle
We are given the equation of the circle as:
(x - 6)² + (y - 3)² = 121
Now, 121 can also be written as 11². Thus, the equation of the circle can be rewritten as:
(x - 6)² + (y - 3)² = 11²
Comparing with the standard form of equation of a circle gives:
Coordinates of center = (-6, 3)
Radius = 11
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Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 14 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is _?_.
P(X=2) &= {14\choose 2}(0.08)^2(0.92)^{12} \
&= \frac{14!}{2!(14-2)!}(0.08)^2(0.92)^{12} \
[tex]\sf\implies\:&=\frac{14\times13}{2\times1}(0.08)^2(0.92)^{12}[/tex]
&= 91(0.08)^2(0.92)^{12} \
&\approx \boxed{0.2166
[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
Need help on question 20. Plsss help
The calculated distance between the tree and the zip line is 9.21 units
Evaluating the distance between the tree and the zip lineFrom the question, we have the following parameters that can be used in our computation:
y = -6/7x + 7
This represents the zip line
Convert the equation to standard form
This gives
7y = -6x + 49
So, we have
6x + 7y - 49 = 0
This means that
A = 6, B = 7 and C = -49
From the point (6, 14), we have
x = 6 and y = 14
The distance between the tree and the zip line is then calculated as
[tex]d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}[/tex]
By substitution, we have
[tex]d = \frac{|6 * 6 + 7 * 14 - 49|}{\sqrt{6^2 + 7^2}}[/tex]
This gives
[tex]d = \frac{85}{9.22}[/tex]
Divide
d = 9.21
Hence, the distance between the tree and the zip line is 9.21 units
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[5 (8^1/3 + 27^1/3)^3]^1/4 simplify
Answer
5
Solution
[5 (8^1/3 + 27^1/3)^3]^1/4
= [5 ((2^3)^1/3) + (3^3)^1/3)^3]^1/4
= [5((2+3)^3)1/4
= (5×5^3)^1/4
= (5^4)^1/4
= 5
f(x)=2x³-5x²
g(x)=2x-1
Find (f- g)(x)
Answer:
2x³-5x² - 2x + 1
Step-by-step explanation:
We are given
f(x) = 2x³ - 5x²
g(x) = 2x - 1
and asked to find (f - g)(x)
(f - g)(x) is nothing but f(x) - g(x)
(f- g)(x) = f(x) - g(x) = 2x³-5x² - (2x - 1)
= 2x³-5x² - 2x + 1
If f(x) is defined as follows, find (a) f(-3), (b) f(0), and (c) f(4).
x²
if x < 0
if x = 0
3x + 3 ifx>0
f(x) = 0
(a) f(-3)= (Simplify your answer.)
THE
For the given question the values,
f(-1) = 1f(0) = 0f(3) = 13Given value of the function when the condition for x is less than '0' is =
f(x) = x² for x < 0
The value of the function when the condition x is equals to '0' is =
f(x) = 0 for x = 0
The value of the function when the condition x is greater than '0' is =
f(x) = 3x + 4 for x > 0
From the above information,
To find f(-1) we have to use the x value as x². So, f(-1) = (-1)² = 1
To find f(0) we have to use x value as 0. So, f(0) = 0
To find f(3) we have to use the x value as 3x + 4. So, f(3) = 3(3) + 4 = 13.
From the above analysis, we find the values of f(-1), f(0), and f(3).
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3⋅f(−4)−3⋅g(−2) = ?
Ayuda por favor
The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40
Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;
f( - 4 ) = 15
g( - 2 ) = 5
Substitute the given parameters into the expression to have:
3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5
= 45 - 5
= 40
Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40
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If your starting salary is $50,000 and you receive a 4% increase at the end of
every year, what is the total amount, in dollars, you will earn over the first 16
years that you work?
Round your answer to the nearest whole dollar, and express your answer
without using commas.
Answer here
SUBMIT
Answer:
Total amount of becomes after 16 year is $93649 .
Consider the five points
(0,0),(0,5),(6,0),(3,4),(−1,8)
in
R
2
and name them
(x
i
,y
i
)
for
i=1,…,5
. The objective is to find two coefficients
a,b∈R
such that the boundary of the ellipse
ax
2
+by
2
=1
is as close to the above 5 points as possible. To this end, we define the error function: \[ f(a, b)=\sum_{i=1}^{5}\left(a x_{i}^{2}+b y_{i}^{2}-1\right)^{2} \] Calculate the optimal values of
(a,b)
by finding the local minima of the error function
f(a,b)
.
The optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
To find the optimal values of (a,b), we need to minimize the error function f(a,b). We can do this by taking partial derivatives of f(a,b) with respect to both a and b, and then setting them equal to zero:
∂f/∂a = 2∑([tex]x_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex]+ b [tex]y_{i}^{2}[/tex] - 1) = 0
∂f/∂b = 2∑([tex]y_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex] + b [tex]y_{i}^{2}[/tex] - 1) = 0
We can simplify these equations by defining the following sums:
Sxx = ∑[tex]x_{i}^{4}[/tex]
Syy = ∑[tex]y_{i}^{4}[/tex]
Sxy = ∑[tex]x_{i}^{2}y_{i}^{2}[/tex]
Sx = ∑[tex]x_{i}^{2}[/tex]
Sy = ∑[tex]y_{i}^{2}[/tex]
Using these sums, we can rewrite the partial derivatives as:
∂f/∂a = 2(aSx² + bSxy² - Sx)
∂f/∂b = 2(aSxy² + bSy² - Sy)
Setting these equal to zero and solving for a and b, we get:
a = (SySx - Sxy²) / (SxSyy - Sxy²)
b = (SxSy - Sxy²) / (SxSyy - Sxy²)
Plugging in the values for Sxx, Syy, Sxy, Sx, and Sy, we get:
a = 0.7205
b = 0.5369
Therefore, the optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).
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Carmen invested $2,000 in a mutual fund that is front-loaded, with a loading rate of 4.75 %. What was the
loading charge of this fund? (3 points)
Answer:
$95
Step-by-step explanation:
Carmen invested $2,000 in a mutual fund with a loading rate of 4.75%. To calculate the loading charge, we can multiply the amount invested by the loading rate: $2,000 * 4.75% = $95. So, the loading charge for this mutual fund was $95.
What is the equation through the points: (6, 10), (5, -6)
ASAP please
Answer: y=16x - 86
Step-by-step explanation:
Triangle AABC, right angled at C, is given. Height and the median from point C form an angle y.
The measure of larger acute angle of AABC is:
A 45°-
B
C
D
60° +
90°
24
92
2
92
4
The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.
How do you solve for the larger acute angle of ΔABC ?Let's denote the angles of triangle ΔABC as follows:
∠A = x
∠B = y
∠C = 90° (right-angled triangle)
Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.
Since CD is the median, we know that angle ∠ECD = φ.
In right-angled triangle ΔCEB, we have:
∠CEB = 90° - y
Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:
∠CED + ∠CEB + ∠ECD = 180°
Substitute the known values:
∠CED + (90° - β) + φ = 180°
Since ∠CED and ∠A are supplementary angles, we can also write:
∠CED = 180° - x
Now substitute this value into the previous equation:
(180° - x) + (90° - y) + φ = 180°
Simplify the equation:
270° - x - y + φ = 180°
Subtract 90° from both sides:
180° - x - y + φ = 90°
From this equation, we get:
x + y = 90°
Substitute this value back into the equation involving φ:
180° - (90°) + φ = 90°
Simplify:
90° + φ = 90°
Therefore, the measure of the larger acute angle of ΔABC is:
x = 45° + φ/2 (option a)
the above answer is in response to the full question below;
Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:
a. 45⁰ + φ/2
b. 60⁰ + φ/2
c. 90⁰ - φ/2
d. 2φ
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Evaluate (11/16−(3/4)2)×1
Answer:
-166/, -0.82,
Step-by-step explanation:
The above fraction, decimal are all evaluated answer for (11/16−(3/4)2)×1
Please help me!
Sloan keeps quarters and dimes in a jar, he just counted and has $23.45. If Sloane has 52 dimes in the jar, how many quarters does he have?
Answer in standard form, NEED EQUATION
x =
y =
Sloan has 73 quarters and 52 dimes kept in the jar
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Let x represent the number of quarters in the jar.
1 dime = $0.10, and 1 quarter = $0.25
Hence:
He counted $23.45, of which he had 52 dimes, hence:
0.10(52) + 0.25x = 23.45
5.2 + 0.25x = 23.45
x = 73
Sloan has 73 quarters
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This is an example of a(n)
Answer:
shape
Step-by-step explanation:
I need help, I’m struggling with 3 and 4 can someone help me
Answer:
3 and 4 ==> see work below
[tex]5. \quad\quad f^{-1}(x) = x^{1/7}[/tex]
[tex]6. \quad\quad f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]
Step-by-step explanation:
Definition of inverse functions
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
Or, in other words
If f(g(x)) = (g(f(x)) = x
then f and g are inverse functions
Q3
We have f(x) = x + 4 and g(x) = x - 4
To find f(g(x)), substitute g(x) = x - 4 wherever there is an x term in f(x)
f(g(x)) = g(x) + 4
= x - 4 + 4 = x
g(f(x)) = f(x) - 4
= x + 4 - 4 =x
Hence f(x) and g(x) are inverse functions
Q4
[tex]f(x) = \dfrac{1}{4}x^3\\\\g(x) = (4x)^{1/3}[/tex]
[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\\\\end{aligned}[/tex]
[tex]\begin{aligned}(g(x))^3 &= \left((4x)^{1/3} \right)^3 \\& = (4x)^{\frac{1}{3} \cdot 3}\\& = 4x\end{aligned}[/tex]
Therefore
[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\&= \dfrac{1}{4} \cdot 4x\\&= x\\\end{aligned}[/tex]
[tex]\begin{aligned}g\left(f(x)\right) & = \left(4f(x)\right)^{1/3}\\&= \left(4 \cdot \dfrac{1}{4}x^3\right)^{1/3}\\& = \left(x^3\right)^{1/3}\\& =x& \end{aligned}[/tex]
So f(x) and g(x) are inverse functions
Q5
[tex]\text{Given $f(x) = x^7 $ we are asked to find inverse $f^{-1}(x)$}[/tex]
[tex]\rm{Let \: y = f(x) = x^7}\\[/tex]
Interchange x and y:
[tex]x = y^7[/tex]
Solve for y:
[tex]y = x^{1/7}[/tex]
The right hand side is the inverse function of f(x)
[tex]f^{-1}(x) = x^{1/7}[/tex]
Q6
[tex]\rm{Given \;f(x) = -\dfrac{2}{5}x^3 \:find\:the\:inverse,\;f^{-1}(x)}[/tex]
Using the same procedure as for Q5
[tex]y=-\dfrac{2}{5}x^3\\\\x=-\dfrac{2}{5}y^3\\\\\text{Solve for y}\\[/tex]
[tex]y^3=-\dfrac{5x}{2}[/tex]
[tex]y=-\left(\dfrac{5x}{2}\right)^{1/3}\\\\\\\text{Inverse of $f(x)$ is $f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]
Input Signals: P = 0 and Q = 1.
The output of the OR gate will be 1.
What is a NOT Gate?An important component for electronics and computing, the NOT gate or inverter is a basic digital logic gate. It is designed with one input and output that conduct logical negation.
Essentially, this means it turns the input signal to its opposite. When given an input binary value at "1," the method generates "0" as the output and vice versa.
Two input signals, P=0 and Q=1, are subjected to the following process. The message carried by Q is inverted via a NOT gate using its negation feature, returning Q' = 0 at its output.
The resultant value of Q' (evaluated as zero), is then processed using an OR logic operation along with input P into another gate. Outputs from an OR port may only produce "1" if any of the input signal(s) carry a 1. As one of the inputs from this specific procedure provides "0", the result will inevitably be "1".
Consequently, a final analysis reveals that regardless of what the initial value for P was, the result obtained formulating the two signals through a NOT and OR devices matches an outcome of "1".
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The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
The correct option regarding which bus has the least spread among the travel times is given as follows: Bus 14, with an IQR of 6.
How to solveThe interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.
For groups of 15 students, we have that:
The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.
The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.
The quartiles for Bus 14 are given as follows:
Q1 = 12.
Q3 = 18.'
Hence the IQR is of:
IQR = Q3 - Q1 = 18 - 12 = 6.
The quartiles for Bus 18 are given as follows:
Q1 = 9.
Q3 = 16.
Hence the IQR is of:
IQR = Q3 - Q1 = 16 - 9 = 7.
Hence Bus 14 is the more consistent bus, due to the lower IQR.
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100 Points! Algebra question. Only looking for an answer to B. Please show as much work as possible. Thank you! Photo attached.
The quotient of functions f(x) and g(x) is given as follows:
(f/g)(x) = (x + 4)/(x - 3).
How to obtain the quotient function?The quotient function of f(x) and g(x) is given by the division of function f(x) by function g(x), as follows:
(f/g)(x) = f(x)/g(x)
The functions for this problem are given as follows:
f(x) = x² + 7x + 12.g(x) = x² - 9.The functions can be factored as follows:
f(x) = (x + 4)(x + 3) -> according to it's roots.f(x) = (x + 3)(x - 3) -> subtraction of perfect squares.The term (x + 3) is common to both numerator and denominator, hence it is simplified and the quotient function is given as follows:
(f/g)(x) = (x + 4)/(x - 3).
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[tex]if i have 12 yards of ribbon and they use 22 feet of ribbon to decorate the blanket then how many feet[/tex]
The remaining ribbon will be 14 feet.
Olga decorates blankets with ribbon she has 12 yards of ribbon
and, she uses 22 feet of the ribbon to decorates blankets
Now, we have to find the she decorates the blankets how many feet of ribbon will remain?
Firstly, Convert the yard into feet
We know that:
There are 3 feet in 1 yard
So, 36 feet in 12 yards
Now, The remaining ribbon will be the original amount less the amount used.
=> 36 - 12 = 14 feet
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16
Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?
О А.
m. All rights reserved.
2 Fr
Arc
Length
Q Search
I:
3=
IA
>
0
A graph that correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r is: C. graph C.
How to calculate the length of the arc?In Mathematics and Geometry, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle can be calculated by using the following equation (formula):
Arc length = 2πr × θ/360
In this context, we can reasonably infer and logically deduce that the arc length is directly proportional to the radian measure of the central angle.
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The dimensions of the box below are reduced by half. What is the ratio of the volume of the new box to the volume of the original box?
please help!!!!
u will get 100 points!!!!
Answer:
1:8
Step-by-step explanation:
The original volume of the box can be calculated by multiplying the length, height, and width:
V = l x h x w = 40 x 8 x 20 = 6,400 cubic inches
If each of the dimensions is reduced by half, the new dimensions become:
Length = 20 inches
Height = 4 inches
Width = 10 inches
The volume of the new box can be calculated as follows:
V_new = l x h x w = 20 x 4 x 10 = 800 cubic inches
The ratio of the volume of the new box to the volume of the original box is:
V_new / V = 800 / 6,400 = 1/8
Therefore, the ratio of the volume of the new box to the volume of the original box is 1:8.
Answer:
I think it's 1 : 8
Step-by-step explanation:
if you don't understand, you can ask me
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If sun x= 4/5 what is the value of b? 22.5 3b
By following trigonometry identities we get b equals **7**
Define trigonometry identities?Trigonometric identities are equations involving trigonometric functions that hold for all possible values of the variables that occur and for which both sides of the equation are specified. These identities come in use if trigonometric function-based formulas need to be made simpler 1.
There are numerous distinctive trigonometric identities that involve a triangle's side length and angle 2. Only the right-angle triangle 2 is covered by the trigonometric identities. The three main trigonometric functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant.
Some of the most popular trigonometric identities are listed below:
sin²(x) + cos²(x) = 1
- tan(x) = sin(x)/cos(x)
- cot(x) = cos(x)/sin(x)
- sec(x) = 1/cos(x)
- csc(x) = 1/sin(x)
- sin(2x) = 2sin(x)cos(x)
- cos(2x) = cos²(x) - sin²(x)
- tan(2x) = (2tan(x))/(1 - tan²(x))
The use of these identities
.One angle in a right triangle is x°, where sin x°=4/5 . With this knowledge, we can use the inverse sine function (arcsin) to calculate the value of x, which gives us x = arcsin(4/5) = 0.9272952180016122 radians .
In addition, we are informed that NL = 22.5 and NM = 3b. We can get the value of LM, which is equal to√(NL2 + NM2), using the Pythagorean theorem. 2. When the given values are substituted, we obtain LM = √((22.5)2 + (3b)2) = sqrt(506.25 + 9b2).
LM is equivalent to b times cos(x°) since it is the polar opposite of the right angle. Consequently, we can write:
b cos(x°) = √(506.25 + 9b²)
Substituting x = arcsin(4/5), we get:
b cos(arcsin(4/5)) = √(506.25 + 9b²)
Simplifying this equation using trigonometric identities, we get:
b * (√1 - sin²(arcsin(4/5)) = sqrt(506.25 + 9b²)
b × (√(1 - (4/5)²)) = sqrt(506.25 + 9b²)
b× (√(1 - 16/25)) = sqrt(506.25 + 9b²)
b× (√(9/25)) = sqrt(506.25 + 9b²)
3b/5 = √(506.25 + 9b²)
Squaring both sides of the equation, we get:
9b²/25 = 506.25 + 9b²
Solving for b, we get:
b = 7
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Select the statement that is true a.16.7-8=2.9×3 b. 4×3.2=17.8-5 c.10.5÷5+1=8.8÷4 d.
Answer:
b
4 x 3.2 = 12.8
17.8 - 5 =12.8
so,
4 x 3.2 = 17.8-5
12.8=12.8
Question is in the image. Please help me solve these
Answer:
Step-by-step explanation:
Add 2 1/3 + 4 5/8 writ your answer as a mixed number
Usually, a mixed number is the simplest way to express an improper fraction – but sometimes, the fraction ... Don't express the answer as a decimal. Instead ... So, add the whole number back in to get a final result of 6 1/2. ... Write out the factors for the numerator of your fraction, then write out the factors for the denominator.
Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800
kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600
kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700
kg
2,700kg2, comma, 700, start text, k, g, end text.
The effect Lola's mass decreasing has on the the mean and median
: No change in Median weightMean reduced by 180 kgHow do we calculate?Given values :
5 African elephants
The mean mass of the elephants was 3800 kg
The median mass of the elephants was 3600 kg
The smallest elephant, named Lola, weighed 2700 kg
Lola then got very sick and lost weight until her mass reached 1800 kg
2700 , A , 3600 , B , C
as Median is 3600 and lowest is 2700
now 2700 becomes 1800
1800 , A , 3600 , B , C
so Median remains the same as 3600
So we notice no change in Median
The mean mass of the elephants = 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
total mass = 19000 - 2700 + 1800
= 181000 kg
The following can be inferred :
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.
In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually
What is investment compounded annually?When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.
For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960
Then new total amount after one year will be $12,000 + $960 = $12 960 ,
This process will continue for each year of the investment and the formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n
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complete quesation:
You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.
a.
3.99% compounded monthly
b.
4% compounded quarterly
c.
4.175% compounded annually
d.
4.2% simple interest
Help asap!! Please help I don’t get this
The value of arc CD is 110⁰.
The value of arc AD is 120⁰.
What is the measure of the angle?The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)
angle DEC = ¹/₂ (360 - 200)
angle DEC = 80⁰
The value of arc CD is calculated as follows;
80 = ¹/₂ (CD + 50) (intersecting chord theorem)
2 x 80 = CD + 50
160 = CD + 50
CD = 110⁰
Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)
arc AD = 120⁰
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the expression when c=56 and d=10
The numeric value of the expression 3c + 4d when c = 56 and d = 10 is given as follows:
208.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The expression for this problem is given as follows:
3c + 4d.
Hence the numeric value of the expression is given as follows:
3 x 56 + 4 x 10 = 208.
Missing InformationThe expression is:
3c + 4d.
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Find the exact value of each of the remaining trigonometric functions of θ.
tan θ= -3/5, sec θ>0.
If given trigonometric functions of θ are tan θ= -3/5, sec θ>0, the exact value of sin θ is 3/√(34).
To find the value of sin θ, we can use the Pythagorean identity: sin²θ + cos²θ = 1.
First, we need to find the value of cos θ. We know that sec θ = 1/cos θ and sec θ > 0, which means that cos θ > 0. Therefore, we can use the identity: tan²θ + 1 = sec²θ to find the value of cos θ.
tan θ = -3/5
tan²θ = 9/25
sec²θ = tan²θ + 1 = 34/25
cos²θ = 1/sec²θ = 25/34
cos θ = √(25/34) = 5/√(34)
Now, we can use the Pythagorean identity to find sin θ:
sin²θ + cos²θ = 1
sin²θ = 1 - cos²θ
sin²θ = 1 - 25/34
sin²θ = 9/34
sin θ = √(9/34) = 3/√(34)
In trigonometry, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are used to relate the angles of a triangle to its sides. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin θ = opposite/hypotenuse.
Knowing the value of sin θ is important because it allows us to calculate the values of the other trigonometric functions. For example, cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse, so we needed to find the value of cos θ to calculate sin θ.
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