The trigonometric functions sine and cosecant have a positive sign.
How to determine the sign of a trigonometric function associated with a vector
In this problem we must determine what trigonometric functions associated with a vector of the form (x, y) have a positive sign. This can be done by computing on each function:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
cot θ = x / y
sec θ = √(x² + y²) / x
csc θ = √(x² + y²) / y
If we know that x = - 12 and y = 5, then the values of the trigonometric functions are, respectively:
sin θ = 5 / √[(- 12)² + 5²]
sin θ = 5 / 13
cos θ = - 12 / √[(- 12)² + 5²]
cos θ = - 12 / 13
tan θ = - 5 / 12
sec θ = - 13 / 12
csc θ = 13 / 5
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What’s the answer?
I want it now! Please?
Answer:
1.827
Step-by-step explanation:
Is Circumcentre and centroid of a triangle same?
Answer:
no, they are different in their different ways
Help me to find the sum 37.2 + 17.5=
Both pyramids in the figure have the same base area as the prisme
The ratio of the combined volume of the pyramids to the volume of the prism,expressed as a fraction in simplest form,is 1/3.
How to calculate the ratio?The volume of a pyramid is (1/3) (base area) (height)
Volume of the lower pyramid = (1/3) (base area) (height) Volume of the upper pyramid = (1/3) (basearea × height)
The combined volume of both pyramids = (2/3) × (base area) (height) .
Their base area is (length x width) of the prism, and their height is (1/2 the height) of the prism.
From here, we'll work with the dimensions of the prism ... L, W, and H .
Combined volume of the pyramids = (2/3) (L x W) (1/2 H)
= (1/3) (L x W x H) .
Volume of the prism = (L x W x H)
The pyramids occupy 1/3 the volume of the prism.
The ratio is 1/3 .
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Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the prism,expressed as a fraction in simplest form,is
What are the solutions of the original equation?
✓
x = 1 or x = -2
Xx=-1 or x = 2
x = -5 or x = -2
x = 4 or x = -5
2e^x +e^(-2x)=0
help pls
Answer:
No real solutions
Step-by-step explanation:
The left hand side is the sum of two functions that are always positive.
find the center and radios of the given sphere. find the trace of the sphere on the given plane. sphere: x^2 y^2 z^2 - 6x - 4y 8z=0
TheThe sphere x^2 y^2 z^2 - 6x - 4y 8z=0 has a radius of √29 and its center is located at (3, 2, -4).
To find the center and radius of the given sphere, we can rewrite the equation of the sphere in standard form.
The equation of a sphere in standard form is given by:
(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2
Let's rewrite the given equation of the sphere:
x^2 y^2 z^2 - 6x - 4y + 8z = 0
Rearranging the terms, we have:
x^2 - 6x + y^2 - 4y + z^2 + 8z = 0
Now, we complete the square for each variable group:
(x^2 - 6x + 9) + (y^2 - 4y + 4) + (z^2 + 8z + 16) = 9 + 4 + 16
Simplifying further:
(x - 3)^2 + (y - 2)^2 + (z + 4)^2 = 29
Comparing this equation to the standard form equation, we can see that the center of the sphere is (3, 2, -4), and the radius is √29.
To find the trace of the sphere on a given plane, we substitute the equation of the plane into the equation of the sphere and solve for the points of intersection.
Let's say the equation of the plane is given by:
ax + by + cz + d = 0
Substituting this equation into the equation of the sphere, we have:
(x - 3)^2 + (y - 2)^2 + (z + 4)^2 = 29
(ax + by + cz + d - 3)^2 + (ay + by + cz + d - 2)^2 + (az + bz + cz + d + 4)^2 = 29.
Expand and simplify the equation to find the trace of the sphere on the given plane.
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When sketching a normal curve, what
value represents one standard deviation
to the right of the mean for the data set?
56, 54, 45, 52, and 48.
Answer:
The value representing one standard deviation to the right of the mean is 55.
Step-by-step explanation:
The provided data set is:
S = {56, 54, 45, 52, and 48}
Compute the mean and standard deviation as follows:
\(\mu=\frac{1}{n}\sum X=\frac{1}{5}\times [56+54+45+52+48]=51\\\\\sigma=\sqrt{\frac{1}{n}\sum (X-\mu)^{2}}=\sqrt{\frac{1}{5}\cdot {(56-51)^{2}+...+(48-51)^{2}}}=\sqrt{\frac{1}{5}\times 80}=4\)
Compute the value representing one standard deviation to the right of the mean as follows:
\(X=\mu+1\cdot \sigma\)
\(=51+(1\times 4)\\=51+4\\=55\)
Thus, the value representing one standard deviation to the right of the mean is 55.
How can I solve ¾ - (-5/12)?
Answer:
\(1 \frac{1}{6}\)
Step-by-step explanation:
\(\frac{3}{4}+ \frac{5}{12} =?\\\)
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
\((\frac{3}{4}\) × \(\frac{3}{3} )\) + \((\frac{5}{12}\) ×\(\frac{1}{1})=?\)
Complete the multiplication and the equation becomes
\(\frac{9}{12} + \frac{5}{12}\)
The two fractions now have like denominators so you can add the numerators.
\(\frac{9+5}{12} = \frac{14}{12}\)
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 14 and 12 using
GCF(14,12) = 2
14÷2 / 12÷2 =7/6
The fraction
7/6
is the same as
7÷6
Convert to a mixed number using
long division for 7 ÷ 6 = 1R1, so
7/6= \(1 \frac{1}{6}\)
Therefore:
3/4 − (−5/12) = \(1 \frac{1}{6}\)
Solution by Formulas
Apply the fractions formula for subtraction, to
3/4 − (−5/12)
and solve
(3×12) − (−5×4) 4×12
=3/6− (−20/48)
=56/48
Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF( 56,48) = 8
56÷8 / 48÷8 =7/6
Convert to a mixed number using
long division for 7 ÷ 6 = 1R1, so
7/6= \(1 \frac{1}{6}\)
Therefore:
3/4 − (-5/12) = \(1 \frac{1}{6}\)
help me, lol.
Well appreciated!
Answer:
x=-35
Step-by-step explanation:
can you mark me as brainliest pls
What Is the average rate of change f(x) = x ^ 2 - x + 4; x= 2 to x = 4
Answer:
B
Step-by-step explanation:
suppose you train two different machine learners to detect intruders based on network usage data. the performance of each is shown in the two probability tables below. ml1 predictedml2 predicted intrudervalid userintrudervalid user truthintruder0.01290.001630.2000.0115 valid user0.0001260.9850.006900.782 the sensitivity is the probability the machine learner successfully detects when a true intrusion occurs. what is this probability for ml1? (three significant digits) the specificity is the probability the machine learner successfully detects the user as valid when a valid user is using the system. what is this probability for ml2? (three significant digits)
The probability of ml1 is 0.890, or 89.0% the specificity or probability of ml2 is 0.993, or 99.3% to three significant digits
What is the probability for m|1To find the sensitivity of ml1, we need to look at the true positive rate, which is the probability of the machine learner predicting an intrusion given that an intrusion actually occurred. This can be found from the table as:
sensitivity = P(ml1 predicts intrusion | intrusion) = 0.0129/(0.0129 + 0.0016) = 0.890
Therefore, the probability of ml1 is 0.890, or 89.0% (to three significant digits).
To find the probability of ml2, we need to look at the true negative rate, which is the probability of the machine learner predicting a valid user given that a valid user is actually using the system. This can be found from the table as:
specificity = P(ml2 predicts valid user | valid user) = 0.985/(0.985 + 0.007) = 0.993
Therefore, the specificity of ml2 is 0.993, or 99.3% (to three significant digits).
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For the point (r,θ), r is the _____ from O to P and θ is the _____ counterclockwise from the polar axis to the line segment ¯¯¯¯¯¯¯¯OP.
In the point (r, θ), r signifies the distance from O to P, while θ represents the angle counterclockwise from the polar axis to the line segment ¯¯¯¯¯¯¯¯OP.
For the point (r, θ), r is the distance from O to P, and θ is the angle counterclockwise from the polar axis to the line segment ¯¯¯¯¯¯¯¯OP.
In polar coordinates, a point is represented by its distance (r) from the origin (O) and the angle (θ) it forms with the positive x-axis. The distance (r) denotes the length of the line segment connecting the origin to the point P. It indicates how far the point is from the origin. The angle (θ) represents the rotation or angular position of the line segment ¯¯¯¯¯¯¯¯OP from the polar axis (positive x-axis) in a counterclockwise direction. It determines the direction in which the point is located relative to the polar axis.
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Find the value of the variables
Answer:
x = 3y
y + x = 4y = 180
y = 45
x = 135
find an equation of the tangent line to the curve y=8^x at the point (2,64) ( 2 , 64 ) .
The equation of the tangent line to the curve is y = 16ln(8)x + 32 - 64ln(8).
How to find the equation of the tangent line to the curve?To find the equation of the tangent line to the curve \(y=8^x\)at the point (2,64), we need to find the slope of the tangent line at that point.
The derivative of\(y=8^x\) is \(y'=ln(8)8^x\). So at x=2,\(y'=ln(8)8^2=16ln(8)\).
Therefore, the slope of the tangent line at (2,64) is 16ln(8).
Now we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form is y-y1=m(x-x1), where (x1,y1) is the point on the line and m is the slope of the line.
Using the point (2,64) and the slope we just found, we get:
y-64 = 16ln(8)(x-2)
Simplifying, we get:
y = 16ln(8)x + 32 - 64ln(8)
So the equation of the tangent line to the curve \(y=8^x\) at the point (2,64) is y = 16ln(8)x + 32 - 64ln(8).
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The Cartesian components of vectors
A
and
B
are given as: Ax=7.6,Bx=−5.1,Ay=−9.2 and By=−6.8 Calculate the magnitude of the vector
B
−
A
?
To find the magnitude of the vector B - A, we need to subtract the corresponding components of vector A from vector B and then calculate the magnitude of the resulting vector. the magnitude of vector B - A is approximately 12.93.
Vector B - A can be obtained by subtracting the x-component and y-component of vector A from the x-component and y-component of vector B, respectively.
The x-component of B - A is calculated as Bx - Ax, which is equal to (-5.1) - 7.6 = -12.7.
Similarly, the y-component of B - A is By - Ay, which is equal to (-6.8) - (-9.2) = 2.4.
Now, we have the x-component and y-component of vector B - A. To find the magnitude of this vector, we use the Pythagorean theorem:
Magnitude = sqrt((x-component)^2 + (y-component)^2) = sqrt((-12.7)^2 + (2.4)^2) = sqrt(161.29 + 5.76) = sqrt(167.05) ≈ 12.93.
Therefore, the magnitude of vector B - A is approximately 12.93.
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A company sells sports drinks for $2.00 each. The company pays $0.75 for each drink and $10 per week
for a permit to sell the drinks. What is the least number of drinks the company must sell each week to make
a profit?
Finding the side length of a cube from its Volume in liters A technical machinist is asked to build a cubical steel tank that will hold 275 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.001 m. X 5 ?
The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.
The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.
Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):
275 liters / 1000 = 0.275 cubic meters
Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:
∛(0.275) ≈ 0.640
Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.
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Please help please...
Answer:
(2x + 5)
Step-by-step explanation:
2(x + 1) + 6x = 4(2x + 5) + 2
2x + 2 + 6x = 8x + 20 + 2
8x + 2 = 8x + 22
Because both sides are 8x it will have no solution
Second one is "all of these are correct"
Translate this phrase into an algebraic expression.
the quotient of 4 and a number increased by 10.
Does anypne know it?
You construct a tangent to circle O at point X on the circle, as shown below. What do you expect to be the measure of ∠OXY?
Answer: 90 Degrees :)
Step-by-step explanation:
Ur Welcome ;)
A farmer has 30 boxes of eggs.
There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form.
The ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.
How to obtain real measurements from the ratio of two measurements?Suppose the real measurements were "a" and "b". Then their ratio will be formed as;
\(\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}\)
where is a common factor (not 1)? This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly canceled from both the numerator and the denominator.
Thus, a = px, b = qx
We have given that farmer 30 boxes of eggs. and there are 6 eggs in each box.
Thus, we know that the total number of eggs is the same as the number of eggs given in 30 boxes.
Hence, the ratio will be;
2: 30,
then divide both sides by 2 ;
1: 15
Therefore, the ratio of the number of eggs in three boxes to the total number of eggs is 1: 15 in its simplest terms.
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2. In right triangle RST with right angle S the m4R = 24°. What is the
measure of T?*
о
24°
O 56°
0 66°
O 116°
Sum of the interior angles of any triangle equal 180° ;
So :
90° + 24° + T = 180°
114° + T = 180°
subtract both sides 114
T = 180° - 114°
T = 66°
_________________________________
And we're done....
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19-6n is greater than or equal to -8(6n+8-1)
Answer:
13n is greater than or equal to -21n
When a piece of aluminum is placed in a 25 mL graduated cylinder that contains 10.0 mL of water, the water level rises to 13.5mL. What is the mass of the aluminum if the density is 2.69g/mL
The mass of the aluminum can be calculated using the change in volume and the density. the mass of the aluminum is approximately 9.415 grams.
The change in volume when the aluminum is added to the graduated cylinder is equal to the volume of the aluminum. The change in volume is obtained by subtracting the initial volume (10.0 mL) from the final volume (13.5 mL), resulting in 3.5 mL.
Since the density of aluminum is given as 2.69 g/mL, we can use this information to calculate the mass of the aluminum. The density of a substance is defined as the mass per unit volume. Therefore, we can multiply the density by the volume to obtain the mass.
Using the given density of 2.69 g/mL and the volume of 3.5 mL, the mass of the aluminum can be calculated as follows:
Mass = Density x Volume = 2.69 g/mL x 3.5 mL = 9.415 g
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helpp me fast thank u pleasee
The value of x from the given equations is 0.6.
The given equations are y=4x and y=-x+3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Here, 4x=-x+3
⇒ 4x+x=3
⇒ 5x=3
⇒ x=3/5
⇒ x=0.6
Hence, the value of x from the given equations is 0.6.
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Consider the following model:
yhat =2.1+1.0x²
The prediction of y is yhat. What is the estimated marginal effect of x on y when x=1.3?
________
Using the following model and corresponding parameter estimates, predict the (approximate) value of y variable when x=2 :
lny=β₁+β₂x²+u
The parameter estimates are β₁=2 and β₂=1 [Parameter estimates are given in bold font]
a. 2
b. 403.4
c. 103,4
d. 6
The value of u is not provided, we cannot determine the exact value of y. None of the given options (a, b, c, d) can be chosen as the approximate value of y.
For the first question, you are given the model yhat = 2.1 + 1.0x^2 and you want to find the estimated marginal effect of x on y when x = 1.3. To find the estimated marginal effect, you need to take the derivative of yhat with respect to x. In this case, the derivative would be 2.0x.
Now, substitute x = 1.3 into the derivative:
2.0(1.3) = 2.6.
Therefore, the estimated marginal effect of x on y when x = 1.3 is 2.6.
For the second question, you are given the model \(lny = β₁ + β₂x^2 + u\), with parameter estimates
β₁ = 2 and
β₂ = 1.
To predict the value of y when x = 2, substitute the given values into the model:
\(lny = 2 + 1(2^2) + u\)
lny = 2 + 1(4) + u
lny = 2 + 4 + u
lny = 6 + u
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when ratios have the same units we call that ratio _____________
Therefore, When ratios have the same units, we call that ratio a unit ratio.
When ratios have the same units, we call that ratio a unit ratio. An explanation of what is meant by the term ratio would be helpful. A ratio compares the relative sizes of two or more quantities. If the numbers being compared have the same units, then it is called a unit ratio. Unit ratios are ratios that relate to each other in terms of the same measurement unit. They are also sometimes known as unit rates or unit fractions. They are frequently used to compare the relative size of one quantity to another when they are measured in the same units. For example, when we say that there are two apples for every five oranges, we are expressing a ratio between apples and oranges. However, when we say that there are two apples per five oranges, we are using a unit ratio.
Therefore, When ratios have the same units, we call that ratio a unit ratio.
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Melanie’s dog is 3 years older than her cat. Let x represent the age of the cat and y the age of the dog. Express this relationship in an equation, a table, and a graph
Answer:
equation: x+3=y
Step-by-step explanation:
If the dog is 3 years older, then you take the cat + 3 to = the dogs age
The given information Melanie’s dog is 3 years older than her cat in the form of the equation x+3=y.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Melanie’s dog is 3 years older than her cat. Let x represent the age of the cat and y the age of the dog.
If the dog is 3 years older, then you take the cat + 3 to = the dog's age. The expression will be written as below:-
x + 3 = y
y - x = 3
Therefore, the given information Melanie’s dog is 3 years older than her cat in the form of the equation x+3=y.
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Han is multiplying 10x^4 by 5x^3 and gets 5x^7. He says that 0.5x^3 is not a polynomial because 0.5 is not an integer. What is the error in Han’s thinking? Explain your reasoning.
The result of the product with \(5x^7\), we can see that Han neglected the zero taking 50 the same as 5 which is wrong
Given the polynomial functions
r(x) = \(10x^4\)
t(x) = \(5x^3\)
Taking the product of both functions:
P(x) = r(x) * t(x)
P(x)= \(10x^4\times 5x^3\)
P(x) = \((10\times 5) \times(x^4\times x^3) = 50x^7\)
Comparing the result of the product with \(5x^7\), we can see that Han neglected the zero taking 50 the same as 5 which is wrong.
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