The solution to the given equation, 2 tan²x + sec²x - 2 = 0, is x = 1/3 + k, where k is any integer. This option (a) satisfies the equation and is expressed in terms of the given variable x. Therefore, option (a) is the correct answer.
To understand why option (a) is the solution, let's analyze the equation. We can rewrite the equation as:
2 tan²x + sec²x - 2 = 0.
Using the trigonometric identity, sec²x = 1 + tan²x, we can substitute sec²x with 1 + tan²x:
2 tan²x + (1 + tan²x) - 2 = 0.
Simplifying further, we have:
3 tan²x - 1 = 0.
Rearranging the equation, we get:
tan²x = 1/3.
Taking the square root of both sides, we find:
tan x = ± √(1/3).
The solutions for x can be found by taking the inverse tangent (arctan) of ± √(1/3). By evaluating arctan(± √(1/3)), we find that the solutions are:
x = 1/3 + kπ, where k is any integer.
This aligns with option (a) in the given answer choices. Therefore, the correct solution is x = 1/3 + k, where k is any integer.
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Move point C and observe how the
angle measures change.
When AC changes,
m_ABC and mŁADC
vand are
to each other.
Answer:
[tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] will change
[tex]\angle ABC[/tex] equal [tex]\angle ADC[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
What happens when AC changes
(a) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are formed from points A and C. So, a change in AC will result to a change in the measures of [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex].
(b) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are in the same segment, meaning that they will always have the same measure
tory buys a bag of cat food that has a mass of 5 kilograms. torys cat has a mass of 4 kilograms, 575 grams,. what is the difference in mass, in grams, between the bag of food and torys cat?
Answer:
5
Step-by-step explanation:
Answer 424
Step-by-step explanation: you have to change 5 kg to 5,000 grams. then you have to change 4 kg to 4,000 grams. then add 575 to 4,000. then subtract 5,000 by 4,575now your answer is 424Let y+3=xy-6x². Use implicit differentiation to find y' or dy dx
the derivative of y with respect to x, or dy/dx, for the given equation is y' = (y - 12x) / (1 - x).
We start by differentiating both sides of the equation with respect to x.
For the left-hand side, the derivative of y + 3 with respect to x is simply dy/dx, or y'.
For the right-hand side, we need to apply the product and chain rules.
Differentiating xy with respect to x gives us x(dy/dx) + y.
Differentiating -6x² with respect to x gives us -12x.
Putting it all together, we have y' + 0 = x(dy/dx) + y - 12x.
Rearranging the equation, we get y' = (y - 12x) / (1 - x).
Therefore, the derivative of y with respect to x, or dy/dx, for the given equation is y' = (y - 12x) / (1 - x).
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Nia increased her class average by 3%. She now has a 92% in her math class.
Nia's original class average was 89%. After increasing it by 3%, she now has a 92% in her math class.
1. Let's assume Nia's original class average was X.
2. She increased her class average by 3%, which can be represented as X + (3/100)X.
3. According to the question, X + (3/100)X = 92.
4. Simplifying the equation, we have (103/100)X = 92.
5. To find X, we divide both sides of the equation by (103/100): X = (92 * 100) / 103.
6. Calculating the value, X ≈ 89.32.
7. Therefore, Nia's original class average was approximately 89.32%.
8. After increasing it by 3%, her new class average is 89.32% + (3/100) * 89.32% ≈ 92%.
Note: The values have been rounded for simplicity.
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When rolling a die, calculate the probability as a fraction of rolling a 3. The probability is
Answer:
1/6
Step-by-step explanation:
there is only one side in which there is 3 out of total six sides so 1/6
If money in a savings account earned 8% interest per annum, how much nterest would be earned on $150.00 over three years?
Answer:
$36
Step-by-step explanation:
Given :
Interest rate, r = 8% = 0.08
Principal, P = 150
Time, t = 3 years
Simple interest = (principal * rate * time)
Simple interest = (150 * 0.08 * 3)
Simple interest = $36
800 jerseys 6 medium jerseys what percent of the jerseys is medium?
The percent of the jerseys :
6 : 800 = 0,75%
Please answer this is my last few points
Answer:
first is some and second is all
Step-by-step explanation:
PLEASE GIVE BRAINLIEST!!!!!!!!!!
Answer:
1. All
2. Some
Step-by-step explanation:
I belive this awnser is correct
a parallelogram has one angle that measures 65 what are the other three angles
Answer:
Step-by-step explanation:
65,115,115
I need help with this math promblem will anybody help me
Answer:
d = 83
Step-by-step explanation:
Answer:
d=83°
Step-by-step explanation:
the sum of the inner angles is equal to 360°
so
127+67+d+d=360
194+2d=360
2d=166
d=83°
Let W = {a + 2x + bx2 € Pz: a, b E R} with the standard operations in P2. Which of the following statements is true? W is not a subspace of P2 because 0 € W. W is a subspace of P2. a The above is true The above is true None of the mentioned O 1+xEW
The statement "W is a subspace of P2" is true, as W satisfies the conditions for being a subspace: closure under addition and scalar multiplication, and containing the zero vector.
The statement "W is a subspace of P2" is true.
To show that W is a subspace, we need to verify the three conditions for subspace:
W is closed under addition: For any two polynomials p(x) = a + 2x + bx^2 and q(x) = c + 2x + dx^2 in W, their sum p(x) + q(x) = (a + c) + 4x + (b + d)x^2 is also in W. Therefore, W is closed under addition.
W is closed under scalar multiplication: For any polynomial p(x) = a + 2x + bx^2 in W and any scalar k, the scalar multiple kp(x) = ka + 2kx + kbx^2 is also in W. Therefore, W is closed under scalar multiplication.
W contains the zero vector: The zero polynomial 0 = 0 + 0x + 0x^2 is in W since a = b = 0. Therefore, W contains the zero vector.
Since W satisfies all three conditions for subspace, it is indeed a subspace of P2.
Hence, the statement "W is a subspace of P2" is true.
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Ben rolls a number cube 50 times. He records the result of each roll in the table below. RESULTS OF ROLLING NUMBER CUBE Outcome 1 2 3 4 5 6 Frequency 7 6 5 11 10 11 Based on the data, which statement is true? Ben will roll an even number about 250 times if the number cube is rolled 500 times. Ben will roll an even number about 220 times if the number cube is rolled 500 times. Ben will roll an even number about 700 times if the number cube is rolled 1,000 times. Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.
Answer:Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.
Step-by-step explanation:
Convert the time. Enter your answers in the boxes.
324 minutes =
hours,
minutes
Answer:
5 hours and 24 minutes
Step-by-step explanation:
sorry if im wrong
Answer:
5.4 hours
Step-by-step explanation:
I'm not 100 percent sure
hope this helped ;)
Let D be the region enclosed by the two paraboloids z = 3x2 + + y2 z = 16 – x2 Then the projection of D on the xy-plane is: 2 *-* = 1 = 1 16 = 1 4 16 O This option O This option x None of these 16 4
The projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2.
To find the projection of the region D onto the xy-plane, we need to determine the intersection curve of the two paraboloids in the xyz-space. Setting the equations of the paraboloids equal to each other, we have:
3x^2 + y^2 = 16 - x^2.
Combining like terms, we get:
4x^2 + y^2 = 16.
This equation represents an ellipse in the xy-plane. To visualize the projection, let's rewrite the equation in terms of standard form:
(x^2)/4 + (y^2)/16 = 1.
Comparing this equation to the standard equation of an ellipse, (x^2)/(a^2) + (y^2)/(b^2) = 1, we can see that the major axis of the ellipse is along the y-axis, with a length of 4, and the minor axis is along the x-axis, with a length of 2.
Therefore, the projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2. The shape of the ellipse will have its major axis along the y-axis and its minor axis along the x-axis.
In summary, the projection of the region D onto the xy-plane is an ellipse centered at the origin, with a major axis length of 4 and a minor axis length of 2.
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Hello. Please help if you can.
x+10=?
I NEED HELP WE JUST STARTED THIS LESSON
Answer:
I need more info to answer that question.
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
The X is invisible and doesn't have a value causing the answer to still be 10.
Five students wrote a test and the scores were as follows:5,3,7,9 and x. If their total score was 30 find the value of x
Answer:
The value of X is 6.
Step-by-step explanation:
5 + 3 + 7 + 9 = 24
30 - 24 = 6
X = 6
The difference is 6.
help me with the whole problem plssss i do anything plss.
Answer:
8 people can go
Step-by-step explanation:
Which of the following functions are of exponential order c? Find c, if the answer is yes. (a) y(t) = 5t? + 24 +1. (b) y(t) = sin(31) (c) y(t) = 42 y(t) = 93 (e) y(t) 12 if t = 3 gift 3 (1) y(t) = coste
(a) Not of exponential order.
(b) Not of exponential order.
(c) Exponential order with c = 2.
(d) Not of exponential order.
(e) Not of exponential order.
To determine if a function is of exponential order, we need to check if there exist positive constants M and c such that |y(t)| ≤ M[tex]e^{ct}[/tex] for all t ≥ t₀, where t0 is some starting point.
Let's analyze each function:
(a) y(t) = 5t² + 24 + 1
This function is not of exponential order since it contains a quadratic term (t²) and does not satisfy the exponential order condition.
(b) y(t) = sin(3t)
The sine function is periodic and oscillates between -1 and 1. It is not bounded by an exponential function. Therefore, it is not of exponential order.
(c) y(t) = 4[tex]e^{2t}[/tex]
The exponential function [tex]e^{2t}[/tex] grows exponentially as t increases. The constant multiplier 4 does not affect the exponential growth. Therefore, this function is of exponential order with c = 2.
(d) y(t) = [tex]e^{t^{2} }[/tex]
The exponent t² grows faster than any exponential function with a constant base. Therefore, this function is not of exponential order.
(e) y(t) = cost [tex]e^{3t}[/tex]
The exponential function [tex]e^{3t}[/tex] grows exponentially as t increases. However, the cosine function oscillates between -1 and 1, which prevents the overall function from being bounded by an exponential function. Therefore, it is not of exponential order.
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What is the image of (-9,9) after a dilation by a scale factor of 2 centered at the
origin?
Answer:
It would be C since a scale factor of 2 makes the original A coordinate of (3,3) times 2 therefore the new coordinates being (6,6)
Step-by-step explanation:
-7 = 2x - 7
A. 0
B. 4
C. Infinite Solutions
D. No solutions
Answer:
A
Step-by-step explanation:
the variable is how many times the two will be multiplied, so 2 times 0 equals 0, there by making the problem. -7= - 7
Answer:
that will be A. 0
Step-by-step explanation:
first, i flip the equation
2x - 7= -7
next, i add both side by 7
2x−7+7=−7+7
2x=0
and finally, you divided by 2
2x/2 = 0/2
you get x = 0
complete the proof given: AB x BE =CB x BD prove: triangle ABC triangle DBE
The complete proofs with all the reasons and statements; have been enumerated below
Triangle Proofs
The image showing the given triangle is missing and so i have attached it.
From the attached image, we can deduce that;
Statement 1; AB * BE = CB * BD
Reason 1; Given
Statement 2; CB/BE = AB/BD
Reason 2; Property of Cross Multiplication
Statement 3; ∠ABC ≅ ∠DBE
Reason 3; Vertical Angles
Statement 4; ΔABC ~ ΔDBE
Reason 4; SAS property of similarity
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Please help me, I’m struggling
Answer:
28[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
[tex]\sqrt{96}[/tex]
= [tex]\sqrt{16(6)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{6}[/tex]
= 4[tex]\sqrt{6}[/tex]
Then
7[tex]\sqrt{96}[/tex]
= 7 × 4[tex]\sqrt{6}[/tex]
= 28[tex]\sqrt{6}[/tex]
Just find the figure of the rectangle plss
Answer:
x= 21
y= 3
z= 21
Step-by-step explanation:
Let the center be O,
=> Triangle AOD is an Isosceles triangle so AO≅DO, "21 = x"
=> Line AC is divided in two equal parts by the center so if AO= 21 then
7y = 21, and thus "y = 3"
=> BOC is also an Isosceles triangle so CO ≅ BO, if CO = 21 (7y → 7*3) then so will be BO. Therefore "z = 21"
(a) what is the effect on the period of a pendulum if you double its length?
If we double the length of the pendulum, the period of the pendulum will be approximately 1.4 times longer than it was before. This relationship between the length and period of a pendulum is very important, as it allows us to calculate the length of a pendulum needed to produce a desired period. This relationship is also used in many applications, such as clocks and metronomes.
The period of a pendulum is the time it takes to swing back and forth through one complete cycle. The period of a pendulum is affected by the length of the pendulum, the acceleration due to gravity, and the amplitude of the swing. If the length of a pendulum is doubled, the period of the pendulum will also double. The reason for this is that the period of a pendulum is directly proportional to the square root of its length.
This means that if the length of the pendulum is increased by a factor of 2, the period of the pendulum will increase by a factor of sqrt(2).
Mathematically, this can be expressed as: T = 2π * sqrt(L/g).
Where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
If we double the length of the pendulum (L), the equation becomes T = 2π * sqrt(2L/g).
Taking the ratio of the new period to the original period, we get: T_new/T_old = sqrt(2).
Therefore if we double the length of the pendulum, the period of the pendulum will be approximately 1.4 times longer than it was before. This relationship between the length and period of a pendulum is very important, as it allows us to calculate the length of a pendulum needed to produce a desired period. This relationship is also used in many applications, such as clocks and metronomes.
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Suppose a regression was run between y and one x variable. The coefficient of the x variable (slope coefficient) was -0.76. The associated standard error of the slope coefficient was 0.04, and p value of the slope coefficient was 0. The t stat of the slope coefficient is: ________
The t-statistic of the slope coefficient is -19 is the answer.
Suppose a regression was run between y and one x variable.
The coefficient of the x variable (slope coefficient) was -0.76.
The associated standard error of the slope coefficient was 0.04, and p value of the slope coefficient was 0.
The t stat of the slope coefficient is -19.
To find the t-statistic value, divide the slope coefficient by the standard error.
This is given as t = slope / SE.
We have the values of the slope and the SE in the problem.
Substitute these values to get the t-statistic.t = -0.76 / 0.04 = -19
From this calculation, we can see that the t-statistic of the slope coefficient is -19.
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HELP PLEASEE
I’m stuck
Answer:
:-):-)
Step-by-step explanation:
1) p<1000
2)p>500
3)By combining the above two, we get: 500<p<1000
Andre will agree as he thinks that the no. of paper clips in the box is less than 1000. But lin will not as she thinks that the no. of clips is more than 500.
4)This time, they both will agree as the no. of paper clips is more than 500 but less than 1000.
Evaluate the work done between point 1 and point 2 for the conservative field F.
F = 6x i + 6y j + 6z k; P 1(4, 3, 5) , P 2(5, 6, 7)
a)W = - 180
b)W = 480
c)W = 0
d)W = 180
The correct answer is option (c) W = 0.
Given information :F = 6xi + 6yj + 6zk; P1(4, 3, 5), P2(5, 6, 7)The formula for work done by the conservative force is given by: W = U(P2) - U(P1)Where U(P) is the potential energy at point P. The force is conservative. Hence, work done is independent of path and is equal to the difference in potential energy between points 1 and 2.To find the potential energy U at any point, we use the formula: U(x, y, z) = - ∫F.dr where F is the force, and dr is the infinitesimal displacement vector.
To find the potential difference between two points, we integrate the formula: W = - ∫F.dr over a path between those two points, P1 and P2.Now we will find the potential energy at points 1 and 2.∴U(P1) = -∫F.drbetween the limits (4,3,5) and (5,6,7)Let us take the path from P1 to P2 along the straight line. Then the position vector of the path is:r = (5 - 4) i + (6 - 3) j + (7 - 5) k = i + 3j + 2k.dr = dx i + dy j + dz k= i dx + j dy + k dz = i dt + 3j dt + 2k dt = (i + 3j + 2k) dt∴∫F.dr= ∫6x i . (i + 3j + 2k) dt + ∫6y j . (i + 3j + 2k) dt + ∫6z k . (i + 3j + 2k) dt= ∫6x dt + 3 * 6y dt + 2 * 6z dt= (6x + 18y + 12z) |_P1^P2= (6 * 5 + 18 * 6 + 12 * 7) - (6 * 4 + 18 * 3 + 12 * 5)= 30 + 108 + 84 - 24 - 54 - 60= 84Thus, U(P2) - U(P1) = 0 - 84 = -84. Hence, work done = -(-84) = 84Option (d) W = 180 is incorrect as the value of work done is 84.
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What is the factored form of the expressions 4x2 - 25?
Answer:
Explanation: Realize that 4x2−25 is a difference of squares. Differences of squares, such as a2−b2 , can be factored into (a+b)(a−b) . Since 4x2=(2x)2 and 25=(5)2 , we can say that 4x2−25=(2x+5)(2x−5)
Step-by-step explanation:
Answer:
(2x + 5)(2x - 5)
Step-by-step explanation:
a² - b² = (a + b)(a - b)
4x² = 2²x²= (2x)²
25= 5* 5 = 5²
4x² - 25 = (2x)² - 5² {a= 2x ; b = 5}
= (2x + 5)(2x - 5)
2^2 y^-6
-------------
8^1 z^0 x^-7
How do you solve this?