By means of trigonometric functions and trigonometric formulas, the trigonometric equation sec α · (1 - cos² 2α) is equivalent to 4 · cos α - 4 · cos³ α.
How to simplify a trigonometric equation
In this problem we find the case of a trigonometric equation that must be simplified by definitions of trigonometric functions and trigonometric formulas. First, write the trigonometric equation:
sec α · (1 - cos² 2α)
Second, use the fundamental trigonometric formula:
sec α · sin² 2α
Third, use the definition of secant and the formula for the sine of the double angle:
(1 / cos α) · (2 · sin α · cos α)²
4 · sin² α · cos α
Fourth, use the fundamental trigonometric formula:
4 · (1 - cos² α) · cos α
4 · cos α - 4 · cos³ α
None of the options given are equivalent to the trigonometric equation.
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Calvin drew a rectangle with one side greater than 10 but
less than 20. He multiplies to find its area.
Calvin's work: 8x3+8 x 10 = 104
Find the dimensions of Calvin's rectangle.
Explain how you know that your answer is correct.
Please help!!!!
Step-by-step explanation:
LET WIDTH= X
LENGTH= X+5
PERIMETER= 2(L+B)= 170
2(X+X+5)= 170
2X+5= 85
2X= 80
X= 40
WIDTH= 40
LENGTH= 45
The length of a rectangle is five more than the width. The perimeter is 170. What is the length and width? Write the equation and solve.
what is the answer for
y=x−4y=−x+6
Answer: Your answers are Y = 1 and X = 5
Step-by-step explanation:
y=x-4 y=-x+6 Substitute x - 4 for y in y=-x+6 x-4=-x+6Add X on each side x-4+x =-x+6+x 2x - 4 = 6Add 4 on each side 2x-4+4 = 6+4 2x = 10Divide by 2 on each side 2x ÷ 2 = 10 ÷ 2 x = 5 Now we have X To find Y we substitute 5 for x in y= x-4 y = 5 - 4 y = 1 so you answers would be Y= 1 and x = 5 i hoped this helped:)
Write a system of equations to describe the situation below, solve using substitution, and fill
in the blanks.
Nina is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $12,
and her grandmother has pledged $1 per mile. If Nina walks a certain distance, the two
donors will end up owing the same amount. How much will each donor owe? What is that
distance?
Nina's mother and grandmother will each owe $
if she walks
miles.
Nina's mother and grandmother will each owe $12 if she walks 12 miles
What is an equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
According to the question we get to know
mother = 12
Grandmother = x
12 = x
x = 12
$ 12 , she walks 12 miles
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$1450 is invested at 6.5 % compounded continuously. How long will it take for the balance to reach $2900?
Answer:
Step-by-step explanation:
94.25 days
Tell wether the data in the table can be modeled by a linear equation. Explain.
If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.
Answer:
yes
By dividing the difference between each two corresponding data values, we get a constant rate of change.
y = 0.2x + 1.2
Step-by-step explanation:
1. Find the rate of change between each pair of data values in the table and compare to see if they are equal:
(1.4-1.2)/(1-0) = 0.2/1 = 0.2
(1.6-1.4)/(2-1) = 0.2/1 = 0.2
(2-1.6)/(4-2) = 0.4/2 = 0.2
2. Substitute the numbers found in step 1 for m, and the y-value in the data pair (0,1.2) as b in the equation y = mx + b: y = 0.2x + 1.2
One coral reef is located 19 feet below sea level. Another is located 26 feet below sea level. What is the difference in the depths of the two reefs?
help asap 45 points
Do this, for example, 3v x 2t =6vt
Algebraic expressions are mathematical expressions that combine a mathematical constant and variables.
What types of algebraic expressions are used in the multiplication of algebraic expressions?
The four basic mathematical operators are addition (+), subtraction (-), multiplication (), and division. Algebraic expressions are mathematical expressions that combine a mathematical constant and variables connected by one or more of the four basic mathematical operations (). Algebraic expressions include things like 4 x + 8, x - y, etc. The numbers 4 and 8 serve as the expression's given constants in the example 4 x + 8, while the word x serves as the equation's variable.
The process of multiplying two provided expressions made up of variables and constants is known as the multiplication of algebraic expressions. An expression that uses integer constants and variables together is called an algebraic expression.
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describe the transformations from the graph f(x)=|x| to the graph d(x) = -|x-3| + 5
The function d(x) = - |x - 3| + 5 is the result of using an horizontal translation, reflection about the x-axis and vertical translation on the function f(x) = |x|.
What kind of transformations are used to transform of the equation of a given graph?
In this question we have the definition of a function (f(x)) and its image (d(x)), the latter is the result of three rigid transformations:
Horizontal translation
f'(x) = f(x - 3)
Reflection about the x-axis
f''(x) = - f'(x)
Vertical translation
d(x) = f''(x) + 5
If we know that f(x) = |x|, then the series of rigid transformations is shown below:
Horizontal translation
f'(x) = |x - 3|
Reflection about the x-axis
f''(x) = - |x - 3|
Vertical translation
d(x) = - |x - 3| + 5
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How do you solve -y +28 +y^2 =2y +2y^2 for y?
We are given the following:
Solve for y.
[tex]-y+28+y^2=2y+2y^2[/tex]
This being said, lets begin.
~~~~~~~~~~~~~~~~~~~~~~~
1. First, move [tex]2y^2[/tex] to the left side.
[tex]-y+28-y^2=2y[/tex]
2. Move [tex]2y[/tex] to the left side.
[tex]-y^2-3y+28=0[/tex]
3. Solve with the quadratic formula.
[tex]y_{1,2} = \frac{-(-3) -+ \sqrt{(-3)^2-4(-1)*28} }{2(-1)}[/tex]
4. [tex]\sqrt{(-3)^2-4(-1)*28}=11[/tex]
[tex]y_{1,2} =\frac{-(3)-+11}{2(-1)}[/tex]
5. Separate the solutions.
[tex]y=\frac{-(-3)+11}{2(-1)} , y_{2} =\frac{-(-3)-11}{2(-1)}[/tex]
6.
[tex]y=\frac{-(-3)+11}{2(-1)}[/tex] [tex]=-7[/tex] ← First Solution
7.
[tex]y=\frac{-(-3)-11}{2(-1)} =4[/tex] ←Second Solution
Final Solution:
[tex]y=-7,y=4[/tex]
Hope this helps!
which figure comes next in a pattern?
Answer:
square
Step-by-step explanation:
need more information
Kyle ran the width of a field, a distance of 35 meters. Then he ran the length of the field, a distance of 84 meters. Finally, he ran diagonally across it to get back to his starting point. How far did Kyle run?
The total distance travelled by Kyle is 210 m.
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
The given length of the field is 84 m.
And, the width is 35 m.
Now, the diagonal of the field can be calculated using Pythagoras theorem as below,
Diagonal = √((84)² +(35)²)
= 91
Then, the total length is found by summing the length, width and the diagonal as below,
= 84 + 35 + 91
= 210
Hence, Kyle run for the distance of 210 m.
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Which confidence level would produce the widest interval when estimating
the mean of a population based on the mean and standard deviation of a
sample of that population?
Answer:
99%
Step-by-step explanation:
Let X be a continuous random variable with the pdf given by f(x)= ax2 for 0 < x ≤ 3. Determine the value of constant 'a' correct to 2 decimal places.
The value of the constant a in f(x) = ax² such that 0 < x ≤ 3 is 0.11
How to determine the value of the constant a?The probability density function is given as
f(x) = ax²
Such that
0 < x ≤ 3
To determine the value of the constant a, we make use of the following equation
[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]
So, we have:
[tex]\int\limits^3_0 {ax^2} \, dx = 1[/tex]
Factor out the constant
[tex]a\int\limits^3_0 {x^2} \, dx = 1[/tex]
Differentiate the equation
So, we have the following representation
[tex]a\frac{x^3}3 |^3_0 = 1[/tex]
Expand the equation
a[3³ - 0³]/3 = 1
Evaluate the difference
a[3³]/3 = 1
Evaluate the quotient
9a = 1
Divide both sides by 9
a = 0.11
Hence, the variable a is 0.11
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Write a linear function for the graph, and state and interpret the slope and y-intercept for the given scenario:
Bamboo grows very quickly. Use the information in the graph to write an equation that models the height (y) at time (x).
The linear function for the given graph is y = x + 20.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function. It has one independent variable and one dependent variable. For slope (m) and y-intercept (b) form, the equation is given by:
y = mx + b
From the graph,
The coordinates of the given graph are (0,20) and (20,40)
Then, slope (m) = (40-20)/(20-0) = 20/20 = 1
and y-intercept (b) = 20
So, the equation will be y = 1x + 20
Hence, the linear function for the given graph is y = x + 20.
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What is the common ratio and the general term equation, a, of the geometric sequence?
The common ratio and the general term equation, a, of the geometric sequence is A. r = 1/2 , an = 16(1/2)^(n - 1).
What is a geometric sequence?A geometric sequence simply means the sequence of non zero numbers whereby the term after the first is simony found by multiplying the previous number by a common ratio
Based on the information, the common ratio will be:
= Second term / First term
= -8 / -16
= 1/2
The nth term will then be 16(1/2)^(n - 1).
The correct option is A.
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explain what an exponential function is. please do not palgraize
As below it is described what is exponential function with some examples.
What is Function ?A function is simply a “mapping” between 2 sets of objects (usually numbers but they could really be anything) such that, every object in the first set (the domain) is mapped to a single object in the second set. What you usually see as examples of functions (e.g. f(x)=x²) actually define the relationship between the sets. This is what I mean by “mapping”. Often, we don’t explicitly state what the sets are, because it’s understood from the context, but technically, it’s not a function unless we state the sets. E.g., instead of saying f(x)=x², we should say f:x↦x²|x∈ℂ (pronounced “f maps x to x² such that x is a complex number”), meaning that we map the complex numbers to themselves using the rule that we square each input. You can define it differently, so that, for example, we map complex to reals. However, and this is important, that would be a different function, even though the “rule” for turning inputs into outputs is the same.
Exponential Function:
Exponential functions are functions of the form f(x) = b^x where b is a constant.
The real mathematical importance of exponential functions is in their being proportional to their derivatives meaning the bigger x is, the steeper the slope of the function. This means they grow extremely fast: exponentially fast.
A common example of exponential growth is a bacterial population. Since bacteria reproduce rapidly by mitosis, for every bacterium in a culture, there will, before long be two bacteria. Thus, if I have 10 bacteria to start, one minute later I will have 20, and in another minute, each of those twenty will have reproduced and I will have 40; one minute later the same will have happened again and before long, the culture will be overrun with bacteria. The more bacteria there are, the more bacteria there are to make even more bacteria the next minute.
All exponential functions are proportional to their derivatives, but the function f(x) = e^x (where e = 2.718281828459…) is actually equal to its derivative meaning the y value of the function at a particular x value is equal to the slope of the curve at that same x value. Thus when dealing with exponential functions in calculus, e becomes a very natural number to use as a base. This is why e is such a big deal and why teachers try to introduce the number early on in Algebra 2, even though it doesn’t have much use at that point in one’s mathematical education.
When plotting an exponential curve by hand, one ought to simply pick whole number x values and multiply the base by itself an x number of times to calculate the corresponding y value. This will give a rough plot of the graph of the curve, although a calculator is requires to plot the points not on whole number x values. The curve of simple exponential functions is always increasing and concave up, or vice versa for b^-x. For a positive exponential function like f(x) = e^x, as x approaches ∞, f(x) approaches ∞, and as x approaches -∞, f(x) approaches 0. The curve has no absolute maximum or minimum value and has a horizontal asymptote at y = 0.
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If I work from 4:30pm to 9:00pm how many hours did I work?
Answer:
4 hours and 30 minutes.
Step-by-step explanation:
You count, 4, 5, 6, 7, 8, then you take the 30 from 4:30 and add another 30 to it to make it five. 5+4=9 or 4.5 + 4.5=9. (In this case, 30 is half of an hour, hence the 4.5 instead of 4.3).
Answer:
5 hours and 10 minutes.
Step-by-step explanation:
9:00 minus 4:30 = 4:70.
4:70 = 5 hours and 10 minutes.
How many days are in 42 weeks?
294 days
504 days
1,008 days
2,520 days
Answer:
294 days
Step-by-step explanation:
Multiply 42 x 7 and you've got 294 days, which will be your answer.
The length of a rectangle is three times its width. If the perimeter of the rectangle is 72 yd, find its length and width.
Identify the vertex of the parabola given by f(x) = 2x
2 – 12x + 7.
Considering the definition of vertex of a quadratic function, the vertex of the quadratic equation y=2x²−12x+7 is (3; -11).
Vertex of a quadratic functionA quadratic function is a variable of a polynomial function defined by f(x)=ax² + bx +c, where a≠0
The graphs of these functions correspond to vertical parabolas (symmetric axis parallel to the ordinate axis), with the particularity that:
when a>0, the parabola opens "up".when a<0, the parabola opens "down".The vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is calculated as:
The value of -b÷(2a) indicates the value of x of the vertex.Substituting value of x into the function, you get the value of y of the vertex.Vertex in this caseIn this case, the quadratic equation y=2x²−12x+7, where:
a=2b= -12c= 7The value of x of the vertex is calculated as -(-12)÷(2×2)
Solving: -(-12)÷(4)= 12÷4= 3
The value of y of the vertex of the function is calculated as y=2×3²−12×3+7
Solving y= -11
Finally, the vertex in this case is (3; -11).
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In parallelogram DEFG if EH=23 find HG.
The length of HG is also equal to 23, which is the length of EH because the line DF bisects EG in the parallelogram DEFG.
Diagonals of a parallelogramA parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.
For the given parallelogram DEFG; the lines DF and EG are its diagonals, and the both bisect each other, that is the cut each other to form two equal parts.
So EH and HG are equal halves of the line EG
Therefore, since EH = 23 then HG = 23 because they form a diagonal of the parallelogram DEFG bisected by the diagonal DE.
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100 points
Find the maximum value of the objective function and the values of x and y for which it occurs.
f=5x+2y
x+2y[tex]\leq[/tex]=6 x[tex]\geq[/tex]=0 and y[tex]\geq[/tex]=0
2x+y[tex]\leq[/tex]=6
Answer:
Maximum value of the objective function is 15
This occurs at x = 3, y = 0
Step-by-step explanation:
Attached is a plot of the two inequalities. The feasible region is the dark shaded area bounded by the points O, A, B and C
The maximum value of the objective function will occur at one of the corner points
The four corner points are
O (0,0)
A(0,3)
B(2,2)
C(3,0)
Plug in each of these values into the objective function, see which of the corner points will yield the maximum value and those will be the optimal values of x and y
Corner point (x, y) O.F Value (5x + 2y)
(0, 3) 5(0) + 2(3) = 6
(2, 2) 5(2) + 2(2) = 14
(3, 0) 5(3) + 2(0) = 15 (Maximum value)
brad says that if a second number is 125% of the first number, then the first number must be 75% of the second number. is he correct? justify your anwser.
The first number is 80% of the second number, not 75%, hence, Brad is wrong.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, a second number is 125% of the first number.
Let the first number be 100, then the second number will be:
125% of 100
= (125/100) × 100
= 125
Now, divide the first number, 100, by the second number, 125, and then multiply with 100 to know how much % the first number is of the second number:
(100/125) ×100%
=80%
Therefore, the first number is 80% of the second number, not 75%.
Hence, Brad is wrong.
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Sydney wants to make 15 rings, and each ring requires 60 beads. That means you need to multiply 60 beads by 15 rings to see how many beads
Answer:No
Step-by-step explanation:
Sydney wants to make 15 rings, and each ring requires 60 beads. That means you need to multiply 60 beads by 15 rings to see how many beads she needs. 60 times 15 is 900. Sydney only has 852 beads.
9x - 4 - 5x + 7
evaluate the above for x = 2
Answer: 11
Step-by-step explanation:
9(2) - 4 - 5(2) + 7
18 - 4 - 10 + 7
14 - 10 + 7
4 + 7
11
solve asap pls. i need this done right now.
Answer:
-5/12
Step-by-step explanation:
Answer: 3 1/12
Step-by-step explanation: First We Would Do 2 1/2 + -7/6 First. We Would Get 1 1/3 Because We Change The Mixed Fractions Into Improper Fractions. So We Would Do 5/2 + - 7/6. We Would Then Find A Common Denominator Which Would Be 12. So 7/6 Would Be 14/12 & 5/2 Would Be 30/12. If You Did The Math Correctly You Would Get 1 1/3. Now 1 1/3 - 1 3/4 Would Be 3 1/12. You Would Change The Fractions To Improper Fractions And Then Subtract. You Would Also Need To Find The Common Denominator Which Is 12.
Hoped This Helped!
if a1 =2 and an= -2an-1 then find the value of a4
You have an ace, king, queen, and jack from a deck of cards. After shuffling the cards, you draw one card. Then you replace the card, shuffle again, and again draw a card. What is the probability that you will draw a king and a queen in either order? An ace, king, queen, and jack playing card. CLEARCHECK The total number of possible outcomes is x . The probability of drawing a king and a queen in either order is x
Answer:
[tex]\dfrac{2}{169}[/tex]
Step-by-step explanation:
A standard 52-card deck comprises 4 suits (Spades, Hearts, Diamonds, and Clubs).
Each suit comprises 10 numerical cards (numbered 2 through 10, plus an "ace") and 3 "court" cards (jack, queen and king).
Therefore:
The total number of possible outcomes is 52.There are 4 kings and 4 queens in a standard deck of cards.[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
[tex]\implies \sf P(Queen)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]
[tex]\implies \sf P(King)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]
Therefore, the probability of drawing a king, replacing the card, and drawing a queen is:
[tex]\implies \sf P(King)\;and\;P(Queen)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]
Similarly, the probability of drawing a queen, replacing the card, and drawing a king is:
[tex]\implies \sf P(Queen)\;and\;P(King)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]
Therefore, the probability of drawing a king then a queen, or a queen then a king is:
[tex]\implies \sf P(King\;and\;Queen)\;or\;P(Queen\;and\;King)=\dfrac{1}{169}+\dfrac{1}{169}=\dfrac{2}{169}[/tex]
am i shadowbanned why aren't people answering my questions
Answer:
no
Step-by-step explanation:
your questions are so tricky to pass
please help it’s due tomorrow
[x + y = -4
[x - y = 2
Answer:
which one substitution or elimination
Step-by-step explanation:
Substitution: (-1,-3 )
Elimination: (-1,-3)
i hope this helps you :)
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