h is a trigonometric function of the form h(x)=acos(bxc)+d. Below is the graph of h(x) The function has a maximum point at (3,6) and a minimum point at (6.5,-9) find the formula for h(x). Give an exact expression.
h(x)=
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Please Help URGENT
Answers
Answer:
acos(bxc)+d
h(x)=acos(bxc)+d
The function has a maximum point at (3,6) and a minimum point at (6.5,-9) so
h(x)=6-acos(3bx)+9
or
h(x)=-acos(3bx)+15
Step-by-step explanation:
Please analyze and reasure that this answer is correct.
An exact expression of h(x) is 7.5cos(51.4x - 154.3)-1.5.
What is a trigonometric function?Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions.
the difference in y values from max to min = 15. 15/2 = a
max cosine = 1, min cosine =-1
7.5 x 1 - 1.5 = 6
7.5x -1 -1.5 = -7.5-1.5= -9
h(x) = 7.5cos(bx+c) -1.5
now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c
at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...
if x=3, then 3b +c=0 and c=-3b
for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180
c= 180-6.5b
c=-3b
180-6.5b =-3b
add 6.5b to both sides to get
180= 3.5b
b = 180/3.5 = 51 1/7
c=-3b = -153 3/7
h(x) = 7.5cos(51.4x - 154.3)-1.5
Therefore, exact expression of h(x) is 7.5cos(51.4x - 154.3)-1.5.
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Related Questions
The black graph is the graph of y= f(x). Choose the equation for the red graph
a. y=f(x+3)
b. y=f(x-3)
c. y+3=f(x)
d. y-3=f(x)
Answers
Answer:
[tex]D[/tex]
Step-by-step explanation:
Notice that the red graph does not globally differ from the black graph: it would have been approximately the same one unless it had been displaced by 3 units up. Therefore, it was only the ordinate axis that underwent our change: [tex]y - 3 = f(x) \Leftrightarrow y = f(x) + 3[/tex].
Answer:
C
Step-by-step explanation:
Please help ASAP
Please help ASAP
Please help ASAP
Please help ASAP
Answers
Substituting L = 7.29,
[tex]t = 2.01 \sqrt{7.29} \approx \boxed {5.4}[/tex]
Write an equation to model this proportional relationship, where x represents the length of the rectangle and y represents the width of the rectangle.
Answers
When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle.
[tex]x\propto \frac{1}{y} [/tex]
We know that the area of a rectangle is given by the product of the length and width of the rectangle.
Area = Length*Width
In this given problem,
The length of the rerectanglctangle is represented by x
and the width of the rectangle is represented by y
If the area of the rectangle is represented by A now.
So by the formula,
A = x*y
When A is constant then,
x = A/y
[tex]\therefore x \propto \frac{1}{y}[/tex]
So from the above calculation we can conclude that about relation between length and width that,
"When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle."
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Missing value of why worth 20 points pls help
Answers
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The value of x, y and z is 90°, 53°, and 100°, respectively.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In ΔABD is made on the diameter of the circle, therefore, the measure of ∠BAD = 90°. Therefore,
x° = 90°
In ΔAOD, the measure of ∠AOD is 74°, also, the triangle is an isosceles triangle with OA and OD of equal length. Therefore, the sum of the angles can be written as,
y° + y° + 74° = 180°
2y° = 106°
y = 53°
Similarly, ΔBOC is an isosceles triangle with OB and OC having an equal length. Therefore, ∠OBC=∠OCB. Also, the sum of all the angles can be written as,
∠BOC + ∠OBC + ∠OCB = 180°
∠BOC + 40° + 40° = 180°
∠BOC = 100°
Hence, the value of x, y and z is 90°, 53°, and 100°, respectively.
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Select the correct answer.
What are the domain and range of f(x) = -log5(x + 2)?
A.
domain: x > -2; range: all real numbers
B.
domain: x > 2; range: all real numbers
C.
domain: x > -2; range: all positive real numbers
D.
domain: x > 2; range: all positive real numbers
Answers
The correct option is A.
domain: x > -2; range: all real numbers
Which is the domain and range of the given function?
Here we have a logarithmic function.
Remember that the argument of a logarithm must be larger than zero, in this case the argument is:
x + 2
So we must have:
x + 2 > 0
x > -2
Then the domain is: x > -2.
And the range of any logarithmic function is the set of all real numbers.
Then the correct option is A.
domain: x > -2; range: all real numbers
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The following figure shows a square-based pyramid.
5
6
Which expression represents the surface area of the pyramid?
Choose 1 answer:
Answers
The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The surface area of pyramid = sum of individual area of the surface
Surface area = (2 * 2) + 4(0.5 * 2 * 3)
The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)
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Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 4r and height 4h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
Answers
Answer:
The surface area of Cylinder B is 16 times the surface area of Cylinder AStep-by-step explanation:
Note: It is assumed we are looking at the total surface area (but the answer would be same for both cases)
GivenCylinders A with radius - r, height - h,Cylinder B with radius - 4r, height - 4h.To find The ratio of total surface areas of cylinder B to ASolutionTotal surface area of cylinder A is:
[tex]S_A = 2\pi r(h + r)[/tex]Total surface area of cylinder B is:
[tex]S_B = 2\pi(4r)(4r + 4h) = 8\pi(4)(r + h) = 32\pi(r + h)[/tex]Find the ratio of areas:
[tex]\cfrac{S_B}{S_A} =\cfrac{32\pi(r+h)}{2\pi(r+h)} =16[/tex]HELP FAST!! PLEASE will give brainliest!
Answers
Answer:
22
Step-by-step explanation:
3*sqrt 25 + 7
3*5 + 7
15+7
22
Consider the equality xy=k. Write the following inverse proportion: y is inversely proportional to x. When y = 2, x = 14.
2/1 = k/14
1/k = 14/2
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathbf{\dfrac{2}{1} = \dfrac{k}{14}}[/tex]
[tex]\huge\textbf{Cross multiply the given numbers}\\\huge\textbf{you have listed.}[/tex]
[tex]\mathbf{2\times14 = k \times1}[/tex]
[tex]\mathbf{2\times14 = 1\times k}[/tex]
[tex]\mathbf{28 = 1k}[/tex]
[tex]\mathbf{1k = 28}[/tex]
[tex]\huge\textbf{DIVIDE 1 to BOTH SIDES}[/tex]
[tex]\mathbf{\dfrac{28}{1} = \dfrac{1k}{1}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{k = \dfrac{28}{1}}[/tex]
[tex]\mathbf{k = 28}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{k = 28}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathbf{\dfrac{1}{k} = \dfrac{14}{2}}[/tex]
[tex]\huge\textbf{Cross multiply the given numbers}\\\huge\textbf{you have listed.}[/tex]
[tex]\mathbf{1\times 2 = 14\times k}[/tex]
[tex]\mathbf{2 = 14k}[/tex]
[tex]\mathbf{14k = 2}[/tex]
[tex]\huge\textbf{DIVIDE 14 to BOTH SIDES}[/tex]
[tex]\mathbf{\dfrac{14k}{14} = \dfrac{2}{14}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{k = \dfrac{2}{14}}[/tex]
[tex]\mathbf{k = \dfrac{2\div2}{14\div2}}[/tex]
[tex]\mathbf{k = \dfrac{1}{7}}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{k = \dfrac{1}{7}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitritr1040:)}[/tex]There are 400 students at a sports camp. Two hundred students play soccer, 100 students play baseball, and 100 students play basketball. Which circle graph could be used to display this data? A circle graph. About 60 percent is soccer, 15 percent is baseball, 25 percent is basketball. A circle graph. About 25 percent is soccer, 25 percent is baseball, 50 percent is basketball. A circle graph. About 50 percent is soccer, 25 percent is baseball, 25 percent is basketball. A circle graph. About 33 percent is soccer, 33 percent is baseball, 33 percent is basketball.
Answers
Answer:
C. About 50 percent is soccer, 25 percent is baseball, 25 percent is basketball.
Step-by-step explanation:
400 students at a sports camp.
200 play soccer, which is 50% or half of the students at the sports camp.
100 play baseball, which is 25% or a quarter of the students at the camp.
100 play basketball, which is also 25% or a quarter of the students at the camp.
So, the circle graph that shows soccer 50%, baseball 25%, and basketball 25%, is the answer.
Hope this helps!
If not, I am sorry.
Measure of arc CF
please help
And number 9
I’ll give brainiest answer to whoever helps first
Thank youuuu
Answers
Answer:
Step-by-step explanation:
The measure of an angle formed by a Secant and a tangent drawn from the outside point of a circle is half the difference of the intercepted arcs.
[tex]\sf \angle E =\dfrac{arc \ CF - arc \ DF}{2}[/tex]
[tex]\sf53 =\dfrac{arc \ CF-41}{2}[/tex]
53*2 = arc CF - 41
106 = arc CF - 41
106 + 41 = arc CF
[tex]\sf \boxed{\bf \ arc \ CF = 147^\circ}[/tex]
9) If two secants inside a circle, then the angle formed is equal to the half of the sum of intercepted arcs.
[tex]\sf 5x - 7 = \dfrac{27+119}{2}\\\\ 5x - 7 = \dfrac{146}{2}[/tex]
5x - 7 = 73
5x = 73 + 7
5x = 80
x = 80/5
[tex]\sf \boxed{\bf \ x = 16^\circ }[/tex]
Pls help me with the answer , ty
Answers
Using it's concept, the equivalent expression for the perimeter of the figure is:
2 + 3x2 + 4x2 + 5x2 + 8
What is the perimeter of a figure?The perimeter of a figure is given by the total length of it's boundary.
Hence, for the figure given in this problem, the perimeter is:
2 + 3 + 3 + 4 + 4 + 5 + 8 + 5
2 + 3x2 + 4x2 + 5x2 + 8
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A room has a length of 8 m. A scale diagram is drawn of the room. In the diagram, the room has a length of 1 cm. What is the scale of the diagram? Give your answer as a ratio in the form 1 : k , where k is an integer.
Answers
The scale of the diagram as described in the task content is; 1: 8 where k= 8.
What is the scale of the diagram?It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.
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PLEASE HELPPPP!
Susan's calculator has a key that replaces the number displayed with its cube. If a² is displayed, how many times must Susan press the " cubing" key to display a number that is greater than 10?
Please explain it step-by-step! Also, I will give you a brainlist!!
Answers
Answer:
10
Step-by-step explanation:
This is because you would have to start with 109 = 23x
then solve it using logarithms
Then once you get the x value, it becomes
X>_10__(whatever number you found)
If m ∠4 = m ∠5, then r||s. Summarize the postulate or theorem that makes this a true statement.
can someone please explain how to solve this
Answers
The statement, m∠4 = m∠5, then then r||s is true based on the converse of corresponding angles theorem.
What is the Converse of Corresponding Angles Theorem?Based on the converse of corresponding angles theorem, if two corresponding angles, angles 4 and 5 are congruent or equal to each other, then the lines on which they lie on, lines r and s are congruent.
Therefore, based on the converse of corresponding angles theorem, m∠4 = m∠5, then then r||s.
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What term is used to describe the problem of using variables that strongly correlate with one another in a multiple linear regression model
Answers
Multicollinearity is used to describe the problem of using variables that strongly correlate with one another in a multiple linear regression model.
Multiple linear regression refers to a statistical technique that is used to predict the outcome of a variable based on the value of two or more variables. It is sometimes known simply as multiple regression, and it is an extension of linear regression. The variable that we want to predict is known as the dependent variable, while the variables we use to predict the value of the dependent variable are known as independent or explanatory variables.
Multicollinearity, also known as collinearity, is a phenomena in statistics when one predictor variable in a multiple regression model can be linearly predicted from the others with a high level of accuracy. In this case, minor adjustments to the model or the data may cause the multiple regression's coefficient estimates to fluctuate unpredictably. Multicollinearity only impacts calculations pertaining to specific predictors; it has no impact on the predictive capability or reliability of the model as a whole, at least within the sample data set. In other words, a multivariate regression model with collinear predictors can show how well the entire set of predictors predicts the outcome variable, but it might not provide accurate information about any particular predictor or about which predictors are redundant with respect to another predictor.
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simplyfy it -25 + 14 ÷ (5 – 3)
Answers
Step-by-step explanation:
-25 + 14 ÷ (5-3)
= -25 + 14 ÷ (2)
= - 25 + 7
= - 18
• Your equation
[tex] - 25 + 14 \div (5 - 3)[/tex]
• Solving
[tex] - 25 + 14 \div (2)[/tex]
• Dividing the terms.
[tex] - 25 + 7[/tex]
• Answer = -18
Hope it helps you!
What is the product of the matrices [tex]\left[\begin{array}{ccc}-3&3&0\end{array}\right] \left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex] ?
Answers
Answer:
24
Step-by-step explanation:
(-3 * -3) + (3*5) + (0 * -2) = 24
Find the total surface area of the cylinder shown. Leave the answer in terms of π. A cylinder with radius 4.25 inches and height 6 inches. SA=2πrh+2πr2
Answers
Answer:
[tex]87.125\pi in^{2} or 87\frac{1}{8}\pi in^{2}[/tex]
Step-by-step explanation:
Given Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex],
and also given r = 4.25 inches and h = 6 inches.
Let's Substitute r and h into the formula to find the total surface area.
Surface Area of Cylinder = [tex]2\pi (4.25)(6)+2\pi (4.25)^{2} \\=51\pi +36.125\pi \\=87.125\pi in^{2} or 87\frac{1}{8} \pi in^{2}[/tex]
7. A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in miles, , and her running speed, in miles per hour, when she runs:
a. at a constant speed of 4 miles per hour for the entire 30 minutes.
Answers
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The distance travelled in 30 minutes is:
Distance = speed * time = 4 mph * 0.5 h = 2 miles
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
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Judy is a single woman, 25 years old. Her take home pay is $2314.92/month. She also earns $48 interest per month on her savings account. Judy rents a 1-bedroom apartment for $825/month. She does not own a car and uses public transportation to travel to and from work. Judy also has a student loan for which she repays $258/month.
Answers
The monthly budget plan for Judy includes all of her income and expenses, the total balance is $ 2362.92 and she spends $ 1083.
What is the monthly budget?A monthly budget is a personal spending plan that you use to track your monthly income and costs.
The given data in the problem is;
Home pay = $2314.92/month.
Interest earned = $48 / month
House rent = $825/month
EMI of student loan = $258/month
Total earning per month = $2314.92 + $48
Total earning per month = $ 2362.92
Amount she spends per month = $825/month + $258
Amount she spends per month = $ 1083
Hence, the total balance will be $ 2362.92 and she spend $ 1083.
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.
help me please gang
Answers
Answer:
Not similar
Step-by-step explanation:
There is only one side and one angle, which insufficient to prove triangle similarity.
Solve on the interval [0,2%):
2 cos²x+3cosx+1=0
Answers
Answer:
Step-by-step explanation:
I NEED HELP QUICK!!!
Triangle ABC is transformed to triangle A′B′C′, as shown below:
A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Which equation shows the correct relationship between the measures of the angles of the two triangles?
The measure of angle CAB = The measure of angle C prime B prime A prime
The measure of angle BCA = The measure of angle A prime B prime C
The measure of angle CAB = The measure of angle C prime A prime B prime
The measure of angle BCA = The measure of angle C prime A prime B prime
Answers
The equation that shows the correct relationship between the measures of the angles of the two triangles is;
Option D: The measure of angle BCA = The measure of angle C prime A prime B prime
How to Interpret Objects Transformation?We are told that Triangle ABC is transformed to triangle A′B′C′.
Now, the triangle ABC and A'B'C' are similar triangles and we know that similar triangles angles are congruent. Thus;
From the given coordinates, we can say that;
∠BAC = ∠B'A'C'
∠ABC = ∠A'B'C'
∠ACB = ∠A'C'B'
Thus, the equation that shows the correct relationship between the measures of the angles of the two triangles is;
The measure of angle BCA = The measure of angle C prime A prime B prime
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HELP QUICKKK What is the difference between –4 and 6?
–10
–2
2
10
Answers
Answer:
10
Step-by-step explanation:
Plugin your answer: -4 + 10 = 6
Answer:
10
Step-by-step explanation:
Which expressions represent exponential decay? Check all that apply.
900(0.05)t
700(0.9)x
53(1.75)(0.3)x
90(1.2)t
300(2.4)(1.2)y
2x2 + 9
18 – 3y
Answers
The expressions that represent exponential decay are 900(0.05)^t, 700(0.9)^x and 53(1.75)(0.3)^x
How to determine the expressions?An exponential function is represented as:
y = ab^x
The above means that options (f) and (g) are not exponential functions
When b is less than 1, then the function is an exponential decay.
From the list of options, we have:
900(0.05)^t => b = 0.05
700(0.9)^x => b = 0.9
53(1.75)(0.3)^x => b = 0.3
Hence, the expressions that represent exponential decay are 900(0.05)^t, 700(0.9)^x and 53(1.75)(0.3)^x
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Given that y = 12 cm and 0 = 45°, work
out a rounded to 1 DP.
The diagram is not drawn accurately.
X
cm
Answers
The value of x is 8.5 cm
How to solve for x?The complete question is in the image
The given parameters are:
y = 12 cm
[tex]\theta = 45^o[/tex]
The value of x is calculated using the following sine ratio
[tex]\sin(\theta) = \frac xy[/tex]
This gives
[tex]\sin(45^o) = \frac x{12}[/tex]
Multiply by 12
[tex]x = 12 * \sin(45^o)[/tex]
Evaluate
x = 8.5
Hence, the value of x is 8.5 cm
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ILL MARK BRAINLIEST HELP PLS I NEED THE ANSWER TO 9 and 10
Answers
Answer:
28. Y=1x+c
29. -2/3x+c
Hope it helps :)
number 8. use the Steps in the construction to determine which statement is true
Answers
Answer:
choice C
Step-by-step explanation:
The circle is circumscribed because circles drawn on the outside is known as circumscription. The circle is clearly outside touching the three vertices of the triangle.
Members of the band sold juice and popcorn at a college football game to raise money for an
upcoming trip. Each juice bottle sold costs $2.50, and each container of popcorn sold costs
$1.25.
a. write an equation to represent how much money was made
b. be sure to specify what the variables represent.
Answers
Answer:
2.50x+1.25y=z
Step-by-step explanation:
Let the number of juice bottles = x
And the number of containers of popcorns=y
And the total number of juice bottles and containers of popcorns=z
Total number of juice bottles=x times $2.50
Total number of containers of popcorn= y times $ 1.25
equation; 2.50x+1.25y=z