Determine the minimum and maximum value of the following trigonometric function.
f(x)=10sin(2/5x)+5
Answers
ANSWER
[tex]\begin{gathered} Minimum=-5 \\ Maximum=15 \end{gathered}[/tex]EXPLANATION
The trigonometric function given is:
[tex]f(x)=10\sin (\frac{2}{5}x)+5[/tex]The minimum value a sine function can take is -1.
This means that the minimum value of the function is:
[tex]\begin{gathered} 10(-1)+5 \\ \Rightarrow-10+5 \\ \Rightarrow-5 \end{gathered}[/tex]The maximum value a sine function can take is 1.
This means that the maximum value of the function is:
[tex]\begin{gathered} 10(1)+5 \\ \Rightarrow10+5 \\ \Rightarrow15 \end{gathered}[/tex]Related Questions
Let f(x) = x² + 11x + 25 Find a so that f(a) = 1
Answers
A=-3
A=-8
Explanation
Step 1
[tex]f(x)=x^2+11x+25[/tex]there is a number A so f(A) =1, then
[tex]\begin{gathered} f(A)=A^2+11A+25 \\ f(A)=1 \\ \text{then} \\ A^2+11A+25=1 \\ A^2+11A+24=0\text{ equation(1)} \end{gathered}[/tex]Step 2
solve using the quadratic equation
[tex]\begin{gathered} \text{for } \\ ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]a)let
a=1
b=11
c=24
the variable is A,
b) replace
[tex]\begin{gathered} A=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ A=\frac{-11\pm\sqrt[]{121^{}-4\cdot1\cdot24}}{2\cdot1} \\ A=\frac{-11\pm\sqrt[]{121^{}-96}}{2} \\ A=\frac{-11\pm\sqrt[]{25}}{2} \\ A_1=\frac{-11+\sqrt[]{25}}{2}=\frac{-11+5}{2}=\frac{-6}{2}=-3 \\ A_1=-3 \\ A_2=\frac{-11-\sqrt[]{25}}{2}=\frac{-11-5}{2}=\frac{-16}{2}=-8 \\ A_2=-8 \end{gathered}[/tex]I hope this helps you
can you help me with this? i am looking for perimeter and and area
Answers
For this problem, we are given a rectangle with the measurement of its dyagonal and the angle between the dyagonal and the base. We need to determine the perimeter and area for this rectangle.
For this, we need to analyze the right triangle that is formed between the dyagonal, the width and height of the rectangle. This triangle is shown below:
From the image above, we can notice that the height is the opposite side to the known angle. Therefore we can calculate it by using the sine relation on a right triangle.
[tex]\begin{gathered} \sin 29=\frac{\text{ height}}{18} \\ \text{height}=18\cdot\sin 29 \\ \text{height}=18\cdot0.48 \\ \text{height}=8.73 \end{gathered}[/tex]The rectangle's height is equal to 8.73 ft.
On the other hand the width is the adjascent side to the known angle, therefore we can calculate it by using the cossine relation.
[tex]\begin{gathered} \cos 29=\frac{\text{ width}}{18} \\ \text{width}=18\cdot\cos 29 \\ \text{width}=18\cdot0.87 \\ \text{width}=15.74 \end{gathered}[/tex]The rectangle's width is equal to 15.74 ft.
Now we can calculate the perimeter and area for the rectangle.
[tex]\begin{gathered} P=2\cdot(\text{width}+\text{height)} \\ P=2\cdot(15.74+8.73) \\ P=2\cdot24.47 \\ P=48.94\text{ ft} \end{gathered}[/tex]The perimeter for the rectangle is 48.94 ft.
[tex]\begin{gathered} A=\text{width}\cdot\text{height} \\ A=15.74\cdot8.73 \\ A=137.41 \end{gathered}[/tex]The area for the rectangle is 137.41 square ft.
Higher Order Thinking Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1. Can their sum equal 1? Can their sum be greater than 1? Explain.
Answers
1) Gathering the data
2) Since we don't know exactly their numerators we can write, for instance, two fractions with the same bottom number and lesser than 1:
[tex]\begin{gathered} \frac{1}{4},\text{ }\frac{3}{4} \\ \frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1 \\ \frac{2}{4}+\frac{3}{4}=\frac{5}{4}=1.25 \\ \frac{1}{5}+\frac{3}{5}=\frac{4}{5}=0.8 \end{gathered}[/tex]2) Hence, we can conclude that the sum can be equal to 1, greater than 1, and lesser than 1. That'll depend on the numerator, and the fractions Leah can pick.
3) So, they can be less, equal to, and greater than 1.
Jada has 4 meters of ribbon. How many pieces of ribbon of length 1/3 meter can she cut from it. Draw a diagram to illustrate your solutions.
Answers
She can cut twelve 1/3 meters from 4 meters.
The diagram is shown in the explanation below.
Explanation:Parameters:
Total length of ribbon = 4 meters
Let x represent the number of 1/3 meters she can cut, then
[tex]\begin{gathered} \frac{1}{3}x=4 \\ x=4\times3=12 \end{gathered}[/tex]She can cut twelve 1/3 meters from 4 meters.
This is illustrated in the diagram below:
Here are the graphs of three equations:y = 50(1.5) ^xy = 50(2)^xY = 50(2. 5)^xWhich equation matches each graph? Explain how you know
Answers
The graphs below are exponential function graphs, the general formular takes the form
[tex]y=ab^x[/tex]The graph of
[tex]y=50(1.5)^x[/tex]Is shown below
The graph of
[tex]y=50(2^x)[/tex]Is shown below
The graph of
[tex]y=50(2.5^x)[/tex]Is shown below
Hence,
[tex]\begin{gathered} y=50(1.5)^x\rightarrow C \\ y=50(2)^x\rightarrow B \\ y=50(2.5)^x\rightarrow A \end{gathered}[/tex]The equation of the exponential function is
[tex]\begin{gathered} y=ab^x \\ a=50\rightarrow the\text{ initial value} \\ b\rightarrow growht\text{ factor} \end{gathered}[/tex]Thus the higher the growth factor the greater the rate of attaining a higher value within a short period.
That is why you see that the function with growth factor of 2.5 grows faster than that of 2 and also 1.5.
So the at x value of 3, the function with the greatest growth factor will have the highest y-value.
This implies , growth factor of 2.5 will have the highest, that corresponds to graph with colour green. Function with growth factor 2 will be the next to that of 2.5, that is red colored graph, and the last will be blue.
Write the function graphed below in the form g(x)… reference photo
Answers
We will have the following:
First, we can see that the function in the image will have a mother function:
[tex]y=\sqrt[3]{x}[/tex]Where the function has been moved 2 units left, and 2 units down:
[tex]y=\sqrt[3]{x+2}-2[/tex]Now, we known that the function has been expanded on the vertical, so:
[tex]y=a\sqrt[3]{x+2}-2[/tex]Now, we solve for "a" while we replace for a value of the function, we can see that (6, 4) belongs, so:
[tex]\begin{gathered} 4=a\sqrt[3]{6+2}-2\Rightarrow4=a\sqrt[3]{8}-2 \\ \\ \Rightarrow6=2a\Rightarrow a=3 \end{gathered}[/tex]So, the equation of the function will be:
[tex]g(x)=3\sqrt[3]{x+2}-2[/tex]This can be seeing as follows:
Which expression is equivalent to 8c + 6 - 3c - 2 ?A. 5c +4B. 50 + 8C.11c +4D.11c + 8
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This means that the answer is option A
2Select all values of x that make the inequality -x + 8 >11 true.A-2B-6С-4D1E3F.-3
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To solve this problem, we need to know which values of x would make the inequality -x + 8 > 11 true.
To do this, we will need to solve the equation in terms of x, just like how we normally solve for x in any linear equation.
[tex]-x+8>11[/tex]Using the Addition Property of E
Evaluate 0^0.
Provide justifications for your conclusion.
Answers
The power expression 0⁰ leads to an indetermination.
What is the result of 0⁰ according to algebra properties?Let be the power expression 0⁰, whose result has to be found by means of algebra properties, especially those related to operations between powers. First, write the entire expression:
0⁰
Second, use the existence property of additive inverse:
0ⁿ ⁺ ⁽⁻ⁿ⁾, where n is a real number.
Third, use power properties:
0ⁿ · 0⁻ⁿ
0ⁿ · (0ⁿ)⁻¹
0 · 0⁻¹
Fourth, by definition of division:
0 / 0
The term 0 / 0 represents an indetermination.
To learn more on indeterminations: https://brainly.com/question/24335947
#SPJ1
What the percent 7/800
Answers
You have to divide 7 by 800:
[tex]\frac{7}{800}=0.00875[/tex]Now multiply by 100
[tex]0.00875*100=0.875\%[/tex]The answer is 0.875%
35/25 covert fraction to percent
Answers
To convert fraction to decimal you multiply by 100%
Therefore, 35/25 to percentage
[tex]\begin{gathered} =\text{ }\frac{35}{25}\text{ x 100\%} \\ =\text{ }\frac{35\text{ x 100}}{25} \\ =\text{ }\frac{3500}{25} \\ =\text{ 140\%} \end{gathered}[/tex]Pre-Calculus_Unit 1_Math_20-21 / 4 of 16 Find the slope of the line determined by the equation 3x +10y = 11 O A. m = -3 OB. m= 3 O C. 3 m=- 10 11 10 Em: -10
Answers
Brook, this is the solution:
Let's find the slope for this equation:
3x + 10y = 11
10y = -3x + 11
Dividing by 10 at both sides:
10y/10 = -3x/10 + 11/10
y = -3x/10 + 11/10
Therefore,
m = -3/10
Frank has a circle Garden the area of the garden is 100 ft² what is the approximate distance from the edge of Frank's garden to the center of the garden ? (A = pi r²)
Answers
The area of a cirle is given by
[tex]A=\pi(R^2)\text{ where R is the radius, the distance from the edge/circumference to the centre}[/tex]We seek to find R, so let us make it the subject of the formula;
[tex]R=\sqrt[]{\frac{A}{\pi}}[/tex][tex]\begin{gathered} R=\sqrt[]{\frac{100}{3.142}} \\ R=5.64\approx6ft \end{gathered}[/tex]Therefore, the approximate distance from the edge of Frank's garden to the center of the garden is 6ft
A polynomial P is given. P(x) = x3 + 3x2 + 6x(a) Find all zeros of P, real and complex.x = (b) Factor P completely.P(x) =
Answers
P(x) is defined by the expression
[tex]P(x)=x^3+3x^2+6x[/tex]Note
[tex]x^3+3x^2+6x=x(x^2+3x+6)\text{ }[/tex]Therefore, one solution is 0.
The other two solutions come from
[tex]x^2+3x+6=0[/tex]Apply the general solution in order to find complex solutions
[tex]\frac{-3\pm\sqrt{3^2-4(1)(6)}}{2(1)}=\frac{-3\pm\sqrt{-15}}{2}[/tex]The solutions are
[tex]0,\frac{-3+i\sqrt{15}\text{ }}{2},\frac{-3-i\sqrt{15}}{2}[/tex]We calculate the factor from the solutions, like this
[tex]x=\frac{-3+i\sqrt{15}}{2}\Rightarrow x+\frac{3}{2}-\frac{i\sqrt{15}}{2}=0[/tex][tex]x=\frac{-3-i\sqrt{15}}{2}\Rightarrow x+\frac{3}{2}+\frac{i\sqrt{15}}{2}=0[/tex]The factor is
[tex]P(x)=x(x+\frac{3}{2}-\frac{i\sqrt{15}}{2})(x+\frac{3}{2}+\frac{i\sqrt{15}}{2})[/tex]not college I misclicked but the question is in pic
Answers
Answer
x = 13.33 units
Explanation
We can easily tell that the small triangle (with sides 6 and 8) is similar to the bigger triangle with sides (6+4 and x).
And the ratio of corresponding sides is the same for two similar triangles.
From the image, we can see that
6 is corresponding to (6 + 4)
8 is corresponding to x
So,
[tex]\begin{gathered} \frac{6}{6+4}=\frac{8}{x} \\ \frac{6}{10}=\frac{8}{x} \end{gathered}[/tex]We can now cross multiply
6x = (8) (10)
6x = 80
Divide both sides by 6
(6x/6) = (80/6)
x = 13.33 units
Hope this Helps!!!
A gardener builds a rectangular fence around a garden using at most 56 feet of fencing. The length of the fence is four feet longer than the widthWhich inequality represents the perimeter of the fence, and what is the largest measure possible for the length?
Answers
We know that
• The gardener used at most 56 feet of fencing.
,• The length of the fence is four feet longer than the width.
Remember that the perimeter of a rectangle is defined by
[tex]P=2(w+l)[/tex]Now, let's use the given information to express as inequality.
[tex]2(w+l)\leq56[/tex]However, we have to use another expression that relates the width and length.
[tex]l=w+4[/tex]Since the length is 4 units longer than the width. We replace this last expression in the inequality.
[tex]\begin{gathered} 2(w+w+4)\leq56 \\ 2(2w+4)\leq56 \\ 2w+4\leq\frac{56}{2} \\ 2w+4\leq28 \\ 2w\leq28-4 \\ 2w\leq24 \\ w\leq\frac{24}{2} \\ w\leq12 \end{gathered}[/tex]The largest width possible is 12 feet.
Now, we look for the length.
[tex]\begin{gathered} 2(12+l)\leq56 \\ 24+2l\leq56 \\ 2l\leq56-24 \\ 2l\leq32 \\ l\leq\frac{32}{2} \\ l\leq16 \end{gathered}[/tex]Therefore, the largest measure possible for the length is 16 feet.At the sewing store, Kimi bought a bag of mixed buttons.The bag included 100 buttons, of which 10% were large.How many large buttons did kimi get?
Answers
to find the 10% of 100 buttons, we multiply 100 by 0.1 to get the following:
[tex]100\cdot0.1=10[/tex]therefore, Kimi got 10 large buttons
showing all your work for problem 1 divide simplify and state the domain and problem 2 multiply simplify and state the domain
Answers
The domain of the problem is given as
[tex](-\infty,\text{ 0) U (0, +}\infty)[/tex]Six times a number is greater than 20 more than that number. What are the possible values of that number?a. n<4b. n>4c. n>20/7d. n<20/7
Answers
Let's call n to the number of interest. The following inequality represents this problem:
6n > 20 + n
Solving for n
6n - n > 20
5n > 20
n > 20/5
n > 4
$800 is deposited in a bank account which is compounded continuously at 8.5% annual interest rate. The future balance of the accourby the function: A = 800e0.085t. How long will it take for the initial deposit to double? Round off to the nearest tenth of a year.
Answers
Given:
Function :
[tex]A=800e^{0.085t}[/tex]Initial deposit =$800
Annual interest rate =8.5%
[tex]A=A_0e^{rt}[/tex]Where,
[tex]\begin{gathered} A=\text{Amount after t time} \\ A_0=\text{Initial amount} \\ r=\text{interest rate} \\ t=\text{time} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{8.5}{100} \\ r=0.085 \end{gathered}[/tex]When deposit is double of initial deposit .
[tex]\begin{gathered} 2\times800=800e^{0.085t} \\ \frac{2\times800}{800}=e^{0.085t} \\ 2=e^{0.085t} \\ \ln 2=\ln e^{0.085t} \\ 0.085t=0.69314 \\ t=\frac{0.69314}{0.085} \\ t=8.15 \end{gathered}[/tex]So after 8.15 year initial amount will be double.
Mrs. Davis has 20 people in her 6th period class. 12 of the people are boys. What percent of Mrs. Davis's 6th period class are boys? 70% 40% 50% 60%
Answers
Mrs. Davis has 20 people in her 6th period class. 12 of the people are boys. What percent of Mrs. Davis's 6th period class are boys? 70% 40% 50% 60%
we know that
20 people represent 100%
so
Applying proportion
20/100%=12/x
solve for x
x=(100*12)/20
x=60%
therefore
the answer is 60%A local bakery, theprice for abughouts for his employeespurchasedAFX) -0.65- 3.5prie for $3.50 and some doudoughnuts 30.05. Each day the manager at the store buyswhich equation represents the total cosa function of the number of doughtswhich equation on where represents the number of tires produced over resismodels the function ?BFX) - 0.65x + 3.5CX-3.5x + 0.85DX) - 3.5x -0.85Aebire manufacturing plant produces soo tires a day on average. If the production ofAFX) - 500 + xB (x) - 500 -Cx) - 500xDX) - 5006.Bushra purchases a car for $12,900. The car will depreciate at a rate of 15% each year,After how many years will the value of the car bethan $3,000?A 6 yearsB 7 yearsC8 yearsD 9 years
Answers
In order to create a function that represents the cost of the manager as a function of the number of doughnuts he buys, we need to multiply the cost of each doughnut ($ 0.85) by the number of employees the manager has and add the value of the pie ($ 3.5). This is done below:
[tex]f(x)\text{ = }0.85\cdot x\text{ + 3.5}[/tex]The correct option is the letter B.
The car starts at $ 12,900 and depreciate at a rate of 15% each year. This means that the value of the car on any given year is ruled by the tollowing expression:
[tex]M\text{ = C}\cdot(1-r)^t[/tex]Where "M" is the value of the car after "t" years, C is the initial value of the car and "r" is the rate at which the car depreciates every year divided by 100. Aplying the data from the problem on the expression gives us:
[tex]3000\text{ = 12900}\cdot(1\text{ - }\frac{15}{100})^t[/tex]We want to solve for the variable "t", because we want to know how many years it'll take until the car reaches the final value of 3000.
[tex]\begin{gathered} 12900\cdot(1\text{ - }\frac{15}{100})^t\text{ = 3000} \\ (1\text{ - }\frac{15}{100})^t\text{ = }\frac{3000}{12900} \\ (1-0.15)^t\text{ = }\frac{30}{129} \\ (0.85)^t\text{ = }\frac{30}{129} \end{gathered}[/tex]We have reached an exponential equation. To solve it we need to aply a logarithm on both sides of the equation.
[tex]\begin{gathered} \ln (0.85^t)\text{ = }\ln (\frac{30}{129}) \\ t\cdot\ln (0.85)\text{ = }ln(30)\text{ - ln(129)} \\ t\cdot(-0.1625)\text{ = }3.4\text{ - 4.86} \\ t\text{ = }\frac{-1.46}{-0.1625}\text{ = 8.98} \end{gathered}[/tex]It'll take approximately 9 years to reach that value. The correct option is the letter "D".
A roll of 50 dimes weighs 4 ounces. Which proportion can be used to find the weight in ounces, w, of 300 dimes?
Answers
50 dimes = 4 ounces
300 dimes = w ounces
[tex]\begin{gathered} \frac{50}{300}=\frac{4}{w} \\ \frac{1}{6}=\frac{4}{w} \\ w=24 \end{gathered}[/tex]300 dimes = 24 ounces
the proportion is 1/6 =4/w
What is the answer for this question? Why would it be helpful to rewrite the equation that way?
Answers
To solve the equation for "x", we will use operations in both sides of the equation.
[tex]3x+5y=500[/tex]First, we already have the "x" in the left side, but there is also a term with "y", so let's put it to the right side.
to do this, we can substract "5y" in both sides:
[tex]\begin{gathered} 3x+5y-5y=500-5y \\ 3x=500-5y \end{gathered}[/tex]Now, we just need to pass the "3" to the other side, which we can do by dividing both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{500-5y}{3} \\ x=\frac{500}{3}-\frac{5}{3}y \end{gathered}[/tex]Tha is the equation solved for "x".
This way of writing the equation can be usefull if we want to calculate "x" for a given "y" value, that is, if we know the number of adult tickets sold, we can substitute it into the equation in this form and just evaluate the right part to obtain the "x" value.
This expression represents the amount of money, in dollars, that will be in a savings account after 4 years.1500 [1 + 0.05/12)^12]^4Which of these is equivalent to the expression?A). 1500 (1.05/12)^48B). 1500 (1.05/12)^16C). 1500 (1 +0.05/12)^16D). 1500 (1 + 0.05/12)^48
Answers
The expression below represents the amount of money, in dollars, that will be in a savings account after 4 years.
[tex]1500\lbrack(1+\frac{0.05}{12})^{12}\rbrack^4[/tex]Recall from the laws of exponents, the power of a power rule is given by
[tex](a^x)^y=a^{x\cdot y}[/tex]So applying the above rule on the given expression, we get
[tex]\begin{gathered} 1500\lbrack(1+\frac{0.05}{12})^{12}\rbrack^4 \\ 1500(1+\frac{0.05}{12})^{12\cdot4} \\ 1500(1+\frac{0.05}{12})^{48} \end{gathered}[/tex]Therefore, the equivalent expression is
[tex]1500(1+\frac{0.05}{12})^{48}[/tex]Option D is the correct answer.
A train leaves Little Rock, Arkansas, and travels North at 60 kilometers per hour. Another train leaves at the same time and travels South at 65 kilometers per hour. how many hours will it take before they are 250 kilometers apart?
Answers
After "t" seconds they will be
65*t + 60*t seconds apart, therefore we are looking for a "t" such that
65*t + 60*t = 250
125*t = 250
so t=2
I narrowly answered the first question on my homework but for some reason EF really confuses me.
Answers
Solution
Part 1
For this case we can find DF with the following proportion formula:
[tex]\frac{AC}{AB}=\frac{DF}{DE}[/tex]And replacing we got:
[tex]\frac{4}{2}=\frac{DF}{1.34},DF=2.68[/tex]Part 2
[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]And solving for EF we got:
[tex]EF=1.34\cdot\frac{3}{2}=2.01[/tex]Use the law of sines Find each missing side or angle
Answers
The law of sine states that the ratio of Sine A and side a is just equal to the ratio of Sine B and side b which is also equal to the ratio of Sine C and side c. In formula, we have:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]where the big letter A, B, C are the angles and the small letters are the side opposite of the angle.
In our triangle, we have angle 19 and its opposite side is "x" whereas the angle opposite of the side that has a length of 32 units is unknown.
To solve the unknown angle, we know that the total measure of the angle in a triangle is 180 degrees. Therefore, the measure of the missing angle is 180 - 19 - 26 = 135 degrees.
So, going back to the law of sine, we have:
[tex]\begin{gathered} \frac{\sin19}{x}=\frac{\sin 135}{32} \\ \text{Cross multiply.} \\ 32\sin 19=x\sin 135 \\ \text{Divide both sides by sin 135.} \\ \frac{32\sin 19}{\sin 135}=\frac{x\sin 135}{\sin 135} \\ \frac{32\sin 19}{\sin 135}=x \\ \frac{10.41818094}{0.7071067812}=x \\ 14.73\approx x \end{gathered}[/tex]Therefore, the measure of the side x is approximately 14.73 units.
To solve the length of the other side, say y, the side opposite angle 26, we can make use of the law of sine again.
[tex]\begin{gathered} \frac{\sin135}{32}=\frac{\sin 26}{y} \\ y\sin 135=32\sin 26 \\ y=\frac{32\sin 26}{\sin 135} \\ y=\frac{14.0278767}{0.7071067812} \\ y\approx19.84 \end{gathered}[/tex]The length of the other missing side opposite angle 26 is approximately 19.84 units.
Answer:
14.7
Step-by-step explanation:
yes
7/9 + 2/7pls help me
Answers
We have to sum fractions:
[tex]\frac{7}{9}+\frac{2}{7}=\frac{7\cdot7+2\cdot9}{7\cdot9}=\frac{49+18}{63}=\frac{67}{63}[/tex]What is the value of the expression belowwhen y = 9 and z = 3?10y - 7z
Answers
y= 9 & z = 3
10y - 7z
put y= 9 & z = 3
= 10 (9) - 7(3)
= 90 - 21
= 69
so the answer is 69