What is the volume of the cone? 1 Use the formula 1 = 6 cm 1 1 18 cm 1 1 1 1 A 16-em> or < 50.3 cm B) 32cm or 100.5 CMS 8 cm or
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Let f(x) = 6.4 sin(x) + 5.9 cos(x). What is the maximum and minimum value of thisfunction?
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SOLUTION
From f(x) = 6.4 sin(x) + 5.9 cos(x)
[tex]\begin{gathered} \text{The maximum value occurs at where }\frac{d\text{ y}}{d\text{ x}}\text{ = 0 } \\ \end{gathered}[/tex]So we will differentiate the function f(x) = 6.4 sin(x) + 5.9 cos(x)
f(x) = 6.4 sin(x) + 5.9 cos(x)
f'(x) = 6.4 cos(x) - 5.9 sin(x)
6.4 cosx - 5.9 sinx = 0
Squaring both sides we have
[tex]\begin{gathered} 6.4\cos x\text{ + 5.9sinx = 0 } \\ \text{recall that cos x = }\sqrt[]{1-sin^2x} \\ 6.4\text{ }\sqrt[]{1-sin^2x}\text{ + 5.9sinx = 0 } \\ 6.4\text{ }\sqrt[]{1-sin^2x}=\text{ -5.9sinx} \\ \text{square both sides } \\ 40.96(1-sin^2x)=34.81sin^2x \\ 40.96-40.96sin^2x\text{ = }34.81sin^2x \\ 40.96=75.77sin^2x \\ \sin ^2x\text{ = 0.541 taking squaroot} \\ \text{sinx = }\sqrt[]{0.541} \\ \sin x\text{ = 0.735} \\ x\text{ = }\sin ^{-1}0.735 \\ x\text{ = 47.35} \end{gathered}[/tex]We have gotten the value for x, now let's find our maximum and minimum values
[tex]\begin{gathered} f(x)\text{ = 6.4sin(47.35) + 5.9cos(47.35)} \\ =\text{ 4.707 + 3.997} \\ =\text{ 8.70}4 \end{gathered}[/tex]Therefore, the maximum value is 8.704 and the minimum value is -8.707
Note that maximum value is just the direct opposite of minimum value
In the past year, the number of frogs living in a pond had increased by 10% to 528, and the number of newts living there too had increased by 15% to 621. How many frogs and newts lived in the pond a year ago
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Answer:
480 frogs, 540 newts
Step-by-step explanation:
528 ÷ 1.10 = 480 frogs
621 ÷ 1.15 = 540 newts
Aaaaaaaaaaaaaaaaaaaaaaa
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To be Liam's puzzle true, then the numbers must be one positive and one negative, that way their products will always be less than the numbers.
Hence, the answer is D.would adam snitch agree that gross domestic product is the best way to measure
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GDP measures our ability to obtain many of the inputs into a worthwhile existence but does not directly measure the things that make life valuable.
What is meant by GDP?GDP accounts for both total income and total expenditure on goods and services in the economy. Thus, GDP per person tells us about the average person's income and expenditure in the economy. Because most people would prefer to have a higher income and spend more money, The average person's GDP per person appears to be a straightforward indicator of their financial security.
People want to know whether an economy's total output of goods and services is increasing or decreasing. However, because GDP is collected at current, or nominal, prices, it is impossible to compare two periods without accounting for inflation.
To calculate "real" GDP, the nominal value must be adjusted to account for price changes, allowing us to see whether the value of output has increased because more is produced or simply because prices have risen.
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Acellus Find the area of the shaded region. 60° 5 cm A = [?] cm2 Enter a decimal rounded to the nearest tenth.
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hello
to solve this question, we simply need to apply the formula of area of a segment
the formula is given as
[tex]A_{\text{segment}}=\frac{1}{2}\times(\theta-\sin \theta)\times r^2[/tex]let's write out the variables given in the question
[tex]\begin{gathered} \theta=60^0 \\ r=5\operatorname{cm} \end{gathered}[/tex]we can now input those values into the equation
[tex]\begin{gathered} A_{\text{segment}}=\frac{1}{2}\times(\theta-\sin \theta)\times r^2 \\ A_{\text{segment}}=\frac{1}{2}\times(60-\sin 60)\times5^2 \\ A_{\text{segment}}=\frac{1}{2}\times(60-0.8660)\times25 \\ A_{\text{segment}}=\frac{1}{2}\times1478.35 \\ A_{\text{segement}}=739.175\operatorname{cm}^2 \end{gathered}[/tex]to get the value of the area of the shaded region,
[tex]\text{area of shaded region=area of circle - area of segment}[/tex]let's calculate the area of the circle
[tex]undefined[/tex]A tract of land, indicated by Quadrilateral MNPQ, is shown on this grid where one square unit represents 50 square feet.What is the area, in square feet, of the tract of land?
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We have to find the area of the quadrilateral MNPQ.
We can divide it in two right triangles and then calculate the area as the sum of the area of the two triangles. To do that we would have to calculate the distances between N and P and M and N, as this are the legs of the upper triangle.
We can simplify it by making three right triangles by adding one vertex R(1,0):
Now, the length of the legs of the triangles are easier to find.
We then can calculate the area of the quadrilateral (A) as:
[tex]\begin{gathered} A=A_{\text{MRN}}+A_{\text{PRN}}+A_{\text{MPQ}} \\ A=\frac{(MR)\cdot(RN)}{2}+\frac{(PR)\cdot(RN)}{2}+\frac{(MP)(PQ)}{2} \\ A=\frac{1}{2}(9\cdot6+4\cdot6+13\cdot8) \\ A=\frac{1}{2}(54+24+104) \\ A=\frac{1}{2}\cdot182 \\ A=91 \end{gathered}[/tex]The area covers 91 square units.
As each unit represents 50 square feet, we can calculate the area in feet as:
[tex]A=91\text{ sq. units}\cdot\frac{50\text{ sq. ft.}}{1\text{ sq. unit}}=4550\text{ sq. ft.}[/tex]Answer: the land's area is 4550 square feet.
Can anyone help me this please this is my last question to pass
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Lets take 2 pair of points from the table:
[tex]\begin{gathered} (x_1,y_1)=(0,4) \\ (x_2,y_2)=(2,10) \end{gathered}[/tex]The equation of line is y = mx + b
Where
m is slope
b is y-intercept
Let's find the slope (m):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{10-4}{2-0} \\ m=\frac{6}{2} \\ m=3 \end{gathered}[/tex]So, the equation becomes:
[tex]y=3x+b[/tex]Let's plug in the first point (x, y) = (0,4) to find b:
[tex]\begin{gathered} y=3x+b \\ 4=3(0)+b \\ 4=0+b \\ b=4 \end{gathered}[/tex]Final Equation of the line:
[tex]y=3x+4[/tex]What is the slope of the line shown below?10(-6,3)5(12,5)5101610OAA.6B. -6C. -D. 6
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Consider that the slope (m) of a line passing through two given points is calculated using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]It is evident from the graph that points (-6,3) and (12,6) lie on the line,
[tex]\begin{gathered} (x_1,y_1)=(-6,3) \\ (x_2,y_2)=(12,6) \end{gathered}[/tex]Then, substitute the values in the formula to obtain the slope of the given line,
[tex]\begin{gathered} m=\frac{6-3}{12-(-6)} \\ m=\frac{3}{12+6} \\ m=\frac{3}{18} \\ m=\frac{3}{6\cdot3} \\ m=\frac{1}{6} \end{gathered}[/tex]Thus, the slope of the given line is,
[tex]\frac{1}{6}[/tex]Therefore, option A is the correct choice.
The coordinates of quadrilateral ABCD are A(3,4), B(2,7), C(2,8), and D(5,3). Do thediagonals bisect each other?
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The image below shoes the given quadrilateral.
An important fact we need to know is that diagonals bisect when we have a symmetrical quadrilateral. As you can see in the image above, the quadrilateral is not symmetrical, it's not square like nor rectangle like.
Therefore, its diagonals don't intersect.Find the solution set of the quadratic inequalities3x^2 - 15x - 18 > 0
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Given -
3x²- 15x - 18 > 0
To Find -
The solution set of the quadratic inequalities =?
Step-by-Step Explanation -
Firstly, We will find the solution to the quadratic equation.
3x²- 15x - 18 = 0
[tex][/tex]you are machinist setting up a part that requires a5/8 inch diameter finished hole.stardart practice is to drill an initial g hole with a diameter that is undersided by 1/32 inch before finishing What should be the diameter inches of the initial hole?
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We will have that the initial size of the hole should be:
[tex]\frac{5}{8}-\frac{1}{32}=\frac{19}{32}[/tex]So, the diameter of the initial hole should be 19/32 inches.
I need help I think I’m supposed to multiply straight across
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To find the whole answer, let's look at each multiplication:
[tex]\frac{5280ft}{1\text{ mile}}\cdot\frac{30\text{ miles}}{1\text{ hour}}=\frac{5280ft\cdot30\text{miles}}{miles\cdot hour}=\frac{158400ft}{\text{hour}}[/tex]Now, it changes from hours to minutes:
Use, 1hour = 60 minutes
[tex]\frac{158400\text{ ft}}{1\text{ hour}}\cdot\frac{1\text{ hour}}{60\text{ minutes}}=\frac{158400\text{ ft}\cdot\text{hour}}{\text{hour}\cdot\text{ 60 minutes }}=\frac{158400ft}{60\text{ minutes}}[/tex]Then, it changes from minutes to seconds:
Use, 1 minute = 60 seconds
[tex]\frac{158400\text{ ft}}{60\text{ minutes}}\cdot\frac{1\text{ minute}}{60\text{ seconds}}=\frac{158400\text{ ft}\cdot1\text{ minute}}{60minutes\cdot60\text{seconds}}=\frac{158400\text{ ft}}{3600\text{ seconds}}[/tex]Then:
[tex]\frac{158400\text{ ft}}{3600\text{ second}}=44\text{ f}eet\text{ per second}[/tex]need help asappppppp
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To find a, we will use the Pythagoras theorem,
adjacent² + opposite² = hypotenuse²
From the diagram, opposite = 5 adjacent = a hypotenuse =13
substitute the values into the formula and evaluate
a² + 5² = 13²
a² + 25 =169
subtract 25 from both-side of the equation
a² = 169 - 25
a² =144
Take the square root of both-side
a = 12
find the grade-point average. assume A=4,B=3,C=2,D=1 and F=0
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Average is define as the ratio of sum of all the data to the total number of data
[tex]\text{Average=}\frac{Sum\text{ of all the data}}{Total\text{ number of data}}[/tex]In the given question , we hvae five grades
[tex]\begin{gathered} A=4 \\ B=3 \\ C=2 \\ D=1 \\ F=0 \end{gathered}[/tex]Total number of data=5
Use the expression of average to find the average of grade point
[tex]\begin{gathered} \text{Average}=\frac{4+3+2+1+0}{5} \\ \text{Average}=\frac{10}{5} \\ \text{Average}=2 \end{gathered}[/tex]The average of the grade-point is 2.
Help me solve this hw problem pls formula for getting g(x)
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Answer:
Explanation:
Given:
A graph of f(x) in red and a graph of g(x) in blue
To find:
the formula for getting g(x)
First, we need to determine the function for f(x) from the graph
The roots of the function for f(x) are -4, 0, 4
The line crosses the x axis at x = -4, x = 0 and x = 4
x + 4 = 0, x - 0 = 0, x - 4 = 0
The factors: (x + 4)(x - 0)(x - 4)
[tex]\begin{gathered} f(x)\text{ = \lparen x + 4\rparen\lparen x\rparen\lparen x - 4\rparen} \\ Expanding\text{ the function:} \\ f(x)\text{ = \lparen x}^2\text{ + 4x\rparen\lparen x - 4\rparen} \\ f(x)\text{ = x}^2(x\text{ - 4\rparen + 4x\lparen x - 4\rparen} \\ f(x)\text{ = x}^3\text{ - 4x}^2\text{ + 4x}^2\text{ - 16x} \\ f(x)\text{ = x}^3\text{ - 16x} \end{gathered}[/tex]Comparing the coordinates of f(x) and g(x):
[tex]\begin{gathered} From\text{ the graph of g\lparen x\rparen in blue} \\ when\text{ x = -4, y = 3, g\lparen x\rparen} \\ \text{ when x = 0, y = 0 f\lparen x\rparen} \\ \\ when\text{ x = 2, y = 2 g\lparen x\rparen} \\ when\text{ x = 2, y = -4 f\lparen x\rparen} \\ \\ when\text{ x = 4, y = 0 f\lparen x\rparen} \\ when\text{ x= 4, y = 3 g\lparen x\rparen} \end{gathered}[/tex]
Find the area 21 m 7 m 21 m O A. 1543.5 m2 O B. 220.5 m2 OC. 294 m2 OD. 588 m2
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EXPLANATION
Given the sides: 21m , 7m and 21 m
The Area is equal to:
Are
There are 100 jelly beans in a jar, 15 are black. 20 are red, 25 are yellow and 30 are green and the are orange. Write a fraction in the simplest form of the number of jelly beans that are orange Explain your reasoning for your answer.
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Answer:
The fraction of the number of jelly beans that are orange is;
[tex]\frac{1}{10}[/tex]Explanation:
Given that;
There is a total of 100 jelly beans in the jar.
Of the total;
15 are black
20 are red
25 are yellow
30 are green
And the rest are orange.
The number of orange jelly beans can be calculated by deducting the number of black,red,yellow,and green jelly beans from the total.
[tex]\begin{gathered} n=100-(15+20+25+30) \\ n=100-90 \\ n=10 \end{gathered}[/tex]So, there are 10 orange jelly beans in the jar.
We now need to write a fraction of the number of jelly beans that are orange;
[tex]\begin{gathered} f_o=\frac{\text{ number of orange jelly beans }}{\text{Total number of jelly beans}} \\ f_o=\frac{10}{100} \\ f_o=\frac{1}{10} \end{gathered}[/tex]Therefore, the fraction of the number of jelly beans that are orange is;
[tex]\frac{1}{10}[/tex]
Solve for x in the equation x2+2x+ 1 = 17.X=-1+ /15X=-1+ /17X=-2+2.15X=-1+ /13
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First, write the quadratic equation in standard form. Then, use the quadratic formula to find the solutions for the quadratic equation.
Remember that if a quadratic equation is written in standard form:
[tex]ax^2+bx+c=0[/tex]Where a, b and c are constants, then the solutions for x are given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Starting with the given equation:
[tex]x^2+2x+1=17[/tex]Substract 17 from both members to write the equation in standard form:
[tex]\begin{gathered} \Rightarrow x^2+2x+1-17=17-17 \\ \Rightarrow x^2+2x-16=0 \end{gathered}[/tex]Use the quadratic formula, setting a=1, b=2 and c=-16:
[tex]\begin{gathered} x=\frac{-(2)\pm\sqrt[]{(2)^2-4(1)(-16)}}{2(1)} \\ =\frac{-2\pm\sqrt[]{4+64}}{2} \\ =\frac{-2\pm\sqrt[]{68}}{2} \end{gathered}[/tex]Simplify the expression using the properties of radicals. Since 68 is equal to 4 times 17, then:
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{68}}{2} \\ =\frac{-2\pm\sqrt[]{4\cdot17}}{2} \\ =\frac{-2\pm\sqrt[]{4}\cdot\sqrt[]{17}}{2} \\ =\frac{-2\pm2\cdot\sqrt[]{17}}{2} \\ =\frac{2(-1\pm\sqrt[]{17})}{2} \\ =-1\pm\sqrt[]{17} \end{gathered}[/tex]Therefore, the solutions for x in the given equation are:
[tex]\begin{gathered} x_1=-1+\sqrt[]{17} \\ x_2=-1-\sqrt[]{17} \end{gathered}[/tex]A rectangular room is 2 times as long as it is wide, and its perimeter is 48 meters. Find the dimension of the room.
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Answer:
=16cm
Step-by-step explanation:
Let's read the problem carefully:
it says that one side of the rectangular room (let's call it b) is twice as long as the other (let's call it a), which in mathematical terms would be b = 2*a
It also says that the perimeter of the room is 48 meters, which means that (a + b)*2 = 48 => a + 2*a = 48/2 =>
3*a = 24 => a = 8, b = 16
surface area for 3ft length 3ft width and 3ft height
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We are given a cube of side 3 ft and we are asked to determine its surface area. The surface area of a cube is 6 times the area of one of its faces. The area of its faces is the side squared, therefore, the total surface area is:
[tex]S=6l^2[/tex]Where:
[tex]l=\text{ length of the side }[/tex]Now, we plug in the value of the side:
[tex]S=6(3ft)^2[/tex]Solving the operations:
[tex]S=54ft^2[/tex]Therefore, the surface area is 54 square feet.
Distributive Property: -3 1/2 divided by 1/2
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ANSWER
-7
EXPLANATION
We want to solve the given fractional division by using the distributive property.
Basically, we are going to split the numerator into smaller pieces to make the division simpler.
That is:
[tex]\begin{gathered} \frac{-3\frac{1}{2}}{\frac{1}{2}} \\ =\text{ }\frac{\frac{-7}{2}}{\frac{1}{2}} \\ =\text{ }\frac{(\frac{-6}{2}\text{ - }\frac{1}{2})}{\frac{1}{2}} \\ =\frac{(-3\text{ - }\frac{1}{2})}{\frac{1}{2}} \\ =\frac{-3}{\frac{1}{2}}\text{ - }\frac{\frac{1}{2}}{\frac{1}{2}} \\ =\text{ -6 - 1} \\ =\text{ -7} \end{gathered}[/tex]Use angle relationships (complementary, supplementary, vertical, or adjacent) to find the measure of angle b.
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Answer:
vertical, b = 46
Explanation:
Two angles are vertical if they are formed by intersection of two lines.
For examole, the follwing angles are vertical.
The angles b and 46 are vertical, and therefore, their measures are the same.
Therefore,
[tex]b=46^o[/tex]if a plane can travel 480 miles per hour with the wind and 380 miles per hour against the wind,find the speed of the wind and the speed of the plane in still air . what is the speed of the plane in still air .
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Let x be the speed of the plane while still in the air and let y be the speed of the wind
so
x + y = 480mph ......(1)
x - y = 380mph ...... (2)
add both equations and solve for x
2x = 860 mph
x = 860/2=430mph = speed of the plane while stil in air
using equation .....(1)
430 + y =480 mph
y = 480 - 430 = 50 mph =speed of the wind
Which system type is a linear system with infinitely many solutions?InconsistentConsistent dependentInconsistent dependentConsistent independent
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We are asked which system type is a linear system with infinitely many solutions.
Inconsistent = No solution
Consistent independent = One solution
Consistent dependent = infinitely many solutions.
In a consistent dependent system, the lines are merged and they basically become the same line. Hence, every coordinate pair on the line is a solution to both lines.
Therefore, the correct answer is Consistent dependent.
A consistent dependent system is a linear system with infinitely many solutions.
Which graph represents y as a function of x? please help!! im sorry if not all photos show up
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The graph does not represent a function between y and x.
How to check if the graph is a function?A function is a relation that maps inputs x into outputs y, such that each input is mapped into at most one output.
To check if a graph belongs to a function, we need to do the vertical line test, this means that if we draw a vertical line on the coordinate axis where we have the graph, and that vertical line touches the graph at more than one point, then the graph does not represent a function.
In this case, if we draw a line at x = 1 we will intersect the graph twice, then it is not a function.
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Sket the right triangle and find the length of decide not given it necessari approximate the length to the nearest thousand
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Since we are dealing with a right triangle, we can use the Pythagorean theorem, shown below
[tex]\begin{gathered} H^2=L^2_1+L^2_2 \\ H\to\text{ hypotenuse} \\ L_1,L_2\to\text{ legs} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} H=15,L_1=3 \\ \Rightarrow L^2_2=15^2-3^2=216 \\ \Rightarrow L_2=\sqrt[]{216}=14.6969\ldots\approx14.697 \\ \Rightarrow L_2=14.697 \end{gathered}[/tex]The answer is 14.697
car is coasting backwards downhill at a speed of 2.9 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 4.8 m/s. Assuming that the uphill is the positive direction, what is the car's average acceleration? m/s2
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The average acceleration of the car is 3.08 m/s² .
The speed of the car down hill = - 2.9m/s
The speed of the car uphill = 4.8 m/s
An object's average acceleration over time is determined by dividing the change in velocity, Δv, by the duration of the period, Δt.
Average acceleration = Δv ÷ Δt
Now the change in velocity ΔV = 4.8 - (-2.9) = 7.7 m/s
Change is time Δt = 2.5 seconds
Average acceleration of the car = 7.7 / 2.5 m/s² = 3.08 m/s²
In mechanics, the acceleration is the change is speed that refers to the exact rate at which the object's velocity varies with respect to time varies. Acceleration is a vector quantity since it has both a magnitude and a direction. The direction of an object's acceleration is determined by the direction of the net force acting on it.
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What do you notice and /or wonder about the second graph in the image above
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The second graph A'B'C' is the result of a reflection over x axis of the figure ABC; You can see that because the coordinates of the points follow the next rule:
[tex]P(x,y)\rightarrow P^{\prime}(x,-y)[/tex]Point A: (-2,1) becomes A'(-2,-1)
Point B: (1,4) becomes B'(1,-4)
Point C: (3,2) becomes C'(3,-2)
I will show you the question
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The given system is
[tex]\begin{cases}3x+6y=12 \\ x+2y=4\end{cases}[/tex]First, we multiply the second equation by -3.
[tex]\begin{cases}3x+6y=12 \\ -3x-6y=-12\end{cases}[/tex]Then, we combine the equations
[tex]\begin{gathered} 3x-3x+6y-6y=12-12 \\ 0=0 \end{gathered}[/tex]This means the system has infinitely many solutions.
Hence, the answer is D.How would I solve Question 1 & 2 to find g(x)-f(x)
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We will have the following:
1)
[tex]g(x)-f(x)=5^x-12-3x[/tex]2)
[tex]\begin{gathered} f(x)-g(x)=log_3(5x-5)-log_3(x-1) \\ \\ \Rightarrow f(x)-g(x)=log_3(\frac{5x-5}{x-1}) \\ \\ \Rightarrow f(x)-g(x)=log_3(5) \end{gathered}[/tex]