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Problem N 4
we have the function
[tex]f\mleft(x\mright)=x^4-3x^2+2x-1[/tex]Interval (-2,2)
using a graphing tool
Local minimum value at (1,-1)
Local maximum value at (0.37,-0.65)
Increasing functionIntervals (-1.37,0.37) U (1, infinite)
Decreasing functionIntervals (-infinite, -1.37) U (0.37,1)
Related Questions
Bev got six dollars from her mom and four from her dad. she wants to buy a game that cost 18 dollars how many more she needs
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Answer
Bev needs 8 dollars more to buy her game.
Explanation
Let the amount of dollars that Bev needs be x dollars
She needs 18 dollars
She gets 6 dollars from her mom
And 4 dollars from her dad
Mathematically,
(Amount that she has currently) + (Amount that she needs) = 18
Amount that she has currently = 6 + 4 = 10 dollars
Amount that she needs = x dollars
(Amount that she has currently) + (Amount that she needs) = 18
10 + x = 18
Subtract 10 from both sides
10 + x - 10 = 18 - 10
x = 8 dollars
Hope this Helps!!!
A student solved the equation sin2x/cos x and found an answer of pi/2 Describe the student's error
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To find:
To determine whether the x = pi/2 is the answer of the equation
[tex]\frac{\sin2x}{\cos x}=2[/tex]Solution:
The solution of the equation is as follows:
[tex]\begin{gathered} \frac{\sin2x}{\cos x}=2 \\ \frac{2\sin x\cos x}{\cos x}=2 \\ \sin x=1 \\ x=\frac{\pi}{2} \end{gathered}[/tex]But at x = pi/2, the denominator of the function is zero, so, the function is not defined at x = pi/2.
Thus, the answer is "The function is not defined at x = pi/2. So, it is not the answer to the equation."
Simplify the expression, if possible. Write the answer without negative exponents. (If the solution is not a real number, enter NOT REAL.)(-216) 1/3
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The simplified expression without using negative exponents is -6 .
The given expression is of the form [tex](-216)^{\frac{1}{3}}[/tex] .
this can be written using the radical sign as ∛(-216)
Now we know that the cube root of a negative number is always a negative number .
using the properties of exponents we can write
∛(-216) = ∛(-1) × ∛216
now we know that ∛(-1) = -1 as -1³ = -1 and ∛216 = 6
Exponents are a way to show sudden increases in power. So to speak, the exponent is the amount of times a number has been multiplied by itself.
The exponent determines how many times a number is multiplied by itself, as was shown above. The mathematical notion known as the power serves as an example of the recurring multiple of the same integer or factor.
Therefore the simplified expression is -6.
To learn more about exponents visit:
https://brainly.com/question/15993626
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Farmer Ed has 2,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?
Answers
500,000cm²
Explanations:
The formula for calculating the perimeter of the fence is expressed as:
[tex]P=2(l+w)[/tex]where:
• L is the ,length, of the fencing
,• W is the ,width ,of the fencing
If Farmer Ed does not fence the side along the river, the perimeter of the river will become;
[tex]\begin{gathered} P=l+2w \\ 2000=l+2w \\ l=2000-2w \end{gathered}[/tex]The area of the rectangular plot will be expressed as:
[tex]A=lw[/tex]Substitute the expression for the length into the area to have:
[tex]\begin{gathered} A=w(2000-2w) \\ A=2000w-2w^2 \end{gathered}[/tex]If the area of the plot is maximized, then dA/dw = 0. Taking the derivative will give:
[tex]\begin{gathered} \frac{dA}{dw}=0 \\ 2000-4w=0 \\ 4w=2000 \\ w=\frac{2000}{4} \\ w=500m \end{gathered}[/tex]Calculate the length of the plot. Recall that:
[tex]\begin{gathered} l=2000-2w \\ l=2000-2(500) \\ l=2000-1000 \\ l=1000m \end{gathered}[/tex]Determine the largest area that can be enclosed
[tex]\begin{gathered} A=lw \\ A=500m\times1000m \\ A=500,000m^2 \end{gathered}[/tex]Hence the largest area that can be enclosed is 500,000cm²
2) y = x + 3 + 3 A) Domain: x 2-3 Range: y = 3 B) Domain: x 2-3 Range: y s3 C) Domain: x 2 3 Range: y 2-3 D) Domain: x 2-3 Range: y 2-3
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Domain : Domain of a function is the set of input values for which the function is real and defined.
Given function is :
[tex]y=\sqrt[]{x+3}+3[/tex]Since if x less than - 3 then the square root will be into the form of complex number i,
So x ≥ -3
So Domain will be : x ≥ -3
Interval notation : [ -3, infinity)
Range : Range is the set of all the output values of the function :
The range of the funtion is:
[tex]f(x)\ge3[/tex]Intervale notation : [3, infinity)
Domain = x ≥ -3, [-3, inifinity)
Range : f(x)≥3, Interval notation [ 3, infinity)
Answer : A)
Domain x ≥- 3
Range y ≥ 3
Suppose some government bonds are paying 5.8% simple interest. How much should you invest in the bonds if you want them to be worth $5,000 in 9 years? Round your final answer to two decimal places.
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The simple interest formula is given by:
[tex]FV=PV(1+in)[/tex]FV: future value
PV: present value
i: interest rate
n: interest periods
We have from the question:
FV: $5000
PV: ?
i: 5.8%
n: 9.
Then:
[tex]5000=PV(1+(0.058\cdot9))[/tex]Thus
[tex]PV=\frac{5000}{1.522}\Rightarrow PV=3285.15[/tex]Then, we should invest in $3285.15 to have $5000 in 9 years.
The radius of circle O (not shown) is 4, and the radian measure of central angle AOB is between 3pi/4 and 5pi/4. which could be the length of arc AB?
Answers
SOLUTION
Write out the formula for the length of an arc
[tex]\begin{gathered} \text{length of Arc=}\theta\times r \\ \text{Where }\theta\text{ is in radians } \\ r=4 \end{gathered}[/tex]Angle given is between
[tex]\frac{3\pi}{4}\text{ and }\frac{\text{5}\pi}{4}[/tex]Substitute each of the value for Θ in the formula above
[tex]\begin{gathered} \text{When }\theta=\frac{3\pi}{4} \\ \text{Then} \\ \text{Length of Arc=}\theta\times r=\frac{3\pi}{4}\times4=3\pi \end{gathered}[/tex]Also
[tex]\begin{gathered} \text{when }\theta=\frac{5\pi}{4} \\ \text{Then} \\ \text{Length of Arc=}\frac{5\pi}{4}\times4=5\pi \end{gathered}[/tex]Hence
The length of the Arc is between
[tex]\begin{gathered} 5\pi\text{ } \\ \text{and } \\ 3\pi \end{gathered}[/tex]Therefore
The length of the Arc AB could be 4π
Answer :Option B
Simplify:(2+i)-(2+3i)
Answers
Answer:
-2i
Explanation:
Given the expression:
[tex]\mleft(2+i\mright)-\mleft(2+3i\mright)[/tex]To simplify, first, we remove the brackets.
[tex]=2+i-2-3i[/tex]Next, we collect like terms and simplify.
[tex]\begin{gathered} =2-2+i-3i \\ =-2i \end{gathered}[/tex]
2 numbers whose product is -84 and whose sum is -17
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Solution
- We are asked to find two numbers with a product of -84 and a sum of -17.
- Let the two numbers be x and y.
- We can form equations using the above statement. These equations are formed below
[tex]\begin{gathered} x\times y=-84 \\ xy=-84\text{ (Equation 1)} \\ \\ x+y=-17\text{ (Equation 2)} \end{gathered}[/tex]- Now that we have the two equations, we can proceed to solve them simultaneously.
- This is done using substitution as shown below
[tex]undefined[/tex]*16. What is the leading coefficient of the polynomial function f(x) = 9-2x + 6x² + 5x³?A. 9 B. 3 C. 5 D. 4
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ANSWER :
C. 5
EXPLANATION :
The Leading coefficient is the coefficient of the leading term.
The leading term is the term with the highest degree.
From the problem, we have the polynomial :
[tex]f(x)=9-2x+6x^2+5x^3[/tex]The term with the highest degree is 5x^3
Therefore, the leading coefficient is 5
How many ways can a person toss a coin 14 times so that the number of heads is between 6 and 9 inclusive?
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How many ways can a person toss a coin 14 times so that the number of heads is between 6 and 9 inclusive?
the formula of combination is equal to
[tex]\text{nCr}=\frac{n!}{r!(n-r)!}[/tex]For r between 6 and 9
For r=6
n=14
substitute
[tex]14\text{C6}=\frac{14!}{6!(14-6)!}=\frac{14!}{6!(8)!}=\frac{14\cdot13\cdot12\cdot11\cdot10\cdot9}{6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]14C6=3,003
For r=7
n=14
substitute
[tex]14\text{C7}=\frac{14!}{7!(14-7)!}=\frac{14!}{7!(7)!}=\frac{14\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8}{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]14C7=3,432
For r=8
n=14
substitute
[tex]14\text{C8}=\frac{14!}{8!(14-8)!}=\frac{14!}{8!(6)!}=\frac{14\cdot13\cdot12\cdot11\cdot10\cdot9}{6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]14C8=3,003
For r=9
n=14
substitute
[tex]14\text{C9}=\frac{14!}{9!(14-9)!}=\frac{14!}{9!(5)!}=\frac{14\cdot13\cdot12\cdot11\cdot10}{5\cdot4\cdot3\cdot2\cdot1}[/tex]14C9=2,002
adds the combinations
3,003+3,432+3,003+2,002=11,440
11,440 waysHere are the ages (in years) of 10 professors at a college. , 44,38,45,34,28,56,54,28,61,48.what is the percentage of these professors who is younger than 47
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Solution:
Given:
The ages in years of the 10 professors at a college to be;
44,38,45,34,28,56,54,28,61,48
Professors who are younger than 47 = 44,38,45,34,28,28
Number of Professors who are younger than 47 = 6
The percentage of these professors who is younger than 47 =
[tex]\begin{gathered} =\frac{6}{10}\text{ x 100} \\ =60\text{ \%} \end{gathered}[/tex]Therefore, the percentage of professors who is younger than 47 is 60%
Which graph shows a function with a range of all real numbers greater than or equal to -1?55444-3+3+3+2-2-2+14 4-5-4-3-2-1₁ 1 2 3 4 5 x-5-4-3-111 2 3 4 5 x--5--3-2-11 1 2 3 4 5 x-2+-24-3+-3-3--4<-4O-5-4-3-2-1₁. 12-2-11-4 5 X543214+3YO
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Answer:
The graph that has a range of all real numbers greater than or equal to -1 is the graph below (top middle graph).
Explanation:
Since the range or the y-values of the graph must be greater than or equal to -1, then the graph must be increasing starting from y = -1.
Out of the 4 graphs, only the two graphs in the middle shows a graph that is increasing.
The graph at the top part is increasing starting from y = -1 while the graph at the bottom part is increasing starting from y = 1 hence, the answer is the graph at the top middle part.
4. Solve for the variable in the following proportion: 36/c = 45/10
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We need to solve for "c"in the proportion:
36/c = 45/10
so we cross multiply:
36 * 10 = 45 * c
operate
360 = 45 * c
divide by 45 on both sides to isolate "c"
360 / 45 = c
c = 8
Can you please help me answer the question?
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We have the equation:
[tex]48h-6=426[/tex]Then solve for h:
[tex]\begin{gathered} 48h-6+6=426+6 \\ 48h=432 \\ \frac{48h}{48}=\frac{432}{48} \\ h=9 \end{gathered}[/tex]Answer: B. 9 feet
Demonstrate your understanding of segment edition postulate by writing an example of a using the picture below.
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hello
segment addition postulate implies given two points and a third point between them, the sum of the first two point equals the distance of ot the third point.
i'll explain better using the question given
[tex]\begin{gathered} DN=DO+OW+WN \\ we\text{ can also say} \\ DW=DO+OW \\ ON=OW+WN \end{gathered}[/tex]given a line DN with segment O and W, the sum of DO + OW + WN = DN
Given the rectangle above, what is a possible representation of the area?
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The area of a rectangle is it's width multiplied by it's length.
For this rectangle, it's lenght is:
[tex]L=x+5[/tex]And it's width is
[tex]W=x[/tex]When you multiply both of them you get the area A:
[tex]A=L\cdot W=(x+5)\cdot x[/tex]It can also be writen as:
[tex]A=x^2+5x[/tex]Solve the system of equations by any method. -2x + 8y = 14 x – 4y= -7
Answers
-2x+8y = 14 (a)
x-4y = -7 (b)
Multiply (b) by 2 and add both equations:
-2x + 8y = 14
2x -8y = -14
___________
0 = 0
Since both variables were eliminated there is an infinite number of solutions.
1 Х 15 8 sin-1 8 =mZT 15 T 17 U
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Given:
In a right angled traingle with hypotenuse 17.
The other two length of the sides are 15 and 8.
The objective is to find the correct way of finding the angle T.
While solving a trigonometric ratio, the hypotenuse always present opposite to angle. 90 degree.
The opposite side of the triangle depends on the angle which we have to find out.
In this case, the objective is to find the measure of angle T.
So, the side opposite to angle T will be named as opposite side of right angled triangle and the reminig side will be named as adjacent side of the right angled triangle.
Since, the formula of sin is,
[tex]\sin \theta=\frac{opposite\text{ }}{hypotenuse}[/tex]If T is the angle, then opposite side is 8 and the hypotenuse is 17.
So the correct formula will be,
[tex]\begin{gathered} \sin \angle T=\frac{8}{17} \\ \angle T=\sin ^{-1}\frac{8}{17} \\ \angle T=\sin ^{-1}0.47058 \\ \angle T=28.07 \end{gathered}[/tex]Hence, the correct correct value is sin^-1 (8/17) and the measure of angle T is 28.07.
6(k-8)=96k=?help please!
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answer: k = 24
Identify the diameter of⊙Q, given that A=169π2please help
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Solution:
Given that the area of circle Q is;
[tex]A=169\pi in^2[/tex]Also, the general formula is;
[tex]\begin{gathered} A=\pi r^2 \\ \\ \text{ Where }r=radius \end{gathered}[/tex]Thus, the radius, r, of the circle is;
[tex]\begin{gathered} 169\pi=\pi r^2 \\ \\ r^2=169 \\ \\ r=\sqrt{169} \\ \\ r=13in \end{gathered}[/tex]Thus, the diameter, d, is;
[tex]\begin{gathered} d=2r \\ \\ d=2(13in) \\ \\ d=26in \end{gathered}[/tex]ANSWER: The diameter of the circle is 26in
What is the slope of the line that passes through points (0, 7) and (−3, 0)?A.–7/3B.7/3C.–3/7D.3/7
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Given:
Two points are (0,7) and (-3,0).
To find the slope of the line:
Using the slope formula,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{0-7}{-3-0} \\ =\frac{-7}{-3} \\ =\frac{7}{3} \end{gathered}[/tex]Hence, the slope is,
[tex]m=\frac{7}{3}[/tex]Therefore, the correct option is B.
Suppose that three geological study areas are set up on a map at points please check photo
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So we must find the center of the earthquake. We have three points and we know the distances from each of these points to the earthquake. In order to find the center we just need to make three circles, each centered in one of the three points and its radius must be the distance to the center of the earthquake. If we do this correctly then the three circles will meet in a given point D which is the center of the earthquake.
In order to draw a circle using the tool given by the question you'll need its center and a point in the circumference. So let's construct each of the circles:
First we have point A=(-15,2) which is at a distance of 13mi from the earthquake. So we must construct a circle centered around A with a radius of 13 units. Any point at a distance of 13 units from A will be useful, for example a point that has a horizontal distance of 13 units from A. We'll name this point E and we have:
[tex]E=(-15+13,2)=(-2,2)[/tex]So the first circle is the one that passes through (-2,2) and is centered around (-15,2).
Now we repeat this process with the other circles. We have B=(-11,1) and its distance to the earthquake is 10 miles so we can add 10 to its x-value to find a point that is at a distance of 10 units from it:
[tex]F=(-11+10,1)=(-1,1)[/tex]So this circle is centered around (-11,1) and it passes through (-1,1).
For the third circle we have C=(-6,3) and its distance to the earthquake is 5 miles. Then a point located at 5 miles from C could be:
[tex]G=(-6+5,3)=(-1,3)[/tex]So the third circle is centered around (-6,3) and passes through (-1,3).
With all this information we can graph the three circles:
As you can see these three circles intercept each other at (-3,7). Then the earth quake is located at (-3,7).
AnswerThe graphs are displayed in the picture above. The center of the earthquake is located at (-3,7).
Reason that y=f(x+a) is a horizontal translation by -a and not +a
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Solution:
Given:
[tex]y=f(x+a)[/tex]y = f(x + a) is a horizontal translation left by a units.
Hence, the coordinate is transformed as shown;
[tex](x,y)\rightarrow(x-a,y)[/tex]Hence, since it is a horizontal translation to the left, it is translated by -a units from the original x-coordinate given.
i wasn’t sure what the real answer was i did l x w and got 168
Answers
Solution
The area of the parallelogram is
[tex]\begin{gathered} A=bh \\ A=21\times8 \\ A=168in^2 \end{gathered}[/tex]Therefore the area of the figure = 168in²
The table shows coffee preference from a survey. …If a person is chosen at random in the survey what is P (regular or creamer)?
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The formula we will use to calculate the probability is given to be:
[tex]P(A\text{ or }B)=P(A)+P(B)-P(A\cap B)[/tex]Let A represent regular and B represent creamer.
We have the following parameters:
[tex]\begin{gathered} P(A)=0.78 \\ P(B)=0.41 \\ P(A\cap B)=0.32 \end{gathered}[/tex]Therefore, we can calculate the probability to be:
[tex]\begin{gathered} P(A\text{ or }B)=0.78+0.41-0.32 \\ P(A\text{ or }B)=0.87 \end{gathered}[/tex]The FOURTH OPTION is correct.
Need help with #3, also might not respond very quick. Please don’t end session if I don’t!!
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from the question,
if it takes the rate of 2 seats in 11 minutes
then we will we will set up a proportion to show how many minutes it will take at the rate of 1 seat.
so if,
so lets make the munites to make 1 seat be x
2 seats = 11 minutes
1 seat = x
lets cross multiply
2 X x = 11 X 1
2x = 11
divide both sides by 2
2x/2 = 11/2
x = 5.5 minutes
so i will take 5.5 minutes to make 1 seat.
Simplify the expression. (W6) (w^8)^3=
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We must simplify the following expression:
[tex](w^8)^3.[/tex]To simplify this expression, we must take into account the following property:
[tex](x^a)^b=x^{a\cdot b}.[/tex]Using the property above, we have:
[tex](w^8)^3=w^{8\cdot3}=w^{24}\text{.}[/tex]Answer
[tex](w^8)^3=w^{24}[/tex]At a coffee shop, the first 100customers' orders were as follows.SmallMediumLargeHot54822Cold8125What is the probability that a customerordered a small given that he or sheordered a hot drink?P(Small | Hot ) = [?]Round to the nearest hundredth.
Answers
Explanation
The probability of P(Small | Hot ) is easily observable from the table. This is given as
[tex]\begin{gathered} P(Small|Hot)=\frac{5}{5+48+22}= \\ =\frac{5}{75} \\ =0.07 \end{gathered}[/tex]The final answer is 0.07
I dont know how to do number 18 on my homework
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Beth walked 3 blocks in 15 minutes.
Then, we have that:
[tex]\frac{3}{15}\cdot\frac{3}{3}=\frac{9}{45}[/tex]We have that multiplying the rate (ratio) by the same number in the numerator and in the denominator, we will have equivalent fractions (and the same ratio).
Option a is true. We have the result above.
Then, for option b, we cannot obtain an equivalent fraction. It is false.
For option c, we have the same as for option b. It is false.
For option d:
[tex]\frac{3}{15}\cdot\frac{4}{4}=\frac{12}{60}[/tex]Then, option d is true.