The athlete will cover 17 yards in 22 minutes of his running.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.
We will use the unit conversions to solve the given problem.
The speed of the athlete is 9 mph. We can write it as -
9 mph = (9 x 1760) yards per hour = 15840 yards per hour.
15840 yards per hour = (15840/60) yards per minute = 264 yards per min.
Total yards covered in 22 minutes = 22 x 264 = 5808 yards
one lap is equivalent to 349 yards.
1 yard is equivalent to (1/349) laps
5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.
Therefore, the athlete will cover 17 yards in 22 minutes of his running.
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hello can you help me with this trigonometry question and in the question I have to answer it in radians hopefully you can help me please
Answer
(34π/7) = (6π/7) in the range of 0 and 2π.
Explanation
We are asked to find an angle between 0 and 2π that are coterminal with (that is, equal to) (34π/7).
34π/7 is 4.857π in decimal form, indicating that it is outside the required range. To find its equivalent in the required range, we keep going a full revolution (2π) till we get there.
(34π/7) - 2π = (20π/7)
This is 2.857π, which is still outside the required range, so, we subtract another revolution from this
(20π/7) - 2π = (6π/7)
This is 0.857π and it is solidly in the required region.
Hope this Helps!!!
Which systems of inequalities represents the number of apartments to be built
Given that:
- The office building contains 96,000 square feet of space.
- There will be at most 15 one-bedroom units with an area of 800 square feet. The rent of each unit will be $650.
- The remaining units have 1200 square feet of space.
- The remaining units will have two bedrooms. The rent for each unit will be $900.
Let be "x" the number of one-bedroom apartments and "y" the number of two-bedroom apartments.
• The words "at most 15 one-bedroom units" indicates that the number of these apartments will be less than or equal to 15 units:
[tex]x\leq15[/tex]• You know that the remaining units are two-bedroom apartments. And the number of them is greater than or equal to zero. Then, you can set up the second inequality to represent this:
[tex]y\ge0[/tex]• You know the area of each one-bedroom apartment, the area of each two-bedroom apartment, and the total area that the office building contains. The sum of the areas of the apartments must be less than or equal to the total area of the office building.
Then, the inequality that represents this is:
[tex]800x+1200y\leq96,000[/tex]• Therefore, you can set up this System of Inequalities to represent that situation:
[tex]\begin{gathered} \begin{cases}x\leq15 \\ \\ y\ge0 \\ \\ 800x+1200y\leq96,000 \\ \end{cases} \\ \end{gathered}[/tex]Hence, the answer is: Last option.
Can someone please help me on this question, I'm a little stuck? The question should be down below!
We have a right triangle with a missing side.
When we have two sides given sides on the right triangle and we need to find the missing side, we use the Pythagoras theorem:
The formula is given by:
[tex]a^2=b^2+c^2[/tex]Where:
a = Hypotenuse
b= Opposite side
c= Adjacent side
Now, we need to label the sides of the given triangle:
The largest side, represents the hypotenuse, in this case, a=15m.
The adjacent side is between the 90 degrees angle and the hypotenuse, in this case, c = 9m
Therefore, the missing side is the opposite side, let set b for this side:
Replacing these values:
[tex](15m)^2=b^2+(9m)^2[/tex][tex]225=b^2+81[/tex]Solve the equation for b:
[tex]225-81=b^2[/tex][tex]144=b^2[/tex][tex]\sqrt[]{144}=\sqrt[]{b^2}[/tex]Therefore, the missing side:
[tex]12=b[/tex]
Four research teamed each used a different method to collect data on how fast a new strain of maize sprouts. Assume that they all agree on the sample size and the sample mean ( in hours). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation
We need to identify the team that has the smallest sample standard deviation.
In order to do so, we need to find the stand deviation of each experiment based on the confidence level and confidence interval of each of them.
A. A confidence level of 99.7% corresponds to a confidence interval of 3 standard deviations above and 3 standard deviations below the mean.
Thus, for the confidence interval 42 to 48, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} 3\sigma=48-45=3 \\ \\ \sigma=\frac{3}{3} \\ \\ \sigma=1 \end{gathered}[/tex]B. A confidence level of 95% corresponds to a confident interval of 2 standard deviations above and 2 standard deviations below the mean.
Thus, for the confidence interval 43 to 47, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} 2\sigma=47-45=2 \\ \\ \sigma=\frac{2}{2} \\ \\ \sigma=1 \end{gathered}[/tex]C. A confidence level of 68% corresponds to a confident interval of 1 standard deviation above and 1 standard deviation below the mean.
Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} \sigma=46-45 \\ \\ \sigma=1 \end{gathered}[/tex]D. Again, we have a confidence level of 95%, which corresponds to 2 standard deviations.
Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:
[tex]\begin{gathered} 2\sigma=46-45=1 \\ \\ \sigma=\frac{1}{2} \\ \\ \sigma=0.5 \end{gathered}[/tex]Therefore, the team that has the smallest sample standard deviation is:
Answer
The numbers of trading cards owned by 9 middle- school students are given below. ( note that these are already ordered from least to greatest.
Given the numbers:
355, 382, 383, 427, 500, 572, 601, 638, 669
Total numbers = 9
a) We find the mean:
[tex]\begin{gathered} mean=\frac{355+382+383+427+500+572+601+638+669}{9} \\ mean=\frac{4527}{9}=503 \end{gathered}[/tex]Change 669 to 606:
[tex]\begin{gathered} mean=\frac{355+382+382+427+500+572+601+638+606}{9} \\ mean=\frac{4464}{9}=496 \end{gathered}[/tex]Then:
[tex]\begin{gathered} mean=changed\text{ mean}-original\text{ mean} \\ mean=496-503=-7 \end{gathered}[/tex]Answer: It decreases by 7
b) We find median
Median: 355, 382, 383, 427, 500, 572, 601, 638, 669
Median = 500
669 changed to 606
Median: 355, 382, 383, 427, 500, 572, 601, 606, 638
Median = 500
Answer: It stays the same
Solve the equation on the interval [0, 2\small \pi). Show all work. Do not use a calculator - use your unit circle!
SOLUTION
Write out the equation given
[tex]\cos ^2x+2\cos x-3=0[/tex]Let
[tex]\text{Cosx}=P[/tex]Then by substitution, we obtain the equation
[tex]p^2+2p-3=0[/tex]Solve the quadractic equation using factor method
[tex]\begin{gathered} p^2+3p-p-3=0 \\ p(p+3)-1(p+3)=0 \\ (p-1)(p+3)=0 \end{gathered}[/tex]Then we have
[tex]\begin{gathered} p-1=0,p+3=0 \\ \text{Then} \\ p=1,p=-3 \end{gathered}[/tex]Recall that
[tex]\cos x=p[/tex]Hence
[tex]\begin{gathered} \text{when p=1} \\ \cos x=1 \\ \text{Then } \\ x=\cos ^{-1}(1)=0 \\ \text{hence } \\ x=0 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} \text{When p=-3} \\ \cos x=-3 \\ x=\cos ^{-1}(-3) \\ x=no\text{ solution} \end{gathered}[/tex]Therefore x=0 is the only valid solution on the given interval [0,2π).
Answer; x=0
A car is purchased for 19,00. Each year it loses 25% of its value. After how many years will the car be worth 5800. dollars or less? Write the smallest possible whole number answer
5 years
Explanation
Given
Cost price = $ 19,000
Depreciation yearly is % 25
What to find
Time to depreciate to $ 5, 800 or less
Step- by - Step Solution
After first year St
[tex]\begin{gathered} 25\%\text{ }of\text{ 19,000} \\ \\ \frac{25}{100}\times\text{ 19,000 = 4,750} \\ \\ 19,000\text{ - 4750 = 14, 250} \end{gathered}[/tex]After the year the second year
[tex]\begin{gathered} \frac{25}{100}\text{ }\times\text{ 14, 250 = 3,562.5} \\ \\ 14,250\text{ - 3,562.5 =10, 687.5} \end{gathered}[/tex]After Third year
[tex]\begin{gathered} 25\%\text{ of 10,687.5} \\ \\ \frac{25}{100\text{ }}\times\text{ 10, 687.5 = 2,671.875} \\ \\ 10,687.5\text{ - 2,671.875 = 8,015.625} \\ \end{gathered}[/tex]After Fourth year
[tex]\begin{gathered} 25\%\text{ of 8,015.625} \\ \\ \frac{25}{100}\times\text{ 8,015.625 = 20003.906} \\ \\ 8\text{,015.625 - 20,003.906 = 6011.719} \end{gathered}[/tex]After Fifth year
[tex]\begin{gathered} 25\%\text{ of 6011.719} \\ \\ \frac{25}{100}\times\text{ 6011.719 = 1502.930} \\ \\ 6011.719-1502.930\text{ = 4508.789} \end{gathered}[/tex]Therefore after 5 years the car be worth 5800. dollars or less Therefore after 5 years the car be worth 5800. dollars or less
Write it in reduced form as a ratio of polynomials p(x)/q(x)
We are given the following expression
[tex]\frac{x^2}{x-5}-\frac{8}{x-2}[/tex]Let us re-write the expression as a ratio of polynomials p(x)/q(x)
First of all, find the least common multiple (LCM) of the denominators.
The LCM of the denominators is given by
[tex](x-5)(x-2)[/tex]Now, adjust the fractions based on the LCM
[tex]\begin{gathered} \frac{x^2}{x-5}\times\frac{(x-2)}{(x-2)}=\frac{x^2(x-2)}{(x-5)(x-2)} \\ \frac{8^{}}{x-2}\times\frac{(x-5)}{(x-5)}=\frac{8(x-5)}{(x-2)(x-5)} \end{gathered}[/tex]So, the expression becomes
[tex]\frac{x^2(x-2)}{(x-5)(x-2)}-\frac{8(x-5)}{(x-2)(x-5)}[/tex]Now, apply the fraction rule
[tex]\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]\frac{x^2(x-2)}{(x-5)(x-2)}-\frac{8(x-5)}{(x-2)(x-5)}=\frac{x^2(x-2)-8(x-5)}{(x-5)(x-2)}[/tex]Finally, expand the products in the numerator
[tex]\frac{x^2(x-2)-8(x-5)}{(x-5)(x-2)}=\frac{x^3-2x^2-8x+40}{(x-5)(x-2)}[/tex]Therefore, the given expression as a ratio of polynomials p(x)/q(x) is
[tex]\frac{x^3-2x^2-8x+40}{(x-5)(x-2)}[/tex]writing to explain in your own words tell what it meant by the absolute value of an integer
An absolute value of an integer is defined as a positive value/ digit of an integer regardless of the sign.
The symbol used is as shown below;
[tex]\parallel\text{ -3 }\parallel[/tex]or single lines as;
This means in absolute value of an integer , negative 2 is equal to positive 2.
Answer
In summary, an absolute value of an integer is a non-negative value , and the sign will only indicate direction, if well stated.
If 16 is increased to 23, the increase is what percent of the original number? (This is known as the percent of change.)
Step 1
Given data
Old value = 16
New value = 23
Step 2
Write the percentage increase formula
[tex]\text{Percentage increase = }\frac{I\text{ncrease}}{\text{Old}}\text{ }\times\text{ 100\%}[/tex]Step 3
Increase = 23 - 16 = 7
[tex]\begin{gathered} \text{Percentage increase = }\frac{7}{16}\text{ }\times\text{ 100\%} \\ =\text{ 43.75\%} \end{gathered}[/tex]How many solutions does the equation 5(m + 3) = 6-7m have? Explain how you found your answer.
Expand the left hand side using distributive property:
[tex]\begin{gathered} 5\cdot m+5\cdot3=6-7m \\ 5m+15=6-7m \\ \text{Add 7m to both sides:} \\ 5m+15+7m=6-7m+7m \\ 12m+15=6 \\ \text{subtract 15 from both sides:} \\ 12m+15-15=6-15 \\ 12m=-9 \\ \text{divide both sides by 12:} \\ \frac{12}{12}m=-\frac{9}{12} \\ m=-\frac{3}{4} \end{gathered}[/tex]a circular cylinder with a diameter of 12 cm and a height of 27 cm is filled with water. An aquarium is in the shaoe of a rectangular prism with the dimensions 35 cm 40cm by 42cm. what isvthe maximum number of full cylinders that can be poured into the fish tank without overflowing it?
Given data:
The diameter of cylinder is d=12 cm.
The height of the cylinder is h= 27 cm.
The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).
The volume of the cylinder is,
[tex]\begin{gathered} V^{\prime}=\frac{\pi}{4}(d)^2h \\ =\frac{\pi}{4}(12cm)^2(27\text{ cm)} \\ =3053.628cm^3 \end{gathered}[/tex]The volume of the aquarium is,
[tex]\begin{gathered} V=(35\text{ cm)(40 cm)(42 cm)} \\ =58800cm^3 \end{gathered}[/tex]The number of cylinders that can be pour into aquarium is,
[tex]\begin{gathered} n=\frac{V}{V^{\prime}} \\ =\frac{58800}{3053.628} \\ =19.25 \end{gathered}[/tex]Thus, the number of cylinders that can be pour into aquarium is 19.25.
Help 50 points (show ur work)
1. The value of 34% of 850 is 289.
3. The amount that Kepley paid for the tool is $120.
How to calculate the value?From the information, we want to calculate 34% of 850. This will be calculated thus:
= 34% ×850
= 34/100 × 850
= 0.34 × 850
= 289
The amount paid for the tool will be:
= Price or tool - Discount
= $200 - (40% × $200)
= $200 - $80
= $120
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Which type of statically graphic uses bars to describe the data ?Dot plot Box plot Histogram
HISTOGRAM
Explanations:
Data are reported using visuals to make reporting easier and ease the understanding of the audience.
Some of the graphic used in statistics to report data and make inference include:
• Bar charts
,• line charts
,• Dot plot
,• Box plot
,• Histogram etc.
Bar charts and histograms make use of bars to report data. This charts are important to detect outliers that may be present in our data.
We can therefore conclude that the type of statically graphic that uses bars to describe data is the HISTOGRAM
x=-3
f(x)= -2
f’(x)=2
g(x)=3
g’(x)=-1
h(x) = g(x)/2f(x)
Find h'(-3)
Answer: [tex]-1[/tex]
Step-by-step explanation:
Using the quotient rule,
[tex]h'(x)=\frac{2f(x)g'(x)-2g(x)f'(x)}{(2f(x))^2}\\\\h'(3)=\frac{2f(3)g'(3)-2g(3)f'(3)}{(2f(3))^2}\\\\=\frac{2(-2)(-1)-2(3)(2)}{2(-2)^2}\\\\=-1[/tex]
Write the equation of the line that passes through the points (12, 4) and (22,9).
Given the following points that pass through the line:
Point A : 12,4
Point B : 22,9
Step 1: Let's determine the slope of the line (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{9\text{ - 4}}{22\text{ - 12}}[/tex][tex]\text{ m = }\frac{5}{10}\text{ = }\frac{1}{2}[/tex]Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 12,4 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 4 = (}\frac{1}{2})(12)\text{ + b }\rightarrow\text{ 4 = }\frac{12}{2}\text{ + b}[/tex][tex]\text{ 4 = 6 + b}[/tex][tex]4\text{ - 6 = b}[/tex][tex]\text{ -2 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1/2 and b = -2 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (}\frac{1}{2})x\text{ + (-2)}[/tex][tex]\text{ y = }\frac{1}{2}x\text{ - 2}[/tex]Therefore, the equation of the line is y = 1/2x - 2.
if 453 runners out of 620 completed a marathon, what percent of the funners finished the race?
Answer: 73.1%
Step-by-step explanation:
620/453 = 73.1%
Pls check so you can see if correct
Given two functions f(x) and g(x):f(x) = 8x - 5,8(x) = 2x2 + 8Step 1 of 2 Form the composition f(g(x)).Answer 2 PointsKeypadKeyboard Shortcutsf(g(x)) =>Next
we have the functions
[tex]\begin{gathered} f(x)=8x-5 \\ g(x)=2x^2+8 \end{gathered}[/tex]Find out f(g(x))
Substitute the variable x in the function f(x) by the function g(x)
so
[tex]\begin{gathered} f\mleft(g\mleft(x\mright)\mright)=8(2x^2+8)-5 \\ f(g(x))=16x^2+64-5 \\ f(g(x))=16x^2+59 \end{gathered}[/tex]Find the value when x = 2 and y = 3.x ^-3y^ -3A. 54B. 216C. 1/216
Explanation:
x ^-3y^ -3
Abby scored 88, 91, 95, and 89 on her first four history quizzes. What score does Abby need to get on her fifth quiz to have an average of exactly 90 on her history quizzes? a.85b.86c.87a.88
Solution
For this case we can use the definition of average given by:
[tex]\text{Mean}=\frac{x_1+x_2+x_3+x_4+x_5}{5}[/tex]The final score needs to be 90 so we can do this:
[tex]90=\frac{88+91+95+89+x_5}{5}[/tex]And solving for x5 we got:
5*90 = 88+91+95+89+ x5
x5= 450 - 88- 91- 95 -89 = 87
Final answer:
c.87
help me please I love when I can get help
To determine in how many pices of 2/3ft can a 9ft long ribbon be cut, you have to divide 9 by 2/3:
[tex]9\div\frac{2}{3}[/tex]To divide both fractions, first turn the 9 into a fraction by adding 1 as a denominator
[tex]\frac{9}{1}\div\frac{2}{3}[/tex]Now you have to invert the fraction that is the denominator of the division
[tex]\frac{2}{3}\to\frac{3}{2}[/tex]And multiply it by the first fraction
[tex]\frac{9}{1}\cdot\frac{3}{2}=\frac{9\cdot3}{1\cdot2}=\frac{27}{2}\cong13.5[/tex]She can divide the ribbon in 13 pieces of 2/3ft each
3. Trigonometric Function a. Describe two real-world situations that could be modelled by a trigonometric function. Cannot be Ferris Wheel ride, tides, hours of daylight. Cite any Internet source you may have used for reference. b. Clearly define all variables in the relationship. c. Clearly justify why this model fits the real applications with specific reference to key features of the function. d. Your justification should also include reference to the graphical and algebraic models. e. Accurately describe what changes to the base function y = sin x would be necessary to fit both real applications.
For this problem, we need to describe a real-life situation where trigonometric functions can be used to model the problem.
Let's assume that a certain vehicle's position is controlled by the speeds of the wheels on each side of the car. Whenever the speeds on the left wheels and right wheels are equal, then the car moves forward, if the speed on the left side is greater than the one on the right side the car goes right, and if the speed on the right side is greater, then the vehicle goes to the left side. This type of car is called a differential drive car, and it's very common on remote-controlled (RC) vehicles.
If we want to model the speed of the car in a two dimensional grid, such as below:
We need to assume that the vehicle will have two components of velocity, one that is parallel to the x-axis and one that is parallel to the y-axis. These will form the linear velocity for the vehicle. We also need an angular velocity, which is the rate at which the angle of the vehicle changes.
If we assume that the wheels of the vehicles are at a distance of "L" apart from each other, then we can model the angular velocity of the vehicle as:
[tex]\omega=\frac{v_r-v_l}{L}[/tex]Where "vr" is the speed on the right wheel, and "vl" is the speed on the left wheel. The movement will happen with the center of the car as the center of the movement, with this we can assume that the velocity of the vehicle on the two axes should be:
[tex]\begin{gathered} v_x=\frac{1}{2}(v_r+v_l)\cdot cos(\theta)\\ \\ v_y=\frac{1}{2}(v_r+v_l)\cdot sin(\theta) \end{gathered}[/tex]Therefore we can describe the vehicle speed with the following equations:
[tex]\begin{gathered} \omega=\frac{v_{r}-v_{l}}{L}\\ \\ v_x=\frac{1}{2}(v_r+v_l)cos(\theta)\\ \\ v_y=\frac{1}{2}(v_r+v_l)s\imaginaryI n(\theta) \end{gathered}[/tex]The input variables are "vr" and "vl" which are the speeds of each wheel and the angle of the vehicle "theta", the output is the speed at the x coordinate and the speed at the y coordinate, and the angular speed.
This works very well because if the vehicle is moving parallel to the x-axis, the angle will be 0, the cosine of 0 is 1, therefore the speed on the y axis will be 0 and the speed on the x-axis will be given by 0.5(vr+vl). The opposite happens when the vehicle is moving parallel to the y-axis.
A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $540?
Answer
The amount invested at
Step-by-step explanation:
The total amount invested is $5000
Let x be the investment at 5%
Let y be the investment at 15%
Mathematically, this can be expressed as
x + y = 5000 -- equation 1
Since the first part of the investment is invested at 5% and the second part is at 15%
0.05x + 0.15y = 540 --------- equation 2
The systems of equations can be solved simultaneously using the substitution method
x + y =5000 ----- equation 1
0.05x + 0.15y = 540 ------ equation 2
Isolate x in equation 1
x = 5000 - y
Substitute the value of x into equation 2
0.05(5000 - y) + 0.15y = 540
Open the parenthesis
250 - 0.05y + 0.15y = 540
Collect the like terms
-0.05y + 0.15y = 540 - 250
0.1y = 290
Divide both sides by 0.1
0.1y/0.1 =290/0.1
y = $2900
Recall that equation 1 is
x + y = 5000
y = $2900
x = 5000 - y
x = 5000 - 2900
x = $ 2100
Hence, the investment at 5% is $2100 and the investment at 15% is $2900
What is the volume of the figure in cubic inches?
Solution
First, we need to convert the dimensions in feet to inches
[tex]\begin{gathered} \text{ since } \\ 1\text{ ft}=12\text{ inches} \\ \\ \Rightarrow1.5\text{ ft}=1.5\times12\text{ inches}=18\text{ inches} \\ \Rightarrow0.5\text{ ft}=0.5\times12\text{ inches}=6\text{ inches} \end{gathered}[/tex]Hence, the volume is;
[tex]V=l\times b\times h[/tex][tex]V=4\times18\times6=432\text{ inches cubic}[/tex]i have questions on a math problem. i can send when the chats open
The random sample is determined as the simplest forms of collecting data from the total population.
Under random sampling, each member of the subset carries an equal opportunity of being chosen as a part of the sampling process.
So according to the question given
Assign each person of the population a number. Put all the numbers into bowl and choose ten numbers.
is the random sample because every person carries an equal opportunity of being chosen from the total population.
Hence the correct option is A.
Find an equation for the line that passes through the points (2,2) and (-6,4)
Answer:
y=-1x/4+5/2
Step-by-step explanation:
use the slope formula
Find the coordinates of the stationary points of the curve and use the secondderivative to determine the type of each.
Calculate the derivative of the function, as shown below
[tex]\begin{gathered} y=3x+\frac{108}{x}=3x+108x^{-1} \\ \Rightarrow y^{\prime}=3+108((-1)x^{-1-1})=3-108x^{-2} \\ \Rightarrow y^{\prime}=3-108x^{-2} \end{gathered}[/tex]Set y'=0 and solve for x, as shown below
[tex]\begin{gathered} y^{\prime}=0 \\ \Rightarrow3-108x^{-2}=0,x\ne0 \\ \Rightarrow3=\frac{108}{x^2} \\ \Rightarrow x^2=\frac{108}{3} \\ \Rightarrow x^2=36 \\ \Rightarrow x=\pm\sqrt[]{36} \\ \Rightarrow x=\pm6 \end{gathered}[/tex]Their corresponding y-coordinates are
[tex]\begin{gathered} x=\pm6 \\ \Rightarrow y=3(6)+\frac{108}{6}=18+18=36 \\ \Rightarrow(6,36) \\ \text{and} \\ 3(-6)+\frac{108}{-6}=-18-18=-36 \\ \Rightarrow(-6,36) \end{gathered}[/tex]Therefore, the two stationary points are (6,36) and (-6,-36).
Using the second derivative test,
[tex]\begin{gathered} y^{\prime}=3-108x^{-2} \\ \Rightarrow y^{\doubleprime}=-108(-2x^{-2-1})=216x^{-3} \end{gathered}[/tex]Then,
[tex]\begin{gathered} y^{\doubleprime}(6)=\frac{216}{(6)^3}=1>0\to\text{ local minimum at x=6} \\ \text{and} \\ y^{\doubleprime}(-6)=\frac{216}{(-6)^3}=-1<0\to\text{ local maximum at x=-6} \end{gathered}[/tex](6,36) is a local minimum and (-6,-36) is a local maximum.
(b) The area of a rectangular window is 6205 cm .If the width of the window is 73 cm, what is its length?Length of the window: 0cm
We have that the area is 6205 cm^2 and the widht is 73 cm.
since it is a rectangle, we must use
[tex]A_{rect}=widht\cdot length[/tex]Now, we only replace values and find the value of the length
[tex]\begin{gathered} 6205cm^2=73\operatorname{cm}\cdot length \\ \text{length }=\frac{6205\operatorname{cm}}{73\operatorname{cm}} \\ \text{length }=85cm \end{gathered}[/tex]The length of the window is 85 cm.
The sugar sweet company needs to transport sugar to market. The graph below shows the transporting cost (in dollars) versus the weight of sugar being transported (in tons) a.)What is the cost of transporting 0 tonsb.) What is the cost of transporting 1 tons c.) Hos much does the cost increase for each ton of sugar being transported d.) Are the amounts given in parts b. and c. equal?
The cost of transport of tons is the point of intersection between the line and the X axis
Now we see that the point O tons, corresponds in the line to the point Y=1600
this the answer a)
For answer b) the point 1 corresponds to 2000
for answer c) the cost increase per ton is 400 , that is because 2000-1600= 400, and the line is inclined with a slope equal to 1
Tj earns a 20% commission on all sales plus a base salary of 40k. his total income last year was at least 70k. which inequality can be used to calculate the minimum of Tj sales.
Let x be the all sale for individual.
Determine the expression for total income of individual.
[tex]\frac{20}{100}x+40000=0.2x+40000[/tex]The total income was at least 70000. So last year income is 70000 or more than 70000.
Setermine the inequality for the sales.
[tex]\begin{gathered} 0.2x+40000-40000\ge70000-40000 \\ \frac{0.2x}{0.2}\ge\frac{30000}{0.2} \\ x\ge150000 \end{gathered}[/tex]