Answer:
x = 5 or x = -2 or 3 - 2 x (derivative)
Step-by-step explanation:
Solve for x over the real numbers:
-x^2 + 3 x + 10 = 0
Multiply both sides by -1:
x^2 - 3 x - 10 = 0
x = (3 ± sqrt((-3)^2 - 4 (-10)))/2 = (3 ± sqrt(9 + 40))/2 = (3 ± sqrt(49))/2:
x = (3 + sqrt(49))/2 or x = (3 - sqrt(49))/2
sqrt(49) = sqrt(7^2) = 7:
x = (3 + 7)/2 or x = (3 - 7)/2
(3 + 7)/2 = 10/2 = 5:
x = 5 or x = (3 - 7)/2
(3 - 7)/2 = -4/2 = -2:
Answer: x = 5 or x = -2
____________________________________
Find the derivative of the following via implicit differentiation:
d/dx(H(x)) = d/dx(10 + 3 x - x^2)
Using the chain rule, d/dx(H(x)) = ( dH(u))/( du) ( du)/( dx), where u = x and d/( du)(H(u)) = H'(u):
(d/dx(x)) H'(x) = d/dx(10 + 3 x - x^2)
The derivative of x is 1:
1 H'(x) = d/dx(10 + 3 x - x^2)
Differentiate the sum term by term and factor out constants:
H'(x) = d/dx(10) + 3 (d/dx(x)) - d/dx(x^2)
The derivative of 10 is zero:
H'(x) = 3 (d/dx(x)) - d/dx(x^2) + 0
Simplify the expression:
H'(x) = 3 (d/dx(x)) - d/dx(x^2)
The derivative of x is 1:
H'(x) = -(d/dx(x^2)) + 1 3
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.
d/dx(x^2) = 2 x:
H'(x) = 3 - 2 x
Simplify the expression:
Answer: = 3 - 2 x
A model for the average price of a pound of white sugar in a certain country from August 1993 to August 2003 is given by the function
S(t) = −0.00003237t5 + 0.0009037t4 − 0.008956t3 + 0.03629t2 − 0.04547t + 0.4778
where t is measured in years since August of 1993. Estimate the times when sugar was cheapest and most expensive during the period 1993-2003. (Round your answers to three decimal places.)
t= __________________________ (cheapest)
t=__________________________ (most expensive)
Answer:
[tex]t = 0.811\,s[/tex] contains the cheapest reference to sugar; [tex]t = 4.511\,s[/tex] contains the most expensive reference to sugar.
Step-by-step explanation:
Let be [tex]s(t) = -0.00003237\cdot t^{5} + 0.0009037\cdot t^{4}-0.008956\cdot t^{3}+0.03629\cdot t^{2}-0.04547\cdot t + 0.4778[/tex], the times when sugar is the cheapest and the most expensive (absolute minimum and maximum) are determined with the help of first and second derivatives of this function (First and Second Derivative Tests):
First Derivative Test
[tex]s'(t) = -0.00016185\cdot t^{4}+0.0036148\cdot t^{3}-0.026868\cdot t^{2}+0.07258\cdot t - 0.04547[/tex]
Let equalize the polynomial to zero and solve the resulting expression:
[tex]-0.00016185\cdot t^{4}+0.0036148\cdot t^{3}-0.026868\cdot t^{2}+0.07258\cdot t - 0.04547 = 0[/tex]
[tex]t_{1} \approx 9.511\,s[/tex], [tex]t_{2}\approx 7.431\,s[/tex], [tex]t_{3}\approx 4.511\,s[/tex] and [tex]t_{4}\approx 0.881\,s[/tex]
Second Derivative Test
[tex]s''(t) = -0.0006474\cdot t^{3}+0.0108444\cdot t^{2}-0.053736\cdot t+0.07258[/tex]
This function is now evaluated at each root found in the First Derivative section:
[tex]s''(9.511\,s) = -0.0006474\cdot (9.511\,s)^{3}+0.0108444\cdot (9.511\,s)^{2}-0.053736\cdot (9.511\,s)+0.07258[/tex]
[tex]s''(9.511\,s) = -0.015[/tex] (A maximum)
[tex]s''(7.431\,s) = -0.0006474\cdot (7.431\,s)^{3}+0.0108444\cdot (7.431\,s)^{2}-0.053736\cdot (7.431\,s)+0.07258[/tex]
[tex]s''(7.431\,s) = 6.440\times 10^{-3}[/tex] (A minimum)
[tex]s''(4.511\,s) = -0.0006474\cdot (4.511\,s)^{3}+0.0108444\cdot (4.511\,s)^{2}-0.053736\cdot (4.511\,s)+0.07258[/tex]
[tex]s''(4.511\,s) = -8.577\times 10^{-3}[/tex] (A maximum)
[tex]s''(0.811\,s) = -0.0006474\cdot (0.811\,s)^{3}+0.0108444\cdot (0.811\,s)^{2}-0.053736\cdot (0.811\,s)+0.07258[/tex]
[tex]s''(0.811\,s) = 0.036[/tex] (A minimum)
Each value is evaluated in order to determine when sugar was the cheapest and the most expensive:
Cheapest (Absolute minimum)
[tex]s(0.811\,s) = -0.00003237\cdot (0.811\,s)^{5}+0.0009037\cdot (0.811\,s)^{4}-0.008956\cdot (0.811\,s)^{3}+0.03629\cdot (0.811\,s)^{2}-0.04547\cdot (0.811\,s)+0.4778[/tex]
[tex]s(0.811\,s) = 0.460[/tex]
[tex]s(7.431\,s) = -0.00003237\cdot (7.431\,s)^{5}+0.0009037\cdot (7.431\,s)^{4}-0.008956\cdot (7.431\,s)^{3}+0.03629\cdot (7.431\,s)^{2}-0.04547\cdot (7.431\,s)+0.4778[/tex]
[tex]s(7.431\,s) = 0.491[/tex]
[tex]t = 0.811\,s[/tex] contains the cheapest reference to sugar.
Most expensive (Absolute maximum)
[tex]s(4.511\,s) = -0.00003237\cdot (4.511\,s)^{5}+0.0009037\cdot (4.511\,s)^{4}-0.008956\cdot (4.511\,s)^{3}+0.03629\cdot (4.511\,s)^{2}-0.04547\cdot (4.511\,s)+0.4778[/tex]
[tex]s(4.511\,s) = 0.503[/tex]
[tex]s(9.511\,s) = -0.00003237\cdot (9.511\,s)^{5}+0.0009037\cdot (9.511\,s)^{4}-0.008956\cdot (9.511\,s)^{3}+0.03629\cdot (9.511\,s)^{2}-0.04547\cdot (9.511\,s)+0.4778[/tex]
[tex]s(9.511\,s) = 0.498[/tex]
[tex]t = 4.511\,s[/tex] contains the most expensive reference to sugar.
The required values are,
[tex]t=0.881199[/tex] at the cheapest.
[tex]t=4.51081[/tex] at the most expensive.
Minimum or Maximum:A high point is called a maximum (plural maxima ). A low point is called a minimum (plural minima ).
Given equation is,
[tex]S(t) = -0.00003237t^5 + 0.0009037t^4- 0.008956t^3 + 0.03629t^2-0.04547t + 0.4778[/tex]
Differentiating the given equation we get,
[tex]S'(t)=-0.00003237\times 5t^4+0.0009037\times 4t^3-0.008956\times 3t^2+0.03629\times 2t-0.04547+0\\S'(t)=0\\-0.00003237\times 5t^4+0.0009037\times 4t^3-0.008956\times 3t^2+0.03629\times 2t-0.04547+0=0\\t=0.881199\\t=4.51081\\t=7.43087\\t=9.51137\\[/tex]
Now we can directly plug those fours values of t into given function S(t) to find which one gives max or minimum or you can also use the 2nd derivative test. Although that is not compulsory
[tex]t=0.881199,S(t)=0.46031095\\t=4.51081, S(t)=0.50278423\\t=7.43087, S(t)=0.49096762\\t=9.51137, S(t)=0.49832202\\[/tex]
We see that sugar is cheapest at [tex]t=0.881199[/tex] which is approx 1 and corresponds to the year [tex]1993+1=1994[/tex]
Similarly sugar is most expensive at [tex]t=4.51081[/tex] which is approx 5 and corresponds to year [tex]1993+5=1998[/tex]
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A square and a rectangle have the same area. If the dimensions of the rectangle are 4 ft by 16 ft, how long is a side of the square?
Answer:
8
Step-by-step explanation:
4×16=64
[tex] \sqrt{64 } = 8[/tex]
if the current time is 10:35 how long until it turns 3:15
Answer:
10:35-3:15
5 hoursradical 16 * redical 12
[tex]\sqrt{16}\times\sqrt{12}[/tex]
$=\sqrt{4^2}\times\sqrt{2^2\cdot3}$
$=4\times2\sqrt3=8\sqrt3$
Please answer this question
How do you find the equation of a parabola given the coordinates?
Answer:
the general equation of parabola is,
y=ax²+bx+c,
you put the given points in the equation since they will satisfy the equation, after that you should get three equations with only a,b,c in them, solve them for a,b,c and find their values, then just put the values in the main equation, which is, y=ax²+bx+c, that's all you have to do
Find the distance between (-8, 4) and (-8, -2).
10 units
2 units
6 units
8 units
Answer:
10
Step-by-step explanation:
The greater than symbols looks like this ____________, and the less than symbol looks like?
Answer:
The greater than symbols looks like this > , and the less than symbol looks like? <
Answer:
Greater than symbol: >
Less than symbol: <
Greater than or equal to symbol: ≥
Less than or equal to symbol: ≤
Equal symbol: =
In this case, you are answering with the greater than symbol as well as the less than symbol.
The greater than symbols looks like this > , and the less than symbol looks like < .
Solve for
x
Round to the nearest tenth, if necessary.
9514 1404 393
Answer:
x = 5.0
Step-by-step explanation:
The tangent relation is helpful:
Tan = Opposite/Adjacent
tan(50°) = x/4.2
x = 4.2·tan(50°) ≈ 5.0054 . . . . multiply by 4.2
x ≈ 5.0
What is the rate of change from x = 0 to x = pi over 2 ? (6 points) trig graph with points at (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4)
Answer: [tex]\dfrac{8}{\pi}[/tex] .
Step-by-step explanation:
We know that the rate of change of function f(x) from x=a to x= b is given by :-
[tex]k=\dfrac{f(b)-f(a)}{b-a}[/tex]
The given points on graph : (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4).
The rate of change from x = 0 to x = pi over 2 will be :-
[tex]\dfrac{0-(-4)}{\dfrac{\pi}{2}-0}=\dfrac{4}{\dfrac{\pi}{2}}[/tex] [By using points (0, -4) and (pi over 2, 0) ]
[tex]=\dfrac{8}{\pi}[/tex]
Hence, the rate of change from x = 0 to x = pi over 2 is [tex]\dfrac{8}{\pi}[/tex] .
graph 3x-y-2=0 using the x- and y-intercepts
Step-by-step explanation:
I used an app called DESMOS It Is usually super helpful!!!
Please Help Me I will probably post more like this as its the only thing really that's holding me back from passing 5th grade on khan academy math!!
Answer:
330 cm^3
Step-by-step explanation:
Volume of figure=Volume of the cuboid+Volume of the other cuboid
Volume of figure=240+90=330
Tessa’s employee benefits include family health care coverage. She contributes 18% of the cost. Tessa gets paid biweekly and $108.00 is taken out of each paycheck for family health care coverage. How much does her employer contribute annually for the family coverage? Clearly show your work.
The answer is $12792
Explanation:
It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:
1. Write the values you know and use x to represent the value you need to find
108 = 18
x = 82
3. Cross multiply
x 18 = 8856
4. Find the value of x by solving this simple equation
x = 8856 ÷ 18
x = 492 - Amount the employer pays every two weeks for Tessa's family coverage
Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.
1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks
52 ÷ 2 = 26
2. Finally, multiply the money paid by the employer every two weeks by 26
26 weeks x $492 = $12792- This is the total the employer pays annually
5^2x+4×5^-x+1-125=0
Answer:
Take 5^x as y.
Now the question becomes a simple equation.
y + 20y - 125 = 0.
21y = 125.
Thus, y = 125/21.
Now resubstituting we get,
5^x = 125 /21.
Taking log on both sides,
xlog5 = log 125 - log 21
x = (log125/log5) - (log21/log 5)
x= 3- 1.89
Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2).
Answer:
Point-slope form: y-4=2(x+1)
Slope intercept form: y=2x+6
I hope this helps!
Answer:
[tex]y-4=2(x+1)[/tex]
Step-by-step explanation:
Point-slope form is equal to
[tex]y-y_1=m(x-x_1)[/tex]
where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:
[tex]4-2=m(-1-(-2))[/tex]
We can simplify negative one minus negative two as positive 1.
[tex]4-2=m(1)[/tex]
4 minus 2 is 2, so m times 1 is 2. That means m is 2.
Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:
[tex]y-4=2(x+1)[/tex]
Suppose your weekly local lottery has a winning chance of 1/106. You buy lottery from them for x weeks in a row. What is the probability that you never win?
Answer:
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]
Step-by-step explanation:
Given that;
the winning chance of a weekly local lottery = [tex]\dfrac{1}{10^6}[/tex]
= [tex]\dfrac{1}{1000000}[/tex]
The probability of losing = 1 - probability of winning (winning chance)
The probability of losing = [tex]1- \dfrac{1}{1000000}[/tex]
The probability of losing =[tex]\dfrac{999999}{1000000}[/tex]
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{1}{10^6} )^0 ( \dfrac{999999}{1000000})^x[/tex]
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]
_______% of 44 = 22
Answer:
50%
Step-by-step explanation:
22 is half of 44.
So, this means 50% of 44 is 22.
In the Cash Now lottery game there are 8 finalists who submitted entry tickets on time. From these 8 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousand dollars, and the third prize is ten thousand dollars. Determine the total number of different ways in which the winners can be drawn. (Assume that the tickets are not replaced after they are drawn.)
Answer:
The number of ways is [tex]\left n} \atop {}} \right. P_r = 336[/tex]
Step-by-step explanation:
From the question we are told that
The number of tickets are [tex]n = 8[/tex]
The number of finalist are [tex]r =3[/tex]
Generally the number of way by which this winners can be drawn and arrange in the order of [tex]1^{st} , \ 2nd , \ 3rd[/tex] is mathematically represented as
[tex]\left n} \atop {}} \right. P_r = \frac{n\ !}{(n-r) !}[/tex]
substituting values
[tex]\left n} \atop {}} \right. P_r = \frac{ 8!}{(8-3) !}[/tex]
[tex]\left n} \atop {}} \right. P_r = \frac{ 8* 7*6*5*4*3*2*1}{ 5*4*3*2*1}[/tex]
[tex]\left n} \atop {}} \right. P_r = 336[/tex]
Which best describes the relationship between the lines with equations x + 8y = -1 and —8x +y = -1?
Answer:
the lines are perpdicular if you were to get some graph paper and graph u would see
If mL DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc
in circle o.
С
o
B.
mDEB = ?
Answer:
236°
Step-by-step explanation:
The circumference of a circle is 360° since <DOC is given as 44° and <COB is given as 80° and the center angles are equal to the arc it sees the the measure of arc DEB would be 360 - 44 - 80 = 236°
1. On the set of axes below, graph . State the roots of
Is this question complete?
What is the product of all values of b that satisfy (b-2)(b-8) +4= 0 ?
A) 10
B) 12
C) 16
D) 20
Answer:
D
Step-by-step explanation:
(b-2)(b-8)+4=0
b^2-10b+16+4=0
b^2-10b+20=0
Product of roots is given by c/a=20. So the answer is 20
find the least number that can be divided 9and 12 without leaving remainder
Answer:
By finding LCM of 9 and 12 the answer is 36
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Jamal has two investments, one in Company A, and another in Company B. Jamal purchased 300 shares in Company A at $1.45 per share. Since purchasing the shares, the price per share increased to $1.65 per share, after which Jamal decided to sell, realizing a profit. At the same time, Jamal purchased 200 shares in Company B at $1.20 per share. Since purchasing the shares, the share price fell to $1.10 per share, after which Jamal decided to sell the shares, suffering a loss. Calculate the total profit that Jamal received from his two investments.
Answer:
$20
Step-by-step explanation:
Company A:
Buy 300 shares at $1.45 per share.
Sell 300 shares at $1.65 per share.
Profit: ($1.65 - $1.45) * 300 = $60
Company B:
Buy 200 shares at $1.20 per share.
Sell 200 shares at $1.10 per share.
Loss: ($1.20 - $1.10) * 200 = $20
Net profit:
$40 - $20 = $20
Answer:
Step-by-step explanation:
Profit on Company A =$(1.65−1.45)×300=$60.
Loss on Company B =$(1.20−1.10)×200=$20.
Therefore the total profit Jamal achieved was $60−$20=$40.
Which sequence has a common ratio of 2? a{20, 40, 80, 160, 320, 640, …} b{20, 10, 5, 2.5, 1.25, 0.625, …} c{20, 15, 10, 5, 0, -5, …} d{20, 4, 0.80, 0.16, 0.032, 0.0064, …}
Answer:
A
Step-by-step explanation:
40/20=2
80/40=2
Therefore the common ration is 2
The correct sequence which has a common ratio of 2 is,
⇒ {20, 40, 80, 160, 320, 640, …}
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The common ratio of sequence is,
⇒ 2
Now, By option 1;
The sequence is,
⇒ {20, 40, 80, 160, 320, 640, …}
Hence, Common ratio = 40 / 20
= 2
And, 80 / 40 = 2
Thus, The correct sequence which has a common ratio of 2 is,
⇒ {20, 40, 80, 160, 320, 640, …}
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In order to earn an A in her math course,
Bernadette must have an average of at
least 90 on her exam scores. She has
grades of 83, 97, 89, and 82 on her first 4
exams. What is the minimum she can
score on the final exam to earn an A in the
course?
Step-by-step explanation:
Let minimum score on the final exam to earn an A be X
[tex]mean \: = \frac{sum \: of \: observation}{number \: of \: observation} [/tex]
[tex]90 = \frac{83 + 97 + 89 + 82 + x}{5} [/tex]
Further solving :
X = 99 marks
for the first one the answer are
add 5 to both sides
subtract 5 from both sides
add 1/2x to both sides
subtract 1/2 from both sides
the second one is
multiply both sides by 1/5
dived both sides by 1/5
multiply both sides by 6/7
dived both sides by 6/7
Answer:
1. add 1/2x to both sides
a. you want to combine the like terms. in this case, it is the x variable.
you are left with 7/6x = 5
2. multiply by 6/7
a. the reciprocal of 7/6 will cancel out the values
The blueprints of a house have a scale factor of 30. If one side of the house measures 4 inches on the blueprint, how long is the actual side length (in feet)?
A. 7.5 feet
B.10 feet
C. 90 feet
D. 120 feet
If the scale factor is 30, then all you have to do is multiply each measurement by the scale factor. In this case, 4 · 30 = 120.
A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 307 persons, the following data was compiled. Can we conclude that brand perception is dependent on age?
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 41 26 116
Total 186 59 62 307
Find the value of the test statistic.
Answer:
The value for the Chi -square test statistics = 1.149
Step-by-step explanation:
The observed value Table can be shown better as:
Observed Value
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 21 26 116
Total 186 59 62 307
NOTE: when computing the question, in the third row and the second column, there is a mistake , the value is supposed to be 21 and not 41 because :
69 +21+ 26 will eventually give = 116
69 + 41 + 26 = 136
With that error being fix , let's get started.
Expected Value
The expected value can be determined by using the formula:
[tex]Expected \ Value = \dfrac{ row \ total \times column \ total }{grand \ total }[/tex]
For 67; (111 * 186)/307 = 67.251
For 24 : (111 * 59)/307 = 21.332
For 20 : (111 * 62)/307 = 22.417
For 50 :(80*186)/307 = 48.469
For 14 : (80* 59)/307 = 15.375
For 16 : ( 0 * 62)/307 = 16.156
For 69 : (116 * 186)/307 = 70.280
For 21 : (116* 59)/307 = 22.293
For 26 : (116*62)/307 = 23.427
Expected Value :
Age Favorable Unfavorable Neutral Total
18-30 67.251 21.332 22.417 111
30-45 48.469 15.375 16.156 80
Over 45 70.280 22.293 23.427 116
Total 186 59 62 307
The Chi - square test statistics = [tex]\dfrac{(observed \ value - Expected \ value)^2}{Expected \ value}[/tex]
For 67.251 : ( 67 - 67.251)²/67.251 = 0.0009
For 21.332 : ( 24 - 21.332)²/21.332 = 0.3337
For 22.417 : ( 20 - 22.417)²/ 22.417 = 0.2606
For 48.469 : ( 50 - 48.469)²/ 48.469 = 0.0484
For 15.375 : ( 14 - 15.375)²/ 15.375 = 0.1230
For 16.156 : ( 16 - 16.156)²/ 16.156 = 0.0015
For 70.280 : ( 69 - 70.280)²/ 70.280 = 0.0233
For 22.293 : ( 21 - 22.293)²/ 22.293 = 0.0750
For 23.427 : ( 26 - 23.427)²/ 23.427 = 0.2826
The chi square table is as follows:
Age Favorable Unfavorable Neutral Total
18-30 0.0009 0.3337 0.2606 0.5952
30-45 0.0484 0.1230 0.0015 0.1729
Over 45 0.0233 0.0750 0.2826 0.3809
Total 0.0726 0.5317 0.5447 1.149
The value for the Chi -square test statistics = 1.149
PLEASE HELP 30 POINTS
How long will it take in hours for a car traveling from Tucson to Phoenix (120 km)
to reach Phoenix at a rate of 10km/hr.? How long would it take that car to circle the Earth
at the equator? (c= 2 nr) rof earth is 6,378 km.
Answer:
1. It would take the car to get from Tucson to Phoenix 12 hours.
2. for the car to go around the equator it would take 637 hours if it is still travelling at 10km/hr.
hope this helps
Step-by-step explanation:
1. 120 km divided by 10 = 12 hours