Answer:
A) k = 18.75B) R(0.8) = 161419C) R(0.3) = 275Step-by-step explanation:
Given expression
R(x) = 6*e^(kx)A) Given
x = 0.04R = 10Solving for k
10 = 6*e^(0.04k)e^(0.04k) = 10/6ln (e^0.04k) = ln (1.6666)0.04k = 0.51k = 0.51/0.04k = 12.75B) Given
x = 0.8R= ?The value of R(0.8) is:
R(0.8) = 6*e^(0.8*12.75) =6*e^(10.2) = 161419 roundedC) Given
x = 0.3R = ?The value of R(0.3) is:
R(0.3) =6*e^(0.3*12.75) = 6*e^(3.825) =275 roundedplz help I will mark brainlest!
Answer:
-1.71 the answer is d
Step-by-step explanation:
.........
Use the definition:
f'(x)=[tex]\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
to find f'(x) for:
f(x)=[tex]\frac{1}{\sqrt{x}}[/tex]+x
I need the WORK, not the answer. Thanks!
Using the given definition, for [tex]f(x)=\frac1{\sqrt x}+x[/tex], we have
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\left(\frac1{\sqrt{x+h}}+x+h\right)-\left(\frac1{\sqrt x}+x\right)}h[/tex]
Right away, we see x and -x in the numerator, so we can drop those terms.
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac1{\sqrt{x+h}}+h-\frac1{\sqrt x}}h[/tex]
Remember that limits distribute over sums, i.e.
[tex]\displaystyle\lim_{x\to c}(f(x)+g(x))=\lim_{x\to c}f(x)+\lim_{x\to c}g(x)[/tex]
so we can separate the h from everything else in the numerator:
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac1{\sqrt{x+h}}-\frac1{\sqrt x}}h+\lim_{h\to0}\frac hh[/tex]
Since h ≠ 0, we have [tex]\frac hh=1[/tex], so the second limit is simply 1.
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{\frac1{\sqrt{x+h}}-\frac1{\sqrt x}}h+1[/tex]
For the remaining limit, focus on the numerator for now. Combine the fractions in the numerator:
[tex]\dfrac1{\sqrt{x+h}}-\dfrac1{\sqrt x}=\dfrac{\sqrt x-\sqrt{x+h}}{\sqrt x\sqrt{x+h}}[/tex]
Recall the difference of squares identity,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Let [tex]a=\sqrt x[/tex] and [tex]b=\sqrt{x+h}[/tex]. Multiply the numerator and denominator by [tex](a+b)[/tex], so that the numerator can be condensed using the identity above.
[tex]\dfrac{\sqrt x-\sqrt{x+h}}{\sqrt x\sqrt{x+h}}\cdot\dfrac{\sqrt x+\sqrt{x+h}}{\sqrt x+\sqrt{x+h}}[/tex]
[tex]=\dfrac{(\sqrt x)^2-(\sqrt{x+h})^2}{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}[/tex]
[tex]=\dfrac{x-(x+h)}{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}[/tex]
[tex]=-\dfrac h{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}[/tex]
Back to the limit: all this rewriting tells us that
[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{-\frac h{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}}h+1[/tex]
Again, the h's cancel, and we can pull out the factor of -1 from the numerator and simplify the fraction:
[tex]f'(x)=\displaystyle-\lim_{h\to0}\frac1{\sqrt x\sqrt{x+h}(\sqrt x+\sqrt{x+h})}+1[/tex]
The remaining expression is continuous at h = 0, so we can evaluate the limit by substituting directly:
[tex]f'(x)=-\dfrac1{\sqrt x\sqrt{x+0}(\sqrt x+\sqrt{x+0})}+1[/tex]
[tex]f'(x)=-\dfrac1{2x\sqrt x}+1[/tex]
or, if we write [tex]\sqrt x=x^{1/2}[/tex], we get
[tex]f'(x)=-\dfrac12x^{-3/2}+1[/tex]
A Box has a volume of 125 cubic inches. How many 1 inch cubes can fit along the side?
Answer:
OLUME OF A BOX, CUBE, OR CYLINDER V l w = h where l = the length w = the width, and h = the height of the figure 13 6 8 V = 6. Page 1. VOLUME OF A BOX, CUBE, OR CYLINDER. The concept of volume holds great practical importance.
Step-by-step explanation:
Ian walks down a sloped path. After 6 minutes, he is 3 m above street level. Write the equation in slope-intercept form of the line that represents Ian’s height above street level, y, over time x, if he knows the path is parallel to another path with equation y = -2/3x + 12
Answer:
y=-2/3x+7
Step-by-step explanation:
Since you know the path is parallel to the equation y+-2/3x+12, you already know the slope is -2/3.
It says y is the height above street level, so that is 3. The problem says x is time, which is 6, so all you have to solve for is the y intercept.
3 (y, or the height above street level) = (-2/3) 6 (x, or time) + b (unknown y intercept)
3 = -4 + b
7 = b
So, y = -2/3x + 7
Identify the function family to which g(x) belongs. (g(x) x 3 + 5
Solve the following inequalities graphically on the set of axes below state the coordinates of a point in the solution set
Answer:
A solution point is (2,2)
Step-by-step explanation:
Graph the lines. If it is just greater that or less than, use dashed lines. I fits greater than or equal too, or other symbols like that, use a solid line
Use the test point (0,0). If it satisfies the inequality, shade the side of the graph with that point (you can use any test point, not just (0,0)). If it doesn't satisfy, then shade the other side
The Shaded area shared by both lines is the area of the solution
The capacity of one sachet pure water is 500ml. How many sachet of pure water is needed to fill a barrel of 5,685 litres capacity?
Answer:
11370 sachet
Step-by-step explanation:
Answer:
11370 sachets
Step-by-step explanation:
Given parameters:
Capacity of one sachet of pure water = 500ml = 500 x 10⁻³L
Unknown:
Number of sachet of pure water needed to fill a barrel of 5685liters + /
Solution;
To find the number of sachet;
500 x 10⁻³L will fill one sachet of pure water;
For 5685 liters, we would require y sachet of pure water ;
500 x 10⁻³y = 5685
0.5y = 5685
y = [tex]\frac{5685}{0.5}[/tex] = 11370 sachets
Evaluate this exponential expression. 4^5
Answer:
1024
Step-by-step explanation:
4⁵ is 4 multiplied 5 times.
4⁵ = 4 · 4 · 4 · 4 · 4
16 · 4 · 4 · 4
64 · 4 · 4
256 · 4
1024
Need help on this pleaseeeeee
Answer:
I think it's C
Step-by-step explanation:
I just rotated point K 180 degrees and C was the only one with the coordinate points I got for K'
need help again please
Seed are often treated with fungicides to protect them in poor draining, wet environments. A small-scale trial, involving five treated and five untreated seeds, was conducted prior to a large-scale experiment to explore how much fungicide to apply. The seeds were planted in wet soil, and the number of emerging plants were counted. If the solution was not effective and four plants actually sprouted, what is the probability that a b c all four plants emerged from treated seeds
Answer:
2.38%
Step-by-step explanation:
Given that:
The population size involving numbers of treated and untreated seeds N = 10
the number of seeds that are treated which are observed = 5
the number of seeds that sprouted 'n' = 4
Now, use the method of hypergeometric probability, we have the formula:
[tex]p(y) = \dfrac{(^r_y)(^{N-r}_{n-y})}{(^N_n)}[/tex]
∴
[tex]p(4) = \dfrac{(^5_4)(^{5}_{0})}{(^{10}_4)}[/tex]
[tex]p(4) = \dfrac{\dfrac{5!}{4!(5-4)!}* \dfrac{5!}{0!(5-0)!} }{\dfrac{10!}{4!(10-4)!} }[/tex]
[tex]p(4) = \dfrac{\dfrac{5!}{4!}* \dfrac{5!}{(5)!} }{\dfrac{10!}{4!(6)!} }[/tex]
[tex]p(4) = \dfrac{5*1 }{210}[/tex]
p(4) = 0.0238
p(4) = 2.38%
What is the equation for the area of the parallelogram? 3x + x = 74 x + 3x + 74 3x • 74 = x x • 3x = 74
Answer:
x • 3x = 74
Step-by-step explanation:
Answer:
its D ;D
Step-by-step explanation:
NOBODYS HELPING ME ANSWER THIS AND I NEED AN ANSWER ASAP :((( IVE ASKED 2 TIMES ANYWAYS ILL GIVE BRAINLIEST AND 15+
ITS 2 QUESTIONS SEPERATE PLEASE PUT IT AS THIS
QUESTION 1-
______________
QUESTION 2-
______________ m
Answer:
1) 2/3
2) y= 2x+4
Step-by-step explanation:
For number one, use the formula [tex]\frac{(y_{2}-y_{1} ) }{(x_{2}-x_{1} ) }[/tex].
Insert the given coordinates into the formula.
7-1/10-1= 6/9
Simplify 6/9.
6/9÷3= 2/3
For the second one, I used desmos calculator.
Hope this helps! :)
Which one is greater 8 or -12
Answer:
8
Step-by-step explanation:
-12 is below 0 and 8 is above
Answer:
8 is greater
Step-by-step explanation:
the negative sign= - is meaning below so
12 below is -12 which is less so 8 is greater
The value of y is directly PROPORTIONAL to the value of x. If y=44 when x= 240, what is the value of y when x=84?
If you need the answer in fraction form, then it would be 77/5
This is equivalent to the mixed number 15 & 2/5
======================================================
Work Shown:
y = k*x ..... general direct proportion equation
44 = k*240 .... plug in x = 240 and y = 44
240k = 44
k = 44/240
k = 11/60 .... divide both parts by 4
y = k*x .... go back to the general form
y = (11/60)x .... plug in the k value we found earlier
y = (11/60)*84 .... plug in x = 84
y = 15.4
---------------
Extra info:
15.4 = 15 + 0.4
15.4 = 15 + 4/10
15.4 = 15 + 2/5
15.4 = 15 & 2/5 .... mixed number form
and
15.4 = 15 + 2/5
15.4 = 75/5 + 2/5
15.4 = (75+2)/5
15.4 = 77/5 ... improper fraction
The probability of an event must have what value?
Answer:
The probability of an impossible event is 0. The probability of a possible event is 1.
Step-by-step explanation:
I don't know if this is correct but I do hope this helps either way.
HELPPP PLEASE!!!! SHOW ALL WORK!!!
Answer:
x=54
Step-by-step explanation:
these two angles are supplementary to each other. this is because alternate interior angles are congruent, and 2x+42 degrees is supplementary to the alternate interior angle of x-24 degrees. so, we can add these two numbers up and set it equal to 180.
2x+42+x-24=180
3x+18=180
3x=162
x=54
if this question is asking for x, 54 is the answer. if it is asking for the angle measures, plug in 54 for x for each angle and solve.
By using the 20 percent off coupon that she found in the newspaper, Jill saved $4 on the extra large bag of dog food that she bought.
Percents
Total
20%
20%
20%
20%
20%
100%
$4
$4
$4
$4
$4
What was the cost of the bag of dog food without the coupon?
$8
$12
$16
$20
Answer: The answer would be $20, because 20% 5 times is 100% and 4 times 5 is 20
Eight less than the product of 9 and a number equals 2.
Answer:
10/9
Step-by-step explanation:
the question would be 9x - 8 = 2
which simplified you would get 9x = 10
dividing 9 from both sides would leave you with 10/9 in fraction form
A poylgon has -
curved lines
lines that do not connect
lines that do connect
at least 4 sides
Please help
Answer:
the answer is lines that do connect
The second angle of a triangle is twice as large as the first angle. The third angle is 35 greater than the second angle. How large is the first angle?
Answer:
29°
Step-by-step explanation:
Let x represent the first angle. Then the second angle is 2x, and the third angle is 2x+35°. The sum of the angles is 180°, so we have ...
x + 2x + (2x+35) = 180
5x +35 = 180 . . . . collect terms
x +7 = 36 . . . . . . . divide by 5
x = 29 . . . . . . . . . . subtract 7
The first angle is 29°.
Which fractions are equivalent to 3/5 Check all that apply.
Answer:
12/20 21/35 30/50
Step-by-step explanation:
These are all equivalent fractions to 3/5.
Hope this helps!
The fractions that are equivalent to 3/5 are C) 12/20, D) 21/35, and E) 30/50.
To determine which fractions are equivalent to 3/5, we need to find fractions that can be simplified to the same value.
The fraction 3/5 cannot be simplified further because 3 and 5 have no common factors other than 1.
Let's check each option:
A) 8/10 can be simplified to 4/5, which is not equivalent to 3/5.
B) 8/15 cannot be simplified further, but it is not equal to 3/5.
C) 12/20 can be simplified to 3/5, which is equivalent to 3/5.
D) 21/35 can be simplified to 3/5, which is equivalent to 3/5.
E) 30/50 can be simplified to 3/5, which is equivalent to 3/5.
Therefore, the fractions that are equivalent to 3/5 are C) 12/20, D) 21/35, and E) 30/50.
Learn more about the fraction here:
brainly.com/question/10354322
#SPJ6
4
X,
f(x) = (2x -6,
{
x < 2
x > 2
8. f(-2) =
9. f(3) =
10. f(5) =
Answer:
Step-by-step explanation:
Hope it helps
how many license plates can you make when a license plate consists of 6 out of 26 alphabetical letters each of which can be repeated
Need to evaluate 256 and fraction 1/4
Answer:
256fraction=1/4
256÷4=64
64 answer this fraction
If f(x) = 1/9x-2, what is f^-1(x)?
Answer:
1/-9x-2
Step-by-step explanation:
Answer:
Can you tell me in what form
Find all solutions of the equation x^2+3x+5=0 and express them in the form a+ bi
Answer:
in you question there is the ans hibben
Step-by-step explanation:
x^2+3x+5=0 =a+ bi
Which equation is a function?
O A. X = -2
O B. Y= 2x – 9
O C. y² = x - 2
O D. x² + y² = 9
the answer is B -- no matter the x factor y should be single
The chart below shows how far an object travels over a certain time.
A 3-column table with 4 rows. Column 1 is labeled Seconds with entries 4, 8, 12, 16. Column 2 is labeled Inches with entries 18, 36, 54, 72. Column 3 is labeled feet with entries 1.5, 3, blank, 6.
After 12 seconds, how far, in feet, will the object travel?
It will travel ??? feet
Answer:
4.5 Hope this helps
Step-by-step explanation:
Answer: 4.5
Step-by-step explanation: edge. 2022
Reason abstractly. Are all horizontal lines parallel? Use slope
explain how you know.
Answer:
All horizontal lines are NOT parallel.
Step-by-step explanation:
We learned that lines go on forever.
If one line is slightly slanted, and the other line is completely straight, these lines are not parallel, as they will meet at some point.
Hope this helped :)
