Answer:
Three billion eight million nine-hundred seven thousand eight.
Step-by-step explanation:
Write out each of the numbers.
(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x = 2. The graph of g(x) is blue.
Let h(x) = f(g(x)). Find
A. h'(1) =
B. h'(2) =
C. h'(3) =
Derivatives can be calculated from graphed functions.
The values of the derivatives are:
The given parameter is:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Start by calculating the equations of f(x) and g(x)
Graph f(x)
The slopes of f(x) are: 3/2 and -3/2
So, the equations are:
[tex]\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}[/tex]
[tex]\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}[/tex]
Graph g(x)
The slope of g(x) is: -1/2
So, the equation is:
[tex]\mathbf{g(x) = -\frac 12x}[/tex]
For x = 1 and x = 2, we have:
So, we have:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Where:
[tex]\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]
[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes
[tex]\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}[/tex]
Open brackets
[tex]\mathbf{h(x) = -\frac{3}{4}x}[/tex]
Differentiate
[tex]\mathbf{h'(x) = -\frac{3}{4}}[/tex]
So:
[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex]
[tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex]
For x = 3, we have:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Where:
[tex]\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]
[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes
[tex]\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}[/tex]
[tex]\mathbf{h(x) = \frac{3}{4}x}[/tex]
Differentiate
[tex]\mathbf{h'(x) = \frac{3}{4}}[/tex]
Substitute 3 for x
[tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]
Hence, the values of the derivatives are:
[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex], [tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex] and [tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]
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Triangles PQR and XYZ are similar. What is the length of XZ?
Solve for n.
ples help me solv for n
Answer: 50 miles per hour
Step-by-step explanation: It is that because when the line passes on the one hour mark it is 50.
34-18-(-23) write as a single number
Answer: 39
Step-by-step explanation: 34-18=16+23=39. Remember, 2 negatives equals a positive.
Answer: 39 cus 34-18=16+23=39
Step-by-step explanation:
LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (60,0), where unit distance on the coordinate plane is measured in miles A receiver is located somewhere in the first quadrant. The receiver computes that the difference in the distances from the receiver to these transmitters is 100 miles.
What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
LORAN follows an hyperbolic path.
The equation of the hyperbola is: [tex]\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}[/tex]
The coordinates are given as:
[tex]\mathbf{(x,y) = (-60,0)\ (60,0)}[/tex]
The center of the hyperbola is
[tex]\mathbf{(h,k) = (0,0)}[/tex]
The distance from the center to the focal points is given as:
[tex]\mathbf{c = 60}[/tex]
Square both sides
[tex]\mathbf{c^2 = 3600}[/tex]
The distance from the receiver to the transmitters is given as:
[tex]\mathbf{2a = 100}[/tex]
Divide both sides by 2
[tex]\mathbf{a = 50}[/tex]
Square both sides
[tex]\mathbf{a^2 = 2500}[/tex]
We have:
[tex]\mathbf{b^2 = c^2 - a^2}[/tex]
This gives
[tex]\mathbf{b^2 = 3600 - 2500}[/tex]
[tex]\mathbf{b^2 = 1100}[/tex]
The equation of an hyperbola is:
[tex]\mathbf{\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1}[/tex]
So, we have:
[tex]\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}[/tex]
[tex]\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}[/tex]
Hence, the equation of the hyperbola is: [tex]\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}[/tex]
Read more about hyperbolas at:
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fill in the table using this function rule. y=-10x+3
Answer:
-1 = -8
0 = 3
1 = 13
5 = 53
Step-by-step explanation:
-1 times 10 is -11
-11 plus 3 = 8
4. The effects of a certain anesthesia on patients is modeled by the rational function listed below. The
constants A and B are determined by factors such as body mass, age, etc. Suppose a patient who is
about to undergo surgery requires the constants to be A=36 and B=9. If t represents the number of
hours from the time the anesthesia enters the blood stream, and the function describes the percent
concentration needed for the anesthesia to be effective; how long can a surgery take if the percent
concentration needed for the patient to be sedated but not dead is between 4 and 6 percent? Explain
your reasoning and how you found your solution.
Model:C(t)= At/T^2+B
Answer: you will need 10
Step-by-step explanation:
I had the same problem on my hw this is what i got tell i think its correct:
Edit:
C(t)=At/T^2+B
a=36
b=9
t= how long it takes to enter blood stream
c=36/t^2 + 9
I found T to be 6 becuase I searched it up so
36/6^2=36/36=1
c=9+1
C=10
New awnser is 10
sin⁻¹(-[tex]-\frac{\sqrt{3} }{2}[/tex]
Answer:
240,300
[tex] \frac{4\pi}{3} . \: \: \frac{5\pi}{3} [/tex]
100 points! Please show your work :)
Answer:
7.76 minutes
Step-by-step explanation:
The +51 is regardless (being the y intercept) so it does not affect our answer. If the employee has to drive one mile (x=1) it will take 7.76 + 51 min to get there. If they have to drive 0 miles (x=0) it will only take 51 min. This is a difference of 7.76. You really just need to take the slope (I just used this example to make it make more sense) as x is the number of miles the employee has to drive, and therefore that times 7.76 would be how much longer it would take to drive to work.
Please help me thank you!!
Answer:
what the hell
Step-by-step explanation:
A football coach must order 9 new jerseys. The jerseys cost $23.79 each.
What is the total cost for the jerseys?
Answer:
9 x 23.79 = $214.11
The diagram shows rays of light from a point source, P, that reach a detector, D, along two paths. One path is a straight line, while the other is bent by reflection off a mirror. What is the value of b, correct to one decimal place? Assume that all the points in the diagram lie in the same plane.
This can solved using the cosine law which is:
c² = a² + b² - 2ab cos θ
Using the values given from the problem
6² = b² + b² - 2bb cos 112.62
And solving for b
36 = 2b² - 2b² cos 112.62
b = 3.6
The answer is the 3rd option.
Answer:
b = 3.6
Step-by-step explanation:
In one season a basketball player missed 45% of her free throws. How many free throws did she attempt if she made 176 free throws?
Step-by-step explanation:
she missed 45%, so that means she made 55% of her free throws.
and these 55% correlate to the absolute number of 176 successful throws.
so,
55% = 176
1% = 55%/55 = 176/55
100% = 1%×100 = 176×100/55 = 320
so, she attempted 320 free throws in total.
Leon and Thomas have the same number of cherries. Leon eats 5 of his cherries and has 12 cherries left. Thomas eats 9 of his cherries. How many cherries does Thomas have left?
What is this answer need reply ASAP
Answer:
how many boxes is the line on
Which graph represents the function f(x)=4⋅3x?
Answer: Bottom right corner (southwest corner)
Explanation:
Plug in x = 0 to find that
[tex]f(x) = 4*3^x\\\\f(0) = 4*3^0\\\\f(0) = 4*1\\\\f(0) = 4\\\\[/tex]
This shows that the y intercept is (0,4).
Of the four answer choices, only the bottom right corner has this y intercept. Note that the curve goes uphill when moving to the right. This function is increasing which matches with f(x) being an increasing function. In other words, f(x) represents exponential growth.
Help me please i've been stuck on this question for hours.
Answer:
a) x^3 b) y^5
Step-by-step explanation:
you can combine the x's and y's to make a exponent equal to the number of x's or y's.
On Mrs. Sean's desk,
there are pink and yellow
markers. The ratio of pink
markers to total markers
is 1:3. If there are 16
yellow markers, then how
many markershare pink?
Since the ratio of pink markers to total markers is 1:3, then there are 8 pink markers.
Number of yellow markers given = 16
Based on the information given, therefore, the pink markers will be half of the yellow markers. This will be:
= 1/2 × 16
= 8 markers
Therefore, the total markers will be:
= 8 + 16 = 24
In conclusion, pink markers will be 8/24 = 1/3. Therefore, the number of pink markers is 8.
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Trina is cutting ribbon to make bows if she has 7.5 yards of ribbon and she needs 0.4 yards for each bow how many bows can she make
Answer:
She can make 18 bows.
Step-by-step explanation:
0.4 x 18 = 7.2, and you cannot go over since she only has a supply of 7.5.
Hope it helps!
Please mark brainliest if you want to, it'd mean a lot :)
Answer:
skilled readers make use context and predictionskilled readers make use context and predictionskilled readers make use context and prediction
Step-by-step explanation:
Determine the equation of the line passing through the point below having the corresponding slope.
Point: ( -20, -34)
Slope: m =9/5
Write your answer as an equation in the form y=mx+b
Answer:
Step-by-step explanation:
-34 = (9/5)(-20) + b
b = -34 + 36 = 2
y = (9/5)x + 2
??
What is the asnwer plsssss
The arc length is 7/2 pi.
Which table shows a proportional relationship between x and y?
A.
x y
2 4
3 6
4 9
B.
x y
3 4
9 16
15 20
C.
x y
4 12
5 15
6 18
D.
x y
1 4
2 8
3 15
Answer:
c is the answer
Step-by-step explanation:
Let g(x) = (x - 2)2. Find x such that g(x) = 25.
Answer:
x = 14.5
can also be written as;
x = 29/2
Step-by-step explanation:
On Friday, 0.325 of the students in
Keisha's math class were absent. What
percent of the students were absent?
Look at picture for choices!! Quick!!
Solve for x: 34= -2
x= ????
Answer:
You haven't typed the equation correctly
x=-17
Step-by-step explanation:
Consider and define which type of slope the line has.
Answer:
think of the numbers as the grid. zero being the middle and each square being 1 2 3 4 5 6 etc to the right of 0 are your positive, -1 -2 -3 etc move to the left of that line, your other access from zero goes up to positive one positive 2 positive 3 etc, from zero down you would be negative one negative 2 negative 3 etc
Answer:
1) (-7, 8) and (-7, 0) - Undefined Slope.
2) (3, 5) and (-1, 2) - Positive Slope.
3) (2, 4) and (5, 1) - Negative Slope.
4) (6, -3) and (4, -3) - Zero Slope.
1) In the coordinates (-7, 8) and (-7, 0), we can see that the first number in both coordinates (the x point) is -7. If the x values are the same, that means that the line does not change at all horizontally/on the x-axis. The only solution to a line that passes through these points would be a vertical line. Vertical lines always have an undefined slope. To test, use the slope formula with the coordinates. y2 is the y in the second coordinate, y1 is the y from the first coordinate, x1 is the x from the first coordinate, and x2 is the x from the second coordinate.
[tex]\frac{y2 - y1}{x2 - x1} = slope[/tex]
[tex]\frac{0 - 8}{-7 - (-7)} = slope[/tex] 0 - 8 = -8 and -7 - (-7) = -7 + 7 or 0. Any number divided by 0 is undefined.
2) In the coordinates (3, 5) and (-1, 2) there isn't any obvious abnormality in the coordinates that may cause undefined or 0. We can use the slope formula to find if it has a positive or negative slope.
[tex]\frac{y2 - y1}{x2 - x1} = slope[/tex]
[tex]\frac{2 - 5}{-1 - 3} = slope[/tex] 2 - 5 = -3 and -1 - 3 = -4. [tex]\frac{-3}{-4}[/tex] simplifies to 3/4, so the slope is positive.
3) (2, 4) and (5, 1) also don't have any repeating numbers in the coordinates so we can find the slope using the formula.
[tex]\frac{y2 - y1}{x2 - x1} = slope[/tex]
[tex]\frac{1 - 4 }{5-2} = slope[/tex] 1 - 4 = -3 and 5 - 2 = 3 [tex]\frac{-3}{3}[/tex] = -1, so the slope is negative.
4) (6, -3) and (4, -3) have the same y values in them, -3. If the y value stays constant then that means the line does not move along the y-axis. This means that it must be a straight line through 1 point on the y-axis. It is a horizontal line. The slope of a horizontal line is always 0 because is straight. You can check using the slope formula.
[tex]\frac{y2 - y1}{x2 - x1} = slope[/tex]
[tex]\frac{-3 - (-3) }{4 - 6} = slope[/tex] -3 - (-3) = -3 + 3 = 0 and 4 - 6 = -2. [tex]\frac{0}{2}[/tex] = 0. The slope is 0.
Let me know if you have any questions!
A ball is thrown vertically upward from the top of a 100-foot tower, with an initial velocity of 20 ft/sec. Its position function is s(t) = -16t^2 + 20t + 100. What is its velocity in ft/sec when t = 1 second?
The velocity of the ball in ft/sec, when t = 1 second is equal to -12 ft/sec.
Given the following data:
Displacement = 100 feetTime = 1 secondsPosition function = [tex]s(t) = -16t^2 + 20t + 100[/tex]To calculate the velocity of the ball in ft/sec, when t = 1 second:
Mathematically, the velocity of an object or physical body is equal to the differentiation of it's position function.
Velocity = s'(t)
Velocity = [tex]s(t) = -16t^2 + 20t + 100[/tex]
[tex]Velocity = -32t + 20[/tex]
Substituting the value of time (t), we have:
[tex]Velocity = -32(1) +20\\\\Velocity =-32+20[/tex]
Velocity = -12 ft/sec
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Which of the numbers below is greater than zero? Select all that apply.
A)0.8
B)4.5
C)14
D)−2.25
E)−0.5
Solve the following two problems using Calculus. Show all of your work on a separate sheet of paper, making clear how you arrived at all your solutions. Please be aware that you are using similar thinking for both of these problems, but you are solving for maximum area in Part A and minimum cost in Part B. Enjoy
A. If the materials for the fence cost $12 per foot, find the dimensions of the
corral for the largest possible area that can be enclosed with $2400 worth of fence.
B. If he only requires an area of 288 square feet for his vegetable garden, find the minimum cost of putting up this fence, if the cost per foot is $10. Indicate the dimensions of the garden that will minimize the cost.
9514 1404 393
Answer:
A. 50 ft square
B. 12√2 ft square
Step-by-step explanation:
These problems are basically the same, so have the same solution. The rectangle with maximum area for a given perimeter will have the same shape as the one with minimum perimeter for a given area.
We can find it generically. Let p represent the perimeter of a rectangular area with one side that measures x. The area will be ...
A = x(p/2 -x) = -x^2 +(p/2)x
The area will be maximized when dA/dx = 0:
dA/dx = -2x +p/2 = 0
p/2 = 2x . . . . . add 2x
x = p/4 . . . . . . divide by 2
The other dimension is ...
p/2 -x = p/2 -p/4 = p/4
The dimensions of the maximum area for perimeter p are ...
p/4 × p/4 . . . . . . . a square
__
A.$2400 worth of fence at $12 per foot is 2400/12 = 200 ft of fence. The largest possible area that can be enclosed will have dimensions of 200 ft/4 = 50 ft square:
50 ft × 50 ft
__
B.The perimeter of the garden will be at its shortest when the shape of the garden is square.
√(288 ft²) = 12√2 ft
The dimensions of the garden that will minimize the cost are ...
12√2 ft × 12√2 ft
Connor was traveling in Mexico and is returning to his home in the United States.
He has 2,567 pesos left. The current exchange rate is 1 U.S. dollar is equal to 19.43
pesos. How many U.S. dollars will he have if he converts his leftover pesos to
dollars?
$2,567
$102.68
$132.12
$3,414
Answer:
$132.12
Step-by-step explanation:
19.43 pesos = $1
2567 pesos = ?
1. First divide 2567 by 19.43 to find the exact number of dollars:
2567 ÷ 19.43 = 132.1152856
2. Round this value to 2 decimal places:
132.1152856 ≈ $132.12
Step-by-step explanation:
19.43 pesos = 1 U.S. dollar
So 1 peso = [tex]\frac{1}{19.43}[/tex] U.S. dollar
2567 pesos = [tex](\frac{1}{19.43} )(2567)[/tex] U.S. dollar
= 132.115286 U.S. dollar
please give me a brainliest answer
