Select the correct expressions. 1 Identify each expression that represents the slope of a tangent to the curve y= * +1 at any point (x, y)
Answers
The expressions which represents the slope of a tangent to the curve [tex]y=\frac{1}{x+1}[/tex] at any point (x, y) are:
[tex]f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}[/tex]
The slope of a tangent to the curve.Mathematically, the slope of a tangent line to the curve is given by this equation:
[tex]f'(x) =limh \rightarrow 0\frac{f(x+h)-f(x)}{h}[/tex]
Given the function:
[tex]f(x)=y=\frac{1}{x+1}[/tex]
When (x + h), we have:
[tex]f(x+h)=y=\frac{1}{x+h+1}[/tex]
Next, we would find the derivative of f(x):
[tex]f'(x) =limh \rightarrow 0\frac{\frac{1}{x+h+1} -\frac{1}{x+1}}{h}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -(x+h+1)}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -x-h-1}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}\\\\f'(x) = \frac{-1}{(x+1)(x+1)} \\\\f'(x) = \frac{-1}{(x+1)^2}[/tex]
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Related Questions
You have a standard deck of 52 cards. Find the probability of drawing one card, then drawing another without replacement.
A) You draw an even-numbered card and then a face card.
B) Both cards you drew are "4" or higher (if aces are considered low cards and face cards are nonnumerical)
C) You drew a black face card and then a black "5".
Answers
Assuming that the all the cards have the same probability of being drawn we get:
A) P = 0.07B) P = 0.21C) P = 0.001How to find the probabilities?
We have a deck of 52 cards.
A) The probability of drawing an even-numbered card is given by the quotient between the number of even-numbered cards and the total number of cards.
On the 52 card deck, there are 16 even cards (2, 4, 6, 8 for each type), so the probability is:
p = 16/52
Then the probability of drawing a face card is given in the same way, notice that now there are 51 cards in the deck and 12 face cards, so we get:
q = 12/51
The joint probability is the product of these two:
P = (16/52)*(12/51) = 0.07
b) Both cards are 4 or larger.
There are 6 cards equal or larger than 4 for each type, so the probability for the first card is:
p = 24/52
For the second card, there is one card less in the deck (and one card less that is equal or larger than 4) so the probability is:
q = 23/51
The joint probability is:
P = (24/52)*(23/51) = 0.21
C) There are 6 black face cards, so the probability first is:
p = 6/52
Then there are 2 black cards with the number 5, so the probability is:
q = 2/51
The joint probability is:
P = (6/52)*(2/51) = 0.001
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pls answer asap!!! much appreciated
Answers
Answer:
e. 0.308.
Step-by-step explanation:
I can't draw the tree diagram but the answer is
P(red first) = 7/14 = 1/2
P( then black) = 4/13
P(red then black) = 1/2 * 4/13 = 2/13
P(black first) = 4/14 = 2/7
P( then red) = 7/13
P(black then red) =2/7 * 7/13 = 2/13
So Probability of red and black in any order
= 2/13 + 2/13 = 4/13
= 0.308.
A company is designing a new cylindrical water bottle. The volume of the bottle will be 226 cm cubed. The height of the water bottle is 8.2 cm. What is the radius of the water bottle? Use 3.14 for pi
Need answer asap plsss!!
Answers
Answer:
2.96 cm to the nearest hundredth.
Step-by-step explanation:
V = 3.14 r^2 h
226 = 3.14 * r^2 * 8.2
r^2 = 226 / (3.14*8.2)
r^2 = 8.7774
r = 2.96 cm to the nearest hundredth.
What is the length of the diagonal of the rectangle?
a) 2.5 units
b) 4.5 units
c) 5 units
d) 7 units
Answers
Answer:
I do believe its 5 units, if I am incorrect I apologize
Step-by-step explanation:
I will give 20 points to whoever helps me answer this and maybe brainlist
Answers
Answer:
60 degrees
Step-by-step explanation:
since its a vertically opposite angle so angle 1 will equal angle 3
Answer:
60
Step-by-step explanation:
Michael has a room in his house that is shaped like a parallelogram the length of the room measures 16 feet and the width measures 26 what is the perimeter of the
Answers
Answer:
84 ft
Step-by-step explanation:
16 + 16 + 26 +26 = 84
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
ft²
Answers
Answer:
32 1/3
Step-by-step explanation:
Answer:
The answer is [tex]31\frac{9}{10}[/tex].
Step-by-step explanation:
Make sure to follow this formula
[tex]2(lw)+(lh)+(wh)[/tex]
[tex]2(1.3x1.5)+(1.3x5)+(1.5x5) \\= 2(1.95+6.5+7.5)\\=31.9=31\frac{9}{10}[/tex]
3 + 4ab - 5b + m
Number of terms:
Coefficients:
Constant terms:
Answers
Answer:
Number of terms = 4 (there are four terms)
coefficients = the coefficient of ab = 4
✓✓✓ ✓✓✓ ✓ b = -5
✓✓✓ ✓✓✓ ✓ m = 1
constant terms = 3
Hope it helped!!
Number of terms, Coefficients, Constant terms are 4,2 and 1
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
3 + 4ab - 5b + m
Number of terms here are
=4
Coefficients we have
=2
Constant terms
=1
Therefore, the answer to this algebra will be 4,2 and 1
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Which of the following could be calculated using the Pythagorean theorem? Select all that apply.
area of a circle
length of an arch
height of a building
distance to an airport
size of a window pane
Answers
Answer: height of a building
Step-by-step explanation:
a^2 + b^2 = c^2
used for finding missing side angle of a triangle
Reflect the figure over the line x = 0.
The coordinate of J’ is ?
The coordinate of K’ is ?
Answers
After the reflection over the line x = 0, the coordinates will be:
J' = (2, 1)
K' = (0, 4) = K
How to find the coordinates after the reflection?For any point (x, y), if we apply a reflection across the line x = 0, the image after the reflection will be (-x, y).
So it only changes the sign of the x-component.
In the graph, we can see that J = (-2, 1). So after the reflection, we will have:
J' = (2, 1).
And we also can see that K = (0, 4), then after the reflection, we have:
K' = (-0, 4) = (0, 4) = K
So point K does not change under that reflection.
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If the volume of this rectangular prism is 385 cubic inches, what is the value of x?
(x - 2) in.
xin.
W + 4) in
X
inches
Answers
Answer:
x=7
Step-by-step explanation:
x(x-2) (x+4) =385
distribute the x and solve
The value of x is 8 in.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
Length = x + 4
Width = x
Height = x - 2
The volume of the rectangular prism = 385 in³
The volume of the rectangular prism = length x width x height
Now,
length x width x height = 385
(x + 4) x (x - 2) = 385
(x + 4) (x² - 2x) = 385
x³ - 2x² + 4x² - 8x = 385
x³ + 2x² - 8x = 385
This is a cubic polynomial.
f(x) = x³ + 2x² - 8x - 385
f(x) = a³ + bx² + cx + d = 0
Using the calculator we get,
Roots:
x = -3.20181 + 5.96339 i (rejected)
x = -3.20181 - 5.96339 i (rejected)
x = 8.40362 = 8
Thus,
The value of x is 8 in.
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In the figure below, what is the value of x?
Answers
Answer:
x = 31.
Step-by-step explanation:
93 = x + 62 (External Angle Theorem).
x = 93 - 62
= 31
In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student who plays a sport does not play an instrument?
Plays an instrument Does not play an instrument
Plays a sport 12 13
Does not play a sport 3 2
Answers
The probability that a student who plays a sport does not play an instrument is 13 / 30.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a student who plays a sport does not play an instrument = 13 / total number of students
13 / (12 + 13 + 2 + 3) = 13 / 30
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Find the area that the curve encloses and then sketch it.
r = 3 + 8 sin(6)
Answers
Answer:
[tex]A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2[/tex]
Step-by-step explanation:
I assume you mean [tex]r=3+8\sin\theta[/tex]:
Use the formula [tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta[/tex] where [tex]a[/tex] and [tex]b[/tex] are the lower and upper bounds and [tex]r(\theta)[/tex] is the equation of the polar curve.
Since the graph is symmetrical about the line [tex]\displaystyle \theta=\frac{\pi}{2}[/tex], let the bounds of integration be [tex]\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)[/tex] to find half the area of the curve, and then find twice of that area:
[tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta[/tex]
[tex]\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\[/tex]
[tex]A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053[/tex]
Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.
The ratio of number of student wearing sneakers in a class to the number of students wearing sandals in the class is 3:4 How many were are waring sneakers if there are 28 student in the class
Answers
12 students are wearing sneakers.
Answer:
12
Step-by-step explanation:
So, the ratio is 3:4. That means this is for every 7 students. We have 28 students, so we need to know how many times 7 was multiplied to get to 28. 28 divided by 7 gives you 4. Now, we have to multiply both numbers in the ratio by 4. 3 times 4 is 12, and 4 times 4 is 16. The new ratio is 12:16. The students wearing sneakers were originally the 3 that got multiplied into 12, so the answer is 12.
Hope this helps!
Which describes the association between the number of DVDs sold and the number of DVDs rented?
Answers
The integer representing the change in the number of DVDs sold is -10000.
What is a change in number?Given, The number of DVDs shipped to an online retailer was 10,000 less than the previous year.
We have to Use an integer to describe the change in the number of DVDs sold.
Now, let the number of DVDs shipped to an online retailer in the previous year be x.
Then, according to the given information, DVDs shipped to the online retailer this year will become x – 10000
So, now, the change in the number of DVDs sold = DVDs sold this year – DVDs sold last year
= x – 10000 – x
= 0 – 10000
= - 10000
Hence, the integer representing the change in the number of DVDs sold is -10000.
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A cube has a side length of 6 cm. The cube is reduced by a scale factor of 1/3. Find the volume of the reduced cube. 2 cm3 4 cm3 6 cm3 8 cm3
Answers
Answer:
8 cm
Step-by-step explanation:
because when it's reduced we multiply the side length by 1/3 * 6 = 2cm and the volume will equal v = a^3 = 2^3 = 8cm
Answer:
8cm
Step-by-step explanation:
step1: 6/3=2
volume of a cube =x*x*
v
:=8cm
v=2×2×2
vvv v
Y=5+x how do we solve for x?
Answers
I need help with this ASAP
Answers
Answer:
hope this will help you........
1/2 * 6 * 4 * 10
= 120cm (cubed)
What is the resulting ordered pair if the value of the independent variable is –2? f(x)=2x^3+3x^2 A. (–5, –2) B. (–2, –4) C. (–2, –28) D. (–4, –2)
Answers
The resulting ordered pair if the value of the independent variable is –2 will be B. (-2, -4).
How to solve the variable?From the information given, it was stated that we should calculate the resulting ordered pair if the value of the independent variable is –2.
Therefore, in this case, x = -2. Therefore, we will play it into the equation. This will be:
f(x)=2x³ +3x²
= 2(-2)³ + 3(-2)²
= -16 + 12
= -4
Therefore, the ordered pair will be (-2, -4).
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I need help with this problem
Answers
Determine the missing value, x. Then, classify the triangle by side and by angle measure.
Question in below;
Answers
The value of x in the right angle triangle is approximately 45 degrees.
How to find an angle in a right angle triangle?The angle of the right angle triangle can be found as follows:
Therefore, let's find the hypotenuse side using Pythagoras theorem,
6² + 6² = c²
c² = 72
c = √72
c = 8.48528137424
c = 8.5 cm
Hence,
sin x = opposite / hypotenuse
sin x = 6 / 8.5
sin x = 0.70588235294
x = sin⁻¹ 0.70588235294
x = 44.9006818301
x = 45°
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Help I suck at this Please Help Me!
Answers
By using partial products to multiply, 52 × 6 is 312
Multiplying using partial productsFrom the question, we are to use partial products to multiply 52 × 6
The partial multiplication is shown below
5 2
× 6
300 6 × 5 tens (That is, 6 × 5 × 10 = 300)
+ 12 6 × 2 ones (That is, 6 × 2 × 1 = 12)
312
Hence, by using partial products to multiply, 52 × 6 is 312
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Will mark brainlist to whoever answers first
Answers
5. A wheel makes 726 revolutions per minute. How many
revolutions does it make per second?
Answers
Explanation: 726/60 because there are 60 seconds for a minute.
a tv studio has brought in 4 boy kittens and 5 girl kittens for a cat food commercial. the director is going to choose 5 of these kittens at random to be in the commercial.
what is the probability that the director chooses 3 boy kittens and 2 girl kittens? round your answer to three decimal places.
Answers
The probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have total number of kitten = 4+5 = 9
Total number of outcomes if the director is going to choose 5 of these kittens at random to be in the commercial:
= C(9, 5) = 126
The director chooses 3 boy kittens number of ways:
= C(4, 3) = 4
The director chooses 2 girl kittens number of ways:
=C(5, 2) = 10
Total favourable outcomes = 10×4 = 40
The probability = 40/126
= 0.317 ≈ 0.32
Thus, the probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.
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Help me please! so jarring
Answers
Answer:
y = -5x + 4.
Step-by-step explanation:
y = mx + c is the general form
- where m = the slope of the line and c is the y-value where the graph cuts the y-axis.
The graph passes through the points (0, 4) and (1, -1) so the slope
= (Y2 - y1) / (x2 - x1)
= (-1-4) / (1-0)
= -5 = m.
and c = 4.
help plsls I’ll brainlist i promise this one’s abit confusing tho.
Answers
Answer:
25
Step-by-step explanation:
Please refer to the picture;
39 ft.². The length should be 10 feet more than its width. What should the dimensions of
the deck be?
Answers
Answer:
13 x 3 ft
Step-by-step explanation:
RECTANGULAR deck
L x W = 39 ft^2
(w+10) x w = 39
w^2 + 10w - 39 = 0
(w-3)(w+13) = 0 w = 3 or -13 (throw out)
w = 3 then l = 10 +3 = 13
Help with these 10th grade geometry angle problems? I'm desperate and my teacher won't help me. Please also explain how you got your answer. Thank you.
Answers
Answer: 60
Step-by-step explanation:
See
m<COB and m<EOD are opposite anglesHence they are equal in measure.Hence
m<COB=60°