If y = y(x), then the slope of the tangent line to (1, 1) is equal to the value of the derivative dy/dx when x = 1 and y = 1.
Compute the derivative using implicit differentiation:
d/dx [xy ^2 + y] = d/dx [2x]
d/dx [xy ^2] + d/dx [y] = 2 d/dx [x]
(x d/dx [y ^2] + d/dx [x] y ^2) + dy/dx = 2
2xy dy/dx + y ^2 + dy/dx = 2
(2xy + 1) dy/dx = 2 - y ^2
dy/dx = (2 - y ^2) / (2xy + 1)
Plug in x = 1 and y = 1 :
slope = dy/dx = (2 - 1^2) / (2*1*1 + 1) = 1/3
Now use the point-slope formula to get the equation of the line:
y - 1 = 1/3 (x - 1)
y = x/3 + 2/3
a website would like to test the hypotheis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched onlinevideos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. The website owners would like to set =.02 what is the conclusion for this hyptohesis test
Answer:
The p-value of the test is 0.0446 > 0.02, which means that we do not reject the null hypothesis that the average length of an online video watched by a user is of 8 minutes.
Step-by-step explanation:
A website would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes.
At the null hypothesis, we test if the mean is of 8 minutes, that is:
[tex]H_0: \mu = 8[/tex]
At the alternate hypothesis, we test if the mean is of more than 8 minutes, that is:
[tex]H_a: \mu > 8[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
8 is tested at the null hypothesis:
This means that [tex]\mu = 8[/tex]
A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes.
This means that [tex]n = 37, X = 8.7, \sigma = 2.5[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{8.7 - 8}{\frac{2.5}{\sqrt{37}}}[/tex]
[tex]z = 1.70[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 8.7, which is 1 subtracted by the p-value of z = 1.7.
Looking at the z-table, z = 1.7 has a p-value of 0.9554
1 - 0.9554 = 0.0446
The p-value of the test is 0.0446 > 0.02, which means that we do not reject the null hypothesis that the average length of an online video watched by a user is of 8 minutes.
komplike türkçe karşılığı
Answer:
football is better
Step-by-step explanation:
football is better
Cevap: Yapılması zor olan
ẞaşarılar dilerim
8x-11y=-4
-5x+y=26
(need help with showing work , I keep getting stuck on something)
Step-by-step explanation:
Possible question so that I can help you with the solution
Calculate the work done.
A crane lifts 5,000 newtons to the top of a roof which is 6 meters high.
Answer:
30, 000 Nm
Step-by-step explanation:
F = mg = 5000 N
h = 6 m
Work done
W = mgh = 5000*6= 30, 000 Nm
Answer:
30000 nm
Step-by-step explanation:
Arnez bought five shirts from a store and had $10 left. If he had only bought three shirts, he would have had $24 left. If each shirt costs the same, determine x, the cost of each shirt.
Answer:
x=8
Step-by-step explanation:
I WILL GIVE BRAINLIEST IF YOU HELP
A museum has an aquarium in the shape of a right rectangular prism that is 22.9 meters long, 7.5 meters wide, and 5.6 meters high. What is the volume, round to the nearest cubic meter, of the aquarium?
A. 280
B. 623
C. 1288
D. 962
Answer:
D. 962
Step-by-step explanation:
The volume of a rectangular prism is the length x width x height.
22.9*7.5*5.6=961.8
961.8 rounds up to 962
Write a paragraph (4-5 sentences) explaining how we can help or change racism to black people
No copying from internet please
Answer
A few ways we could stop racism against black people in this country is to stop the perpepuation of black stereotypes in media. Such as the loud, aggressive black man, or the rude, catty black woman. It causes a harmful view on black people and can result in racial profiling. Another way to combat this racism is to fight off systemic racism. Black people who have unique names, usually African names, are more likely to get turned down for a job when they turn in their resume to an establishment. This is because they automatically assume that they'll be trouble, and won't be a good worker.
Find the measure of an angle in a regular polygon with 22 sides
What is the answer for both of these questions? please fill in the blanks for me. I will mark you as the brainliest.
find the value of y if 2y +4=8
Answer:
[tex]\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }[/tex]
[tex]2y + 4 = 8 \\ 2y = 8 - 4 \\ 2y = 4 \\ y = \frac{4}{2} \\ y = 2[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\red{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Answer:
y=4/2=2
Step-by-step explanation:
If A+B+C=[tex]\pi[/tex] show that tan A + tan B +tan C = tan A.tan B.tan C
Answer:
[tex]a + b + c = \pi \\ = > c= \pi - a - b \\ < = > \tan(c) = \tan(\pi - a - b) = -\tan(a + b) [/tex]
Step-by-step explanation:
we have:
[tex] \tan(a) + \tan(b) + \tan(c) \\ = \tan(a) + \tan(b) - \tan(a + b) \\ = \tan( a) + \tan(b) - \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{ ( \tan(a) + \tan(b) ) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (1)[/tex]
we also have:
[tex] \tan(a) \tan(b) \tan(c) \\ = - \tan(a) \tan(b) \tan(a + b) \\ = \frac{ -(\tan( a ) + \tan(b) ) \tan(a) \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{( \tan(a) + \tan(b)) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (2)[/tex]
from (1)(2) => proven
one banana contains 105 calories. what percent of a 2000-calorie diet is contained in one banana
More than 6% . I don't know exactly how much, but I know it's more than 6% . Hope that helps..
Identify the type of correlation that is present in the scatterplot
Answer:
The scatter plot shows a positive correlation.
Which is the solution for the system of equations? Y = 2x-3
Y = -x
A. (1, -1)
B. No solution
C. (-1, 1)
D. (-1, -1)
Answer:
(1,-1)
Step-by-step explanation:
[tex] \large{ \begin{cases} y = 2x - 3 \\ y = - x \end{cases}}[/tex]
Since both are y-isolated equation. We can combine both.
[tex] \large{2x - 3 = - x}[/tex]
Since we want to solve for x-term, we need to isolate x-term.
So we move from -x which is the right side to x.
[tex] \large{2x - 3 + x = 0} \\ \large{3x - 3 = 0} \\ \large{3x = 3} \\ \large{x = 1}[/tex]
But we are not done yet. Solving system of equations, you must solve for y-term as well. (Because we have to answer in ordered pairs which are (x, y))
Substitute x = 1 in any given equations but I will substitute x = 1 in y = -x
[tex] \large{y = - x} \\ \large{y = - 1}[/tex]
Since we have got y-value. Therefore the answer is (1,-1)
write the image of a point ( 3 - 2) under reflection about x - axis
Step-by-step explanation:
I m not sure either u have written (-2).. ans is (3,-2)
Answer:
(3, 2 )
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
(3, - 2 ) → (3, 2 )
what is 1/8 times 2/7 in simplest form
Answer:
decimal form: 0.0357
fraction form: 375/10000
Step-by-step explanation:
in right teanglie ABC shown below what is the degree measure of \_ C!!
please help me
Answer:
20 use https://www.calculator.net/triangle-calculator.html
Step-by-step explanation:
Acute Isosceles Triangle
Side a = 1
Side b = 1
Side c = 0.51764
Angle ∠A = 75° = 1.309 rad = 5/12π
Angle ∠B = 75° = 1.309 rad = 5/12π
Angle ∠C = 30° = 0.5236 rad = π/6
C=30°B=75°A=75°b=1a=1c=0.518
Area = 0.25
Perimeter p = 2.51764
Semiperimeter s = 1.25882
Height ha = 0.5
Height hb = 0.5
Height hc = 0.96593
Median ma = 0.61966
Median mb = 0.61966
Median mc = 0.96593
Inradius r = 0.1986
Circumradius R = 0.51764
Vertex coordinates: A[0, 0] B[0.51764, 0] C[0.25882, 0.96593]
Centroid: [0.25882, 0.32198]
Inscribed Circle Center: [0.25882, 0.1986]
Circumscribed Circle Center: [0.25882, 0.44829]
+ Show Calculation Steps
The sixth grade class at Kennedy Middle School participated in a fundraiser. Each day they raised twice as much as the day before. On the first day they raised $24.
How much money did they raise over all five days of the fundraiser?
Answer options with 5 options
A.
$120
B.
$240
C.
$360
D.
$384
E.
$744
Answer:
Day 1- 24
Day 2- 48
Day 3- 96
Day 4- 192
Day 5- 384
Step-by-step explanation:
384, or C.
What is the length of X?
Answer:
x = 85
Step-by-step explanation:
Its a Pythagorean theorem question, being a^2 + b^2 = c^2.
and knowing that 168 is the entire base we would divide by 2 to get 84 as b.
The new equation would be 13^2 + 84^2 = c^2
Then squaring them to get 169 + 7056 = c^2
Then add them together and square root them [tex]\sqrt{x}[/tex] 7225 = c
The square root is 85 making it equal x.
(08.06 LC)
Identify the factors of x2 + 16y? (5 points)
O (x + 4y)(x + 4y)
O (x + 4y)(x - 4y)
Prime
O (x - 4y)(x - 4y)
Answer:
Prime
Step-by-step explanation:
2(x?)+16y
O(x+4y)(x+4y)
x²+4xy+4xy+16y²
x²+8xy+16y²
O(x+4y)(x-4y)
x²-4xy+4xy-16y²
x²-16y
Prime
O(x-4y)(x-4y)
x²-4xy-4xy+16y²
x²-8xy+16y²
All are incorrect except prime, so the answer is prime.
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hope it helps
A race is 5 kilometers long. Harold ran 3/4 of the race. How many kilometers did Harold run? PLEASE HURRY
Answer:
3.75
Step-by-step explanation:
I took a test and that was the answer
Harold ran 3.75 kilometers in 5 kilometers long race.
What is multiplication?The mathematical operation of multiplication is arithmetic. Additionally, it involves repeating the same forms of statements.
Example: 2 + 3 signifies that 2 is multiplied by 3 or that 3 is multiplied by 2 times.
Given, a race is 5 kilometers long.
Harold ran 3/4 of the race.
To find the numbers of kilometers, Harold run
That means,
we multiply 3/4 to the total race's length.
Required length
= 5 x 3/4
= 15/4
= 3.75
Therefore, Harold ran 3.75 kilometers.
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help what's the answer
Answer:
2nt one
Step-by-step explanation:
PLS HELPPPPPP OMG PLSSSSSSSSSSSSSS LOOK AT PHOTO PLSSSS HELPPP
Answer: B
Step-by-step explanation: The line crosses the Y axis at 3
solve the quadratic equation by completing the square: 6x²-11x-10=0
Step-by-step explanation:
6x² - 11x - 10 =0{use splitting middle term method} -60x²| |
-4. +15
(6x² - 4x) (15x - 10)2x( 3x - 2 ) +5( 3x - 2)(2x + 5) (3x - 2)2x = -5 or 3x = 2x = -5 or x = 2there fore x = 2Use the model to find the product of 0.5 x 0.6.
A)
0.27
B)
0.30
C)
0.33
D)
0.35
Answer:
0.3
Step-by-step explanation:
0.5 is equal to 1/2, so 1/2 x 0.6 = 0.3
(05.05 HC) Figure ABCD has vertices A(-4, 1), B(2, 1). C(2, -5), and D(-4, -3). What is the area of figure ABCD?
A:24
B:30
C:36
D:45
Answer:
The answer is A
Step-by-step explanation:
I got it right on the test.
Find the circumference of a circle whose radius is 4 feet. Use 3.14 for Pi.
Answer:
25.12
Step-by-step explanation:
The formula of the circumference of a circle is: C = 2(pi)(r)
Plug in 3.14 for pi and 4 for the radius.
C = 2(3.14)(4)
Multiply.
C = 25.12
Find the missing side. Round to
the nearest tenth.
Х
28°
15
X =
= [?]
Answer:
16.99
Step-by-step explanation:
Because I used trigonometry
13. What is the pressure on the bottom of a water tank filled to a depth of 4 feet? O A. 1.73 psi OB. 62.4 psi C. 249.6 psi D. 184.2 psi
Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. The correct option is A.
What is pressure?Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed.
The density of water is equal to 997 kg/m³, while the acceleration due to gravity is 9.81 m/s², also, given the depth of the water is 4 feet(1.2192 meters). Therefore, the pressure on the bottom of a water tank filled to a depth of 4 feet is,
Pressure = ρ × g × H = 997 × 9.81 × 1.2192 = 11924.47 N/m²
Now, If we convert the pressure from N/m² to psi, then we have to divide 11924.47 N/m² by 6895, therefore, the pressure will be,
Pressure = 11924.47 N/m² / 6895 = 1.729 psi ≈ 1.73 psi
Hence, the correct option is A.
Learn more about the Pressure:
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Henry found his mass on a metric scale. What could Henry's mass be?
O
A. 26 kg
a
B. 2,600 kg
O
C. 8g
0
D. 600 g