What is the approximate value of the y intercept and what does it mean in this example?

Answer:

[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Step-by-step explanation:

[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Answer:

d

Step-by-step explanation:

180-149= 31.

31+ 122= 153

180-153= 27

a= 27

Answer:

(x+7)(x-1)

Step-by-step explanation:

x^2 + 6x -7

so here we need two number that give 7 when multiplied and 6 when subtracted

7 and 1 are the numbers because

7*1=7  and ,

7-1=6  so,

x^2 + (7-1)x -7

x^2 +7x -x -7

take common from first two terms and from third and fourth term

x(x+7)-1(x+7)

take (x+7) as common

(x+7)(x*1 -1*1)

(x+7)(x-1)

Answer:

there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

Step-by-step explanation:

Given the data in the question;

Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,

t is the number of months since January.

Now, we use a cosine curve to model this scenario

Vertical shift will be;

D = ( 6 + 14 ) / 2 = 20 / 2

D = 10

Next is the Amplitude;

|A| = ( 6 - 14 ) / 2

|A| = 4

Now, the horizontal stretch factor will be;

B = 2π / 12

B = π/6

Hence;

S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1

Now we find when there will be less than 9 million square meters of sea ice;

S(t) = 9

so we have

9 = 4cos( π/6 × (t-2) ) + 10

9 - 10 = 4cos( π/6 × (t-2) )

-1 = 4cos( π/6 × (t-2) )

-1/4 = cos( π/6 × (t-2) )

so we have;

cos⁻¹( -1/4 ) = π/6 × (t₁-2)  -------- let this be equation 2

2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2)  -------- let this be equation 3

so we solve equation 2 and 3

we have'

t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )

t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )  

t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )  

t₁ - t₂ = 6/π × ( π - 104.4775 )

t₁ - t₂ = 6/π × ( π - 104.4775 )  

t₁ - t₂ = 5.035

therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.

Answer:

Average rate of change = 5

Step-by-step explanation:

Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,

Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]

From the table,

f(5) = 10

f(4) = 5

Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]

                                                                                    = 5

Answer:

=5

Step-by-step explanation:

Answer:

173 cm

105 kg

Step-by-step explanation:

Given :

BSA= √wh /3600

where w = weight in kg and h = height in cm.

A.)

w = 75 kg ; BSA = 1.9 ; h =?

BSA= √wh /3600

1.9 = √75h /3600

Take the square of both sides

1.9² = 75h /3600

1.9² * 3600 = 75h

12996 = 75h

h = 12996 / 75

h = 173.28 cm

h = 173 cm

B.)

h = 166 ; BSA = 2.2

BSA= √wh /3600

2.2 = √w166 /3600

Take the square of both sides

2.2² = 166w /3600

2.2² * 3600 = 166w

17424 = 166w

w = 17424 / 166

w = 104.96 kg

w = 105 kg

Using the model given, we have that:

a) h = 173 cm.

b) w = 105 kg.

The BSA, for a person of weight w and height h, is given by:

[tex]BSA = \sqrt{\frac{wh}{3600}}[/tex]

Item a:

[tex]BSA = 1.9, w = 75[/tex], hence:

[tex]BSA = \sqrt{\frac{wh}{3600}}[/tex]

[tex]1.9 = \sqrt{\frac{75h}{3600}}[/tex]

[tex]\left(\sqrt{\frac{75h}{3600}}\right)^2 = 1.9^2[/tex]

[tex]\frac{75h}{3600} = 3.61[/tex]

[tex]h = \frac{3600(3.61)}{75}[/tex]

[tex]h = 173[/tex]

Hence:

h = 173 cm.

Item b:

[tex]BSA = 2.2, h = 166[/tex], hence:

[tex]BSA = \sqrt{\frac{wh}{3600}}[/tex]

[tex]2.2 = \sqrt{\frac{166w}{3600}}[/tex]

[tex]\left(\sqrt{\frac{166w}{3600}}\right)^2 = 2.2^2[/tex]

[tex]\frac{166w}{3600} = 4.84[/tex]

[tex]w = \frac{3600(4.84)}{166}[/tex]

[tex]w = 105[/tex]

Hence:

w = 105 kg.

A similar problem, in which there is also an application of a formula, is given at https://brainly.com/question/24348510

9514 1404 393

Answer:

  24.3 ft

Step-by-step explanation:

If h is the height of the ladder up the tree, the geometry can be modeled as a right triangle with legs h and 6, and hypotenuse 25. The Pythagorean theorem gives you the relation ...

  h² +6² = 25²

  h² = 625 -36 = 589

  h = √589 ≈ 24.3

The ladder reaches about 24.3 feet up the tree.

Answer:

v

Step-by-step explanation:

Answer:

Convenience sampling

Step-by-step explanation:

When sampling is done based in degree of ease or samples picked from observations that are easily accessible rather than prioritizing randomness or selection which will most be representative of the population, then such sampling is called convenience sampling. In some texts, it is also referred to as grab sampling as researchers choose from close, easy to reach samples. In the scenario above, the quality control takes the easy procedure of checking the first and last 10 motorcycles as this is easier than having to take samples at random tune intervals which will be a better representation of the entire motorcycles.

Answer: How are we going to point it?

Step-by-step explanation:

Answer:

216 square feet

Step-by-step explanation:

The formula for the surface area of a rectangular prism is:

2 (lw + hl + hw)

w= width

h= height

l= length

Use the formula with the given dimensions:

2 (6 • 2 + 12 • 6 + 12 • 2)

= 2 (12 + 72 + 24)

= 2 (108)

= 216

Surface area is measured in square feet

(feet in this case)

Hope this helps

Did you manage to solve it?

Answer

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

96 / (100%-40%) = 96/ (60%)

= 96/0.6 = 160

Q) 96/(100% - 40%)

→ 96/ 60%

→ 96/ 0.6

→ 160 is the number.

Answer:

4/3

Step-by-step explanation:

Out of the six sides 3 are odd and there's 5 numbers greater than 1. Basically these turn to the fractions 3/6 and 5/6 (these fractions stand for the probability they get rolled on this die).

Since the question says OR and not AND you add these fractions!

3/6 + 5/6 = 4/3

Answer:

the second one for #4 and the third one for #5

Step-by-step explanation:

4. The sum of x and y is 24, so x+y = 24. The difference is 15, so x-y = 15, or

y-x=15 (they didn't specify which was which). Therefore, A, C, and D are correct, so x = 15-y is the answer (x = 15-y is the same as x+y = 15, which is false).

5.

Matt = 6 apple pies + 4 lemon pies and he got 80 dollars.

Ming = 6 apple pies + 5 lemon pies and he got 94 dollars.

If apple pie is "a" and lemon is "l":

6a + 4l = 80

6a + 5l = 94,

so C is the answer

Answer:

There are two major methods of forecasting

One is the Causal method and the 2nd one is the times series method

Causal method mainly tries to find out cause and effect relation between variable and various factors impacting that variable while the time series method infuences the utilization of the historical data and mainly focus to forecast based on the trend present. It simply ignores the other variables. It just tries to give an idea of a trend, it can't predict the impact of other variables as in causal method.

Linear regression analysis can be utilized in both sort of estimating technique. By linear regression analysis we can anticipate effect of different factor on factor variable. It anticipate the pattern, yet additionally gives an idea about connection among variable and different elements affecting it. That is the reason Linear regression is considered as best technique for forecasting.  

Presently, going to the next part of this inquiry, Time period utilized in moving normal is settled based on fluctuation showing up in how much period, to smoothen out the variation. Also, Alpha value is chosen dependent on the time span to smoothen out the variation in the information. Changing of time-frame or distinctive alpha will make estimation complex. And furthermore, it will make computation more probabilistic as opposed to deterministic which may create mistake whenever done by manual calculation. That is the reason program are important in such sort of computation

Answer:

40°

Step-by-step explanation:

because angle In an isosceles triangle base angles are same and angle in a triangle add up to 180° and angle on a straight line add up to 180°

hope this helps:)

Answer:

1

Step-by-step explanation:

Assuming your mean we have the points

(6, -10) and ( 3, -13)

We can use the slope formula

m = (y2-y1)/(x2-x1)

m = ( -13 - -10)/( 3 - 6)

    = (-13+10)/( 3-6)

   = -3 / -3

    = 1

Step-by-step explanation:

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The probability is 1/3 that the number on the counter is not a multiple of three.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

We have to determine the probability that the number on the counter is not a multiple of three.

There are nine counters in a bag numbered from one to nine.

If a counter is drawn at random from the bag.

One to nine, there are three numbers are multiple of three that is (3, 6, 9)

Here favorable outcomes = 3

So the probability that the number on the counter is not a multiple of three as

⇒ 3/9

⇒ 1/3

Therefore, the probability is 1/3 that the number on the counter is not a multiple of three.

Learn more about the probability here:

brainly.com/question/11234923

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There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.

In this question we have a triangle with two known sides and a known angle. By the law of sines we find the possible values of the angle D:

410/sin 120° = 440/sin D

Please notice that the sum of the internal angles of triangles equals 180°. Then,

sin D = (440/410) · sin 120°

sin D ≈ 0.929

There are two solutions for the triangle DEF: ∠ D₁ ≈ 68.3°, ∠ D₂ ≈ 111.7°.

To learn more on law of sines: https://brainly.com/question/17289163

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Answer: True

Step-by-step explanation:

The subjects of an experiment should be selected at random so that they

represent the population is true.

Once the sample size has been decided, a sample should be taken from the sample size which will represent the population. This gives everyone an equal chance of being selected as there's no bias.

Answer:

The total pay would be $50, But there would also be tax to consider in this situation.

Answer: choice D

Step-by-step explanation:

In order for something to be a function for every x input there must be exactly 1 y output. This means that if x is a number then y must always be 1 number and that 1 number only.

Answer:

-8

Step-by-step explanation:

g(4)=8

8÷4=2

g=2

g(-4)=2(-4)

=(-8)

holp it can help you.