Use implicit differentiation to find dy/dx at the given point. Show steps

Answer:

Step-by-step explanation:

The value of the expression a^2 - 2ac + 5b is, 175.

What is the value of expression?

When the variables and constants in the expression are given values, the calculation that this expression describes yields the value. In an algebraic expression, letters can substitute for numbers.

Consider, the given expression,

a^2 - 2ac + 5b

The values of a, b and c are

a = -8, b = 3, c = 6.

Plug these values in the above expression,

So, the expression becomes

(-8)^2 - 2(-8)(6) + 5(3) = 64 + 96 + 15 = 175

Hence, the value of the expression is, 175.

To know more about the value of the expression, click on the link

https://brainly.com/question/28892104

#SPJ1

Answer:

  28.072°, 61.928°

Step-by-step explanation:

You want the measures of the acute angles in a right triangle with sides 8, 15, 17.

Any of the (inverse) trig functions can be used to find the angles. You know the acute angles are complementary, so finding one tells you the measure of the other.

  Tan = Opposite/Adjacent

The smallest angle (A) is adjacent to side 15 and opposite side 8.

  tan(A) = 8/15

  A = arctan(8/15) ≈ 28.072°

The complement is angle B:

  B = 90° -28.072° = 61.928°

__

Additional comment

We have taken sides {a, b, c} = {8, 15, 17}. The angles opposite those sides are A, B, C.

You can also use ...

  A = arcsin(8/17)

  B = arccos(8/17)

At a butcher shop, Hilda bought beef and pork. she left with 18.8/25 pounds of meat. Express the number of pounds of pork she bought using a decimal.

= 18.8/25

= 0.752

The statements on the relations and whether they are proportional relationships is given as follows:

A proportional relationship is a linear function that has intercept of zero and slope as the constant of the proportionality k, as follows:

y = kx.

A relation represents a proportional relationship if the ratio of the output y by the input x is the same for all the points.

For the first relation, the constant for each point is given as follows:

Hence it represents a proportional relationship, and the equation is given as follows:

y = -1.5x.

For the second relationship, the constants are:

Different constants, hence it does not represent a proportional relationship.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer: 23

Step-by-step explanation: Please give brianlist

(a) The respondents who chose silver 2.3 times more than red , and

(b) the respondents who chose either silver or black are 3.8 times more than who chose red .

In the question ,

a table is given which shows popular sports cars colors in North America .

Part(a)

portion of respondents who chose silver = 0.20  ,

portion of respondents who chose red = 0.09 ,

the number of times more respondents chose silver than red = 0.20/0.09

= 20/9

= 2.22222

On rounding to the nearest tenth

≈ 2.3

Part(b)

portion of respondents who chose black = 0.14 ,

portion of respondents who chose either black or silver = 0.20 + 0.14

= 0.34

number of times more respondents chose either silver or black than red

= 0.34/0.09

= 3.7777777

rounding to the nearest tenth

≈ 3.8

Therefore , (a) The respondents who chose silver 2.3 times more than red , and

(b) the respondents who chose either silver or black are 3.8 times more than who chose red .

The given question is incomplete , the complete question is

Use the table that shows popular sports cars colors in North America

(a) how many times more respondents to silver than red round to the nearest 10th if necessary.

(b) How many times more respondents chose either silver or black than red?   Round to the nearest tenth if necessary.

Learn more about Multiple here

https://brainly.com/question/6424430

#SPJ1

The value of x is 90 if the 2+10+18+…+x=552 which is an arithmetic sequence.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

The given is:

2+10+18+…+x=552

The above is the arithmetic sequence:

a = 2

d = 10 - 2 = 8

a(n) = x

a + (n-1)d = x

2 + (n-1)8 = x ..(I)

s(n) = 552

(n/2)[a + x] = 552

(n/2)[2 + x] = 552 ..(II)

From equation (I) and (II)

The values of x and n:

[tex]\rm \begin{pmatrix}x=90,\:&n=12\\ x=-98,\:&n=-\frac{23}{2}\end{pmatrix}[/tex]

the value of n -23/2 is not possible

x = 90

Thus, the value of x is 90 if the 2+10+18+…+x=552 which is an arithmetic sequence.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ1

The value of x is 66°.

What are parallel lines?

No matter how far they may extend in either direction, parallel lines are ones that are equally spaced apart from one another and never cross.

If line m is parallel to line n, the two angles given will be congruent because they will be alternate exterior angles (which are congruent).

Here, we have

m = 132°

n = 2x°

This means we will set both parallel lines equal to each other and solve for x.

132° = 2x°

x = 66°

Hence, the value of x is 66°.

To learn more about the parallel lines from the given link

https://brainly.com/question/26961508

#SPJ1

Answer

34.056 I'm pretty sure it's right. I took a test with the same question

Answer:

34.556

Step-by-step explanation:

= (3x10) + (4x1) + (5x1/10) + (5x1/100) + (6x1/1000)

= 30 + 4 + 0.5 + 0.05 + 0.006

[tex]{ \boxed{ \red{ \sf{y = 3 + 5x}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \tt{y - 5x = 3}}}[/tex]

Shift -5x to right side then,

[tex]{ \boxed{ \blue{ \tt{y = 3 + 5x}}}}[/tex]

Considering the given sample, it is found that:

a) The confidence interval is: (71.43, 77.17).

b) The interval does not contain 78, hence the manufacturer's claim is not correct.

c) The sample size needed is: 55.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 12 - 1 = 11 df, is t = 2.201.

Using a calculator, the other parameters for the interval are given as follows:

[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]

Hence the lower bound of the interval is:

74.3 - 2.201 x 4.52/sqrt(12) = 71.43.

The upper bound is:

74.3 + 2.201 x 4.52/sqrt(12) = 77.17.

For item c, we have that:

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Then the sample size is obtained when M = 1.04 as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]

[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]

n = 55. (rounded up).

More can be learned about confidence intervals at https://brainly.com/question/17073112

#SPJ1

The shares of $2.25 are 200 and the shares of $2.75 are 700.

According to the question,

We have the following information:

An investor bought 700 shares of stock, some at $2.25 per share and some at $2.75 per share. And the total cost was $1825.00.

Now, let's take the shares of $2.25 to be x and the shares of $2.75 to be y.

So, we have the following expression:

x+y = 700

x = 700-y ....(1)

2.25x+2.75y = 1825 ...(2)

Putting the value of x from equation 1:

2.25(700-y)+2.75y = 1825

1575-2.25y+2.75y = 1825

1575+0.5y = 1825

0.5y = 250

y = 250/0.5

y = 500

Now, putting the value of y in equation 1:

x = 700-y

x = 700-500

x = 200

Hence, the shares of $2.25 are 200 and the shares of $2.75 are 700.

To know more about shares here

https://brainly.com/question/21781662

#SPJ1

Answer:

Step-by-step explanation:

You can determine whether a function is increasing or decreasing by taking its derivative.

If the derivative is bigger than 0, then function is increasing.

If the derivative is less than 0, then the function is decreasing.

You can also graph the functions to determine whether they are increasing or decreasing.

The time taken for the rocket to reach its maximum height is; 1.25 seconds.

The maximum height reached by the toy rocket is; 44.5 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 40t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 40 = 0

-32t = -40

t = -40/-32

t = 1.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 1.25 seconds.

Also, the maximum height reached by the rocket is at; h (1.25);

h(1.25) = -16(1.25)² + 40 (1.25) + 7

= -25 + 62.5 + 7

= 44.5

The maximum height reached is; 44.5 feet.

Read more on maximum height;

https://brainly.com/question/82347

#SPJ1

Answer:

step by step answer at least

When the capital letter Y is rotated 180°,  Our point A(x,y) rotates 180 degrees counterclockwise around the origin to become A' (-x,-y). transforming both x and y negative is all we do as a result.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given,

The capital letter Y is rotated 180°.

The coordinates shift from (x, y) to (x, z) when you reflect a figure across the x-axis (x, -y). The coordinates would change from (x, -y) to (x, y) if you then reflected it over the y-axis (-x, -y). As a result, reflecting over the x- and y-axes will be similar to turning 180 degrees counterclockwise. Our point A(x,y) rotates 180 degrees counterclockwise around the origin to become A' (-x,-y). transforming both x and y negative is all we do as a result.

To learn more about transformation, visit:

https://brainly.com/question/11709244

#SPJ13

Answer:

(f o g)(x) = 8x² + 10x + 3

Step-by-step explanation:

(f o g)(x) = f(g(x))

              = 2 (4x² + 5x) + 3

              = 8x² + 10x + 3

The required time taken by the sofia is 15.75 minutes.

Work is defined as the efficiency of the person to do a particular work in the certain period of time. Work is directly proportional to the efficiency and inversely proportional  to time.

Formula, work = efficiency/time

According to the given data in the question:

Let efficiency of sofia be 1, then efficiency of elsa is 3.

We have time for 21 minutes

total work =efficiency/time

time for sofia = 3x and that of elsa = 1x

then time= 4x = 21 = 5.25= x

time taken by sofia is 3(5.25) = 15.75 minutes

To know more about time and work visit:

brainly.com/question/3854047

#SPJ9

Answer:

x = - 1

Step-by-step explanation:

- 9(1 + 6x) = 42 - 3x ← distribute parenthesis on left side by - 9

- 9 - 54x = 42 - 3x ( add 3x to both sides )

- 9 - 51x = 42 ( add 9 to both sides )

- 51x = 51 ( divide both sides by - 51 )

x = - 1

Answer:-1=x

Step-by-step explanation:

-9(1+6x)=42-3x

-9-54x=42-3x

+54x          +54x

-9=42+51x

-42     -42

-51/51=51x/51

-1=x

The ordered pairs that are on the graph of the linear equation are:

{(2,2), (3,5), (– 1,– 7), (0, -4)}

Here we have a list of ordered pairs and we want to see which ones are solutions for the given linear equation:

3x = y + 4

To check that, we can just replace the values of each ordered pair in the equation and see if the equation is true or false. If it is true, then the ordered pair is a point on the graph.

1) (7,– 1)

3*7 = -1 + 4

21 = 3  this is false.

2) (2,2)

3*2 = 2 + 4

6 = 6   this is true.

3) (3,5)

3*3 = 5 + 4

9 = 9  this is true.

4) (0,4)

3*0 = 4 + 4

0 = 8  this is false.

5) (– 1,– 7)

3*-1 = -7 + 4

-3 = -3  this is true.

6) (0, -4)

3*0 = -4 + 4

0 = 0  this is true.

So the correct options are:

{(2,2), (3,5), (– 1,– 7), (0, -4)}

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

Without seeing the picture I would say that all are true

Step-by-step explanation:

A proportional relationship does go through the origin.  It is a straight line.  a straight line does not curve.

Answer:-2.326

Step-by-step explanation:i believe it's that

The value of one fourth squared times one fourth raised to the zero power end quantity all raised to the second power is 1/256.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

From the information, the exponent illustrated will be:

= (1/4^2 × 1/4^0)²

= (1/16 × 1)²

= (1/16)²

= 1/16 × 1/16

= 1/256

The value is 1 / 256.

Learn more about exponents on:

brainly.com/question/13669161

#SPJ1

Answer:

The number "2" does not follow the same pattern

Step-by-step explanation:

as the numbers "2, 20, 4, 8, 300." A pattern is given: 2,20, 4,8,300.

2 is the number which doesn't share the same pattern as 20, 4, 8, 300

A number system is defined as a system of writing to express numbers.

Given,

We need to find the number which doesn't share the same pattern as: 2, 20, 4, 8, 300

We can observe that in the given patterns 2,20, 4,8,300​, all the numbers are divisible by 4 except 2.

Twenty by four equal to five

20/4=5

Four by four equal to one

4/4=1

Eight by four equal to two

8/4=2

Three hundred  by four equal to Seventy five

300/4=75

2 is not divisible by 4.

Hence, 2 is the number which doesn't share the same pattern as 20, 4, 8, 300

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ2