A diff diver plunges from a height of 25 ft above the water surface. The distance the diver falls in t seconds is given by the function (t) - 16eft. Which equation can be solved fort to find the time (in seconds) when the diver hits the water?

Answer:

\(b_0 = 16.471\)

Step-by-step explanation:

Given

\(\begin{array}{ccccc}x & {15} & {12} & {10} & {7} \ \\ y & {5} & {7} & {9} & {11} \ \end{array}\)

Required

The least square estimate \(b_0\)

Calculate the mean of x

\(\bar x = \frac{\sum x}{n}\)

\(\bar x = \frac{15+12+10+7}{4} =\frac{44}{4} = 11\)

Calculate the mean of y

\(\bar y = \frac{\sum y}{n}\)

\(\bar y = \frac{5+7+9+11}{4} =\frac{32}{4} = 8\)

Calculate \(\sum(x - \bar x) * (y - \bar y)\)

\(\sum(x - \bar x) = (15 - 11) * (5 - 8)+ (12 - 11) * (7 - 8) + (10 - 11) * (9 - 8)+ (7 - 11) * (11 - 8)\)

\(\sum(x - \bar x) = -26\)

Calculate \(\sum(x - \bar x)^2\)

\(\sum(x - \bar x)^2 = (15 - 11)^2 + (12 - 11)^2 + (10 - 11)^2 + (7 - 11)^2\)

\(\sum(x - \bar x)^2 = 34\)

So:

\(b = \frac{\sum(x - \bar x) * (y - \bar y)}{\sum(x - \bar x)^2}\)

\(b = \frac{-26}{34}\)

\(b_0 = y - bx\)

\(b_0 = 5 - \frac{-26}{34}*15\)

\(b_0 = 5 + \frac{26*15}{34}\)

\(b_0 = 5 + \frac{390}{34}\)

Take LCM

\(b_0 = \frac{34*5+ 390}{34}\)

\(b_0 = \frac{560}{34}\)

\(b_0 = 16.471\)

Answer: x=-18

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

\( \huge{ \fbox{ \sf{x = - 18}}}\)

Step-by-step explanation:

\( \text{4(7x + 3) = - 3(2 - 9x)}\)

\( \text{Step \: 1 \: : Distribute \: 4 \: through \: the \: parentheses}\)

\( \hookrightarrow{ \sf{28x + 12 = - 3(2 - 9x)}}\)

\( \text{Step \: 2 \: : Distribute \: - 3 \: through \: the \: parentheses}\)

\(\hookrightarrow{ \sf{28x + 12 = - 6 + 27x}}\)

\( \text{Step \: 3 \: : Move \: 27x \: to \: left \: hand \: side \: and \: change \: its \: sign}\)

\( \hookrightarrow{ \sf{28x - 27x + 12 = - 6}}\)

\( \text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \hookrightarrow{ \sf{28x - 27x = - 6 - 12}}\)

\( \text{step \: 5 \: : Collect \: like \: terms}\)

\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)

\( \hookrightarrow{ \sf{x = - 6 - 12}}\)

\( \text{step \: 6 \: : Calculate}\)

\( \text{ \underline{ Remember!}} : \sf{ \: The \: negative \: integers \: are \: always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}\)

\( \hookrightarrow{ \boxed{ \sf{x = - 18}}}\)

Hope I helped!

Best wishes ! :D

~\( \text{TheAnimeGirl}\)

The value of fraction 0.5 7  is equal to 1/2.

We are given that;

Number = 0.57

Now,

There are different ways to express a fraction as a decimal, but one common method is to divide the numerator by the denominator.

For example, 1/2 as a decimal is 1 ÷ 2 = 0.512.

Another method is to use a fraction to decimal conversion chart or calculator345. According to these sources, 0.5 as a fraction is equal to 5/10 or 1/2.

These fractions are equivalent because they have the same value when simplified or reduced.

To simplify a fraction, we can divide both the numerator and the denominator by their greatest common factor (GCF).

Therefore, by algebra the answer will be 1/2.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ6

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

Answer:

75

Step-by-step explanation:

just add them up to get the angle

Answer:

it would be within the range of $0.77 <x< $0.78

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

for more such question on matrix visit

https://brainly.com/question/2456804

#SPJ8

Answer:

S=− \(\frac{4}{Q}\)

Step-by-step explanation:

−5=(QS)−1

Swap sides so that all variable terms are on the left hand side.

QS−1=−5

Add 1 to both sides.

QS=−5+1

Add −5 and 1 to get −4.

QS=−4

Divide both sides by Q.

\(\frac{QS}{Q}\)=\(\frac{-4}{Q}\)

Dividing by Q undoes the multiplication by Q.

S= \(\frac{-4}{Q}\)

Divide −4 by Q.

S=− \(\frac{4}{Q}\)

​

Answer:

  -24

Step-by-step explanation:

\(\sqrt{144}-(16-5\times 2)^2=\sqrt{144}-(16-10)^2=\sqrt{144}-6^2\\\\=12-36=\boxed{-24}\)

Your calculator can be helpful for this.

Answer:

LCM = 18

Step-by-step explanation:

Multiples of 6:  6, 12, 18

Multiples of 9:  9, 18

Answer:

There are 12 blocks in the bottom layer

Step-by-step explanation:

We see from the diagram that in the bottom layer,

length = 3 cm

width = 4 cm

And that there are 3 blocks for the 3 cm length,

Hence each block has a length of 1 cm (the 3 then make up 3 cm)

And there are 4 blocks for the 4 cm width

Hence the width is also 1 cm (4 of these make up 4 cm width)

Now, to find the total number of blocks,

we just multiply the length and width,

so, (3)(4) = 12

so there are 12 blocks in the bottom layer

The function f(x) in slope-intercept form is Y= −3X−10.

In the given question, linear function f, f(2)=0 and f(4)=-6.

We have to write function f(x) in slope-intercept form.

We have to find equation for f(x)

f(2)=0, and f(4)=−6,

Now we have to find slope

Slope(m)=−6−0/4−2

m = −6/2

m=−3

Now the general equation of line is

Y=MX+C

where M = slope of the line, C is the Y intercept value, X is independent variable and Y is dependent variable.

At point (2,4)

4 = (−3)×(2)+C

4 = −6+C

Add 6 on both side, we get

C = 10

Equation for f(x) is.

Y=(−3)X−(10)

Y= −3X−10

To learn more about slope-intercept form link is here

brainly.com/question/9682526

#SPJ4

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer: 4

Step-by-step explanation:

since they are comparing it red to blue marbles and in 3:4 ratio 4 is the second one and it is comparing red to BLUE the second 1 is blue

Answer:

17:53=5:53pm

Step-by-step explanation:

We know that

• The slope is -3.

• The y-intercept is (0,4).

We use the slope-intercept formula.

Where m = -3, and b = 4.

Replacing these values, we have the equation.

Answer:

area is 254.34 circumference is 56.52

Step-by-step explanation:

To find the area you need to follow the formula r^2(pi)

so it would be 9x9x3.14 which is 254.34

to find circumference you need to find diameter which is double the radius (9x2) so the diameter is 18

To find circumference to need to do radius x pi

18x3.14 is 56.52

Answer:

H

Step-by-step explanation:

180-48=132

Answer:

2cot²(x)

Step-by-step explanation:

The simplified expression for cot²x/1+cot²x,  cos²x.

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

Given, A trigonometric function \(\frac{cot^2x}{1 + cot^2x}\),

Now, Using different trig identities we have,

\(= \frac{cot^2x}{cosec^2x}\)

\(= \frac{\frac{cos^2x}{sin^2x}}{\frac{1}{sin^2x}}\)

\(= {\frac{cos^2x}{sin^2x}}\times\frac{sin^2x}{1}\).

= cos²x.

learn more about trig identities here :

https://brainly.com/question/19549073

#SPJ7

The integers are 12,14 and 16

Consecutive even integers are represented as:

x, x + 2 and x + 4

So, the statement is represented as:

7 * (x + x + 2 + x +4) = 140 + 11 * (x + 2)

Evaluate the like terms

7 * (3x + 6) = 140 + 11 * (x + 2)

Open the brackets

21x + 42 = 140 + 11x + 22

Collect the like terms

21x -11x =

Evaluate

10x = 120

Divide by 10

x = 12

So, we have

x + 2 = 14

x + 4 = 16

Hence, the integers are 12,14 and 16

Read more about consecutive numbers at:

https://brainly.com/question/10853762

#SPJ1

Answer:

38

Step-by-step explanation:

f(x)=6x+2

6x6 (6 sqaured)

f(36)=36x+2

Now we add 36+2

        38

Answer:

14 and 50 :)

Step-by-step explanation:

Answer:

To negative numbers makes a positive number.

(only in dividing and multiplying)

Step-by-step explanation:

Please mark me brainliest