What is the value of z for the equation fraction 1 over 4z = −fraction 7 over 8 + fraction 1 over 8z? −3−737

What Is The Value Of Z For The Equation Fraction 1 Over 4z = Fraction 7 Over 8 + Fraction 1 Over 8z?

Answers

Answer 1

-7

Explanation

Step 1

given

[tex]\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z[/tex]

subtrac (1/4)z in both sides

[tex]\begin{gathered} \frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z \\ \frac{1}{4}z-\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z-\frac{1}{4}z \\ 0=-\frac{7}{8}-\frac{1}{8}z \end{gathered}[/tex]

Step 2

add 7/8 in both sides

[tex]\begin{gathered} 0=-\frac{7}{8}-\frac{1}{8}z \\ 0+\frac{7}{8}=-\frac{7}{8}-\frac{1}{8}z+\frac{7}{8} \\ \frac{7}{8}=-\frac{1}{8}z \\ \end{gathered}[/tex]

finally, multiply both sides by -8 in order to isolate z

[tex]\begin{gathered} \frac{7}{8}=-\frac{1}{8}z \\ \frac{7}{8}*-8=-\frac{1}{8}z*-8 \\ -7=z \end{gathered}[/tex]

therefore, the answer is

-7

I hope this helps you


Related Questions

Instructions: Solve the system. Enter your answer as an ordered pair.

Answers

Given the system:

[tex]\begin{gathered} 3x-9y=12\text{ Eq. 1} \\ 3x+4y=-1\text{ Eq. 2} \end{gathered}[/tex]

First, we solve for 3x on both equations, as follows:

[tex]\begin{gathered} 3x=12+9y \\ 3x=-1-4y \end{gathered}[/tex]

Equating both equations:

[tex]\begin{gathered} 12+9y=-1-4y \\ 13=-4-9y \\ 13=-13y \\ y=-1 \end{gathered}[/tex]

Substituting y on equation 2:

[tex]\begin{gathered} 3x+4y=-1\text{ Eq. 2.} \\ 3x+4\times(-1)=-1 \\ 3x=-1+4 \\ 3x=3 \\ x=1 \end{gathered}[/tex]

ANSWER

(1, -1)

Poland Spring Hotel is a 500-room property that offers only rooms, no F&B service. You are in the process of evaluating the business as an investment. Calculate the breakeven sales and rooms using the information below

Answers

Answer: GAS

Step-by-step explanation:

On August 31, 2024, Shocker borrows $57,000 from a local bank. A note is signed with principal and 9% interest to be paid on August 31, 2025. Record the adjusting entry for interest for Shocker at its year-end of December 31.

Answers

(a)Dr Unearned Revenue $1,400

Cr Service Revenue $1,400

(b)Dr Advertising Expense $880

Cr Prepaid Advertising $880

(c)Dr Salaries Expense $7,800

Cr Salaries Payable $7,800

(d)Dr Interest Expense $1,360

Interest Payable $1,360

Journal entry preparation

(a) According to the information provided, Shocker gets a $4,200 payment from a client for services done over the following three months, which implies the journal entry will be:

Unearned Dr. $1,400 in revenue

($4,200 x 1/3)

$1,400 in Cr Service Revenue

(a) Based on the information provided, we were told that the firm pays a local radio station $2,640 for radio advertisements throughout the months of December, January, and February, which implies that the Journal entry would be entered as:

Dr. Advertising Cost $880

($2,640 x 1/3)

$880 in Cr Prepaid Advertising

(c) According to the information provided, the corporation Employee salaries for the month of December were $7,800, which will be paid on January 7, 2022, implying that the Journal entry would be:

Dr Salaries Cost $7,800

$7,800 in Cr Salaries

(d) According to the facts provided, Shocker borrows $68,000 from a local bank, which implies the Journal entry will be:

$1,360 in Dr. Interest Expense

($68,000 x 6% x 4/12)

$1,360 in payable interest

Learn more about Business economics at

https://brainly.com/question/18272508

#SPJ1

how the absolute value is never negative

Answers

Answer:

absolute value is a distance from 0; distance cannot be negative

Step-by-step explanation:

the def of absolute value is a numbers distance from 0

distances cannot be negative no matter what you are talking about

Answer: The point of absolute value is to find the distance from a number to 0, which can never be less than 0.

Step-by-step explanation:

The point of absolute value is to find the distance from a number to 0.

For example, if a number line has a -3 point on it, how far away will it be to 0.

<=====o=======o======>

          -3             0

The answer is 3! Just like the absolute value

|-3| = ?

3 = ?

Find the time (in years) for the investment to double. (Round your answer to two decimal places)

Answers

Solution

Step 1

Write the compound interest formula

[tex]\text{A = P\lparen1 + }\frac{r}{n})^{nt}[/tex]

Step 2

n = 4 (quarterly)

[tex]\begin{gathered} \text{P = x} \\ \text{A = 2x} \\ r\text{ = 7}\frac{3}{4}\text{ = 7.75\% = 0.0775} \end{gathered}[/tex]

Step 3:

Substitute in the formula to find t.

[tex]\begin{gathered} 2x\text{ = x\lparen 1 + }\frac{0.0775}{4})^{4t} \\ \text{2 = \lparen1 + 0.019375\rparen}^4t \\ \text{2 = 1.019375}^{4t} \\ Take\text{ natural logarithm of both sides} \\ In(2)\text{ = 4t In\lparen1.019375\rparen} \\ 4t\text{ = }\frac{ln(2)}{ln(1.019375)} \\ 4t\text{ = 36.12080351} \\ t\text{ = }\frac{36.12080351}{4} \\ t\text{ = 9.03 years} \end{gathered}[/tex]

Final answer

t = 9.03

The adult daily dosage for a certain medicine is 90 mg​ (milligrams) of medicine for every pounds of body weight.
At this​ rate, find the daily dose for a man who weighs 175 pounds.

Answers

A daily dose of 15750 mg is required of a certain medicine for a man weighing 175 pounds

An adult daily dose of a certain medicine = 90 mg for every pound of body weight

Daily dose: The adult daily dose specifies the amount of drug dose in mg that must be taken within 24 hours as per the body weight of the person. The body weight of the person determines how much dose is required for the medicine to be effective in the body.

Weight of the man = 175 pounds

The daily dose for a man is given:

Weight of man*Daily dose per pound of body weight

= 175*90

= 15750

Learn more about weight:

https://brainly.com/question/23312072

#SPJ1

Find the point-slope form of the equation given: g(5) = 10 and g(2) = 8

will give brainliest

Answers

Answer:

[tex]y -10=\cfrac{2}{3} (x -5 )[/tex]

========================

Given

Two points: (5, 10) and (2, 8)

To find

The point-slope form of the equation representing this line

Solution

Point-slope form is:

[tex]y -y_1=m(x - x_1)[/tex], where (x₁, y₁) is one of the points and m is the slope

Find the slope:

[tex]m=\cfrac{y_2-y_1}{x_2-x_1} =\cfrac{8-10}{2-5} =\cfrac{-2}{-3} =\cfrac{2}{3}[/tex]

Use one of the points and the slope to determine the equation of the line:

[tex]y -y_1=m(x - x_1)[/tex], substitute the slope and [tex]y -10=\cfrac{2}{3} (x -5 )[/tex]

Answer:

[tex]y-10=\frac{2}{3} (x-5)[/tex]

Step-by-step explanation:

Pre-Solving

We are given: g(5)=10, and g(2)=8.

The value inside the parentheses is the x value, and the value that it (g(x)) is equal to is the y value.

So, as points, the values are (5, 10), and (2, 8).

The equation wants to be written in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.

Solving Slope

We first want to find the slope of the line.

The slope (m) can be found with two points using the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

We can label the values of the points we were given.

[tex]x_1=5\\y_1=10\\x_2=2\\y_2=8[/tex]

Now, substitute these values into the formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{8-10}{2-5}[/tex]

Subtract.

[tex]m=\frac{-2}{-3}[/tex]

Simplify.

[tex]m=\frac{2}{3}[/tex]

The slope is 2/3.

Since we now have the value of the slope, as well as [tex](x_1, y_1)[/tex], we can plug these values into the formula for point-slope form.

Point-Slope Form

Recall that [tex]x_1=5[/tex] and [tex]y_1=10[/tex]; plug these in for [tex]x_1[/tex] and [tex]y_1[/tex] respectively.

[tex]y-10=m(x-5)[/tex]

We also just found the slope, which is 2/3. Plug that in for m.

[tex]y-10=\frac{2}{3} (x-5)[/tex]

Topics: Point-slope form, functions

See more: https://brainly.com/question/24217374

What is the standard form for yt and factored form

Answers

Given:

The leading coefficient of a polynomial is 3.

And the roots of the polynomial is -1, 1, and 2.

Required:

To write g(t) in factored form and standard form.

Explanation:

From the given data, the factored form is given by

[tex]\begin{gathered} g(t)=3(x-(-1))(x-1)(x-2) \\ =3(x+1)(x-1)(x-2) \end{gathered}[/tex]

The standard form is,

[tex]\begin{gathered} g(t)=3(x+1)(x^2-2x-x+2) \\ =3(x+1)(x^2-3x+2) \\ =3(x^3-3x^2+2x+x^2-3x+2) \\ =3(x^3-2x^2-x+2) \\ =3x^3-6x^2-3x+6 \end{gathered}[/tex]

Final Answer:

The factored form:

[tex]g(t)=3(x+1)(x-1)(x-2)[/tex]

The standard form:

[tex]g(t)=3x^3-6x^2-3x+6[/tex]

A security keypad uses five digits (0 to 9) in a specific order. How many different
keypad patterns are possible if the first three digits must be even and the last digit
cannot be zero?

Answers

The different keypad patterns that are possible if the first three digits must be even and the last digit cannot be zero is 17500 ways.

How to calculate the value?

It should be noted that the security keypad uses five digits (0 to 9) in a specific order. On this case, the numbers from 0 to 9 make up 10 numbers.

In this case, there are 5 even numbers.

The total number of possible codes will be:

= 5 × 5 × 10 × 10 × 7

= 17500

There are 17500 ways.

Learn more about combinations on:

brainly.com/question/4658834

#SPJ1

7/8 × 9/8 , but the answer as a fraction

Answers

We are given the following multiplication problem.

[tex]\frac{7}{8}\times\frac{9}{8}[/tex]

To perform the fractional multiplication, simply multiply the numerators and the denominators

[tex]\frac{7}{8}\times\frac{9}{8}=\frac{7\times9}{8\times8}=\frac{63}{64}[/tex]

Therefore, the result of the multiplication is 63/64

use reference angle to find the exact value of the expression, do not use a calculator sin 2(pi)/3

Answers

Given the expression below:

[tex]\sin (\frac{2\pi}{3})[/tex]

To find the exact value of the expression, let us determine the quadrant of the expression. It should be noted that the value of angles compare with the quadrants is as shown below

[tex]\begin{gathered} First\text{ quadrant, the measure of reference angle in radian is } \\ 0-\frac{\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{second quadrant, the measure of reference angle in radian is} \\ \frac{\pi}{2}-\pi \end{gathered}[/tex][tex]\begin{gathered} \text{third quadrant, the measure of reference angle in radian is} \\ \pi-\frac{3\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{fourth quadrant, the measure of reference angle in radian is} \\ \frac{3\pi}{2}-2\pi \end{gathered}[/tex]

It can be observed that the expression given in the question is a fraction of (pi), greater than half of (pi) but less than (pi). This means that it lies in the second quadrant.

It should be noted that sine is positive in the second quadrant

The equivalent of the expression in the first quadrant is as shown below:

[tex]\begin{gathered} \sin (\frac{2\pi}{3})=\sin (\pi-\frac{2\pi}{3}) \\ =\sin (\frac{3\pi-2\pi}{3}) \\ =\sin (\frac{\pi}{3}) \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ \sin (\frac{2\pi}{3}),in\text{ second quadrant is the same } \\ \sin (\frac{\pi}{3}),in\text{ first quadrant.} \\ \sin (\frac{\pi}{3})=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]

Hence, the exact value of the expression is √3/2

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Answers

[tex]undefined[/tex]

Shona is bundling magazines to recycle he notices at 6 magazines weigh 5/8 pound in all and that the magazines all weigh the same amount. What is the unit rate for pounds per magazine?I don't understand this at all

Answers

Given data:

The given weight of 6 magazines is 5/8 pound.

The given expression is,

6M=5/8 pounds

6M=0.625 pounds

1M=0.1041667 pounds

The weight of one magzine is 0.104167 pounds.

How much solute is in each Percent Solution below

How many grams of KOH are in a 25% w/w solution?

Answers

25% w/w solution has 25 grams of solute.

The expression w/w stands for weight by weight. This expression indicates the amount of solute present in solution. Concerning this, 25 gram of KOH or potassium hydroxide is present in 100 gram of solution.

Further elaborating, the amount of solvent will be calculated by the formula -

Amount of solution = amount of solute + amount of solvent

Amount of solvent = 100 - 25

Performing subtraction to find the amount of solvent

Amount of solvent = 75 grams

Thus, the 100 gram of solution has 25 grams solute and 75 grams of solvent.

Learn more about percentage solution -

https://brainly.com/question/23520050

#SPJ9

harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 3 years how much will they be able to spend

Answers

harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 2 years how much will they be able to spend​

we know that

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$800

r=9%=9/100=0.09

n=12

t=2 years

substitute in the expression above

[tex]\begin{gathered} A=800(1+\frac{0.09}{12})^{12\cdot2} \\ \\ A=800(\frac{12.09}{12})^{(24)} \\ A=\$957.13 \end{gathered}[/tex]the answer is $957.13

Can you do the graph please I left some notes on the yellow sticky notes

Answers

The equation is a linear one, therefore its graph will be a line on the plane.

To completely define a line we need two points.

We can use the information about the y-intercept and use it as one of the points we need. (0, -3)

As for the second point, we can get the x-intercept by setting y=0 and evaluating the function for x:

[tex]\begin{gathered} y=0 \\ \Rightarrow\frac{1}{2}x-3=0 \\ \Rightarrow\frac{1}{2}x=3 \\ \Rightarrow x=6 \\ \Rightarrow(6,0) \end{gathered}[/tex]

Then, we have the points we need: (0, -3) and (6,0).

Now, we only need to mark those points on the plane and draw a line through both of them.

Since the plane in the image only reaches the point (5,0), we need to calculate another point to specifically draw the graph on that grid.

Let set y=-1, then:

[tex]\begin{gathered} y=-1 \\ \Rightarrow\frac{1}{2}x-3=-1 \\ \Rightarrow\frac{1}{2}x=2 \\ \Rightarrow x=4 \\ \Rightarrow(4,-1) \end{gathered}[/tex]

Now, we will use the points (0,-3) and (4,-1)

If the formular-(X-X|Y-Xwere used to find the r-value of the5x буfollowing data, what would be the value of x?XY8496101811912|13A. 8B. 10C. 6D. 4

Answers

The value of x⁻, is the mean of the x values of the table.

The mean of x is obtained by adding all values of x, and divided the result by the total number of data, which is 5.

Then, you have:

[tex]\bar{x}=\frac{8+9+10+11+12}{5}=\frac{50}{5}=10[/tex]

Hence, the mean of x, which is used in the formula to calculate the r-value, is 10

Evaluate the expression |2x – 5| for x = –3 and for x = 3.

Answers

Answer:

9 and 1 respectively

Step-by-step explanation:

|2(-3)-5| = |-9| = 9

|2(2)-5| = |1| = 1

the vertical lines represents absolute value, this just mean that any negative values are then turned into their positive counterparts.

The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.

Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.

Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.

Does Brian's dart land on the dartboard?

Answers

The equation of the circle that represents the dartboard is (x - 12)² + (y - 17/3)² = 9/16, where the origin is the lower left corner of the room and the unit of the radius is feet.  

The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.

What is the equation of a circle?

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

h and k represents the coordinates at the center.r represents the radius of a circle.

From the question, we have the following information:

The height of this standard dartboard, k = 5 feet, 8 inches.

The diameter of this standard dartboard = 18 inches.

The bull's eye, h = 12 feet.

Next, we would convert the all of the units in inches to feet as follows:

Height, k = 5 + 8/12

Height, k = 5 + 2/3

Height, k = 17/3 feet.

For the diameter, we have:

Diameter = 18/12

Diameter = 3/2 feet.

Also, we would determine the radius as follows:

Radius, r = diameter/2

Radius, r = (3/2)/2

Radius, r = 3/4 feet.

Substituting the parameters into the standard equation, we have;

(x - 12)² + (y - 17/3)² = (3/4)²

(x - 12)² + (y - 17/3)² = 9/16

Next, we would determine whether Brian's dart land on the dartboard:

(x - 12)² + (y - 17/3)² < 9/16

(x - 12)² + (y - 17/3)² < 9/16

(11.5 - 12)² + (5.5 - 5.67)² < 0.5625

0.25 + 0.0289 < 0.5625

0.2789 < 0.5625 (Yes, it does land because it's within the circumference of this standard dartboard).

Read more on equation of a circle here: https://brainly.com/question/18430680

#SPJ1


Two bicyclists, 44 miles apart, begin riding toward each other on a long straight avenue. One cyclist
travels 16 miles per hour and the other 17 miles per hour. At the same time, Spot (a greyhound), starting
at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 39
miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?

Answers

The Greyhound has run to a distance equal to 50.7 miles.

This question can be solved using the distance, speed and time relation. The Distance, Speed and time are related to each other by the relation

Speed = Distance/Time, Let the time travelled be equal to t.

Distance travelled by first bicyclist is equal to 16t and Distance travelled by second bicyclist is equal to 17t. The total distance is equal to 44 miles. So, we get

44 = 17t + 16t

44 = 33t

=> t = 44/33

=> t = 1.3 hours

At this time a greyhound starts running back and forth around each cyclist. The speed of Greyhound is equal to 39 miles per hour. Distance will be given by

Distance = Speed × Time

Distance = 39 × 1.3

Distance = 50.7 miles

Learn more about Distance at:

brainly.com/question/12356021

#SPJ9

Which property is shown -2x1/-2=1

Answers

Answer:

Multiplicative inverse

Step-by-step explanation:

1. There is a two digit number where the difference in the units digit and the tens digit is 5. If the digits are reversed, the
new number is the sum of twice the original number and seven. Find the number.

Answers

Answer:

38

Step-by-step explanation:

Let x = the ones digit, and let y = the tens digit.

The number looks like yx.

The value of the original number is

10y + x

"the difference in the units digit and the tens digit is 5."

x - y = 5    Equation 1

When you reverse the digits, you have xy.

The value of the new number is

10x + y

"If the digits are reversed, the new number is the sum of twice the original number and seven."

10x + y = 2(10y + x) + 7      Equation 2

We have a system of 2 equations.

x - y = 5

10x + y = 2(10y + x) + 7

Simplify the second equation.

10x + y = 2(10y + x) + 7

10x + y = 20y + 2x + 7

8x - 19y = 7

x - y = 5

8x - 19y = 7

Solve the first equation for x. Substitute that value for x in the second equation.

x = 5 + y

8(5 + y) - 19y = 7

40 + 8y - 19y = 7

-11y = -33

y = 3

x = 5 + y

x = 5 + 3

x = 8

The digits are:

ones digit: 8

tens digit: 3

The number is 38.

Jaime's football has a mass of 0.435 kilograms. His football helmet has a mass of 2.57 kilograms. Estimate how much more the mass of the helmet is than the mass of the football. Explain your estimate. Show your work.

Answers

Mass of football = 0.435kg

Mass of football helmet = 2.57kg

To find how much more the mass of the helmet is than the mass of football, we have to find the difference

2.57kg - 0.435kg

1. AI = 400 ft2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations

Answers

2. The Pythagorean theorem states:

[tex]c^2=a^2+b^2[/tex]

where a and b are the legs and c is the hypotenuse of a right triangle.

Applying this theorem to triangle AMI (where AI and MA are the legs and MI is the hypotenuse), we get:

[tex]\begin{gathered} MI^2=AI^2+MA^2 \\ MI^2=400^2+100^2 \\ MI^2=160000+10000 \\ MI^2=170000 \\ MI=\sqrt[]{170000} \\ MI\approx412.31\text{ ft} \end{gathered}[/tex]

3. By definition:

[tex]\tan (angle)=\frac{\text{opposite}}{\text{adjacent}}[/tex]

Applying this definition to triangle AMI, considering the angle M, we get:

[tex]\begin{gathered} \tan (\angle M)=\frac{AI}{MA} \\ \tan (\angle M)=\frac{400}{100} \\ \tan (\angle M)=4 \\ \angle M=\arctan (4) \\ \angle M\approx76\text{ \degree} \end{gathered}[/tex]

This angle is greater than 68°, then it satisfies the regulation.

the volume of a cube is 125 cubic centimeters. How many centimeters long is each edge of the cube?

Answers

Answer:

Each edge of the cube is 5 cm

Explanation:

The volume of a cube can be calculated using the formula;

[tex]V=l^3[/tex]

Where;

V = volume of the cube

l = length of each side (since all the sides are equal)

Making length l the subject of formula by cube rooting both sides of the formula;

[tex]\begin{gathered} \sqrt[3]{V}=\sqrt[3]{l^3} \\ \sqrt[3]{V}=l \\ l=\sqrt[3]{V} \end{gathered}[/tex]

Next, let's substitute the value of volume given;

V = 125 cubic centimeters

[tex]\begin{gathered} l=\sqrt[3]{V} \\ l=\sqrt[3]{125} \\ l=5\text{ cm} \end{gathered}[/tex]

Each edge of the cube is 5 cm

Compute the horizontal force P required to prevent the block from sliding down the plane for the 100 lb block shown. Assume the coefficient of static friction to be 0.65.

Answers

canThe first First step we need to do is to make the decomposition of the vectors W and P.

Both will have a component perpendicular and parallel to the plane. The perpendicular will be used to calculate the maximum static friction force, and the horizontal will be used to find the P required to prevent the block from sliding.

From the sketch, we are able to define both, parallel and perpendicular components of P, as it follows:

[tex]\begin{gathered} P_{\text{//}}=P\cos (30\degree)=\frac{P\sqrt[]{3}}{2} \\ P_{perp}=P\sin (30\degree)=\frac{P}{2} \end{gathered}[/tex]

Now, we can do the same for W.

And for W we also can provide the two components as follows:

[tex]\begin{gathered} W_{//}=W\sin (30\degree)=\frac{W}{2} \\ W_{\text{perp}}=W\cos (30\degree)=\frac{W\sqrt[]{3}}{2} \end{gathered}[/tex]

Now, we can elaborate on both equations: one for the perpendicular direction and the other for parallel. In the perpendicular direction, we have a component of W, one component of P, and the normal force N. Because the block is going to move, or change its movement along this direction, the sum of the forces pointing upwards must be equal to the sum of the forces pointing downwards. From this, we can write the following:

[tex]\begin{gathered} N=P_{\text{perp}}+W_{\text{perp}} \\ N=\frac{P}{2}+\frac{W\sqrt[]{3}}{2}=\frac{P+W\sqrt[]{3}}{2} \end{gathered}[/tex]

Now, for the horizontal, we have the P component to the right and the W component to the left. If we imagine the block is almost sliding. We can write the following equation, from the premise the forces will cancel each other just like the perpendicular case:

[tex]\begin{gathered} P_{//}+F_{\mu}=W_{//} \\ \frac{P\sqrt[]{3}}{2}+N\times\mu_{static}=\frac{W}{2} \end{gathered}[/tex]

Here it is used the fact that the friction force is equal to the multiplication of the coefficient of static friction by the normal force. Here we assumed also that the friction is maximum because the block is on the verge of motion downwards, and for this reason, the Friction is upwards, with the P component.

Now, substituting N and the coefficient, we find:

[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}+\frac{P+100\sqrt[]{3}}{2}0.65=\frac{100}{2}=50 \\ \frac{P(\sqrt[]{3}+0.65)+65\sqrt[]{3}}{2}=50 \\ P(\sqrt[]{3}+0.65)+65\sqrt[]{3}=100 \\ P(\sqrt[]{3}+0.65)=100-65\sqrt[]{3} \\ P=\frac{100-65\sqrt[]{3}}{\sqrt[]{3}+0.65}\cong\frac{100-65\times1.732}{1.732+0.65}=\frac{100-112.58}{2.382} \\ P=-\frac{12.58}{2.382}\cong-5.275\text{lbf} \end{gathered}[/tex]

From this, we can see that the force P made to the left with an intensity equal to -5.275 lbf will bring the block on the verge of motion downwards. If we consider that P is strong enough to make it almost move upwards, it is, the Normal Force will be downwards, we can remake the calculation as it follows:

[tex]\begin{gathered} P_{//}=W_{//}+F_{\mu} \\ \frac{P\sqrt[]{3}}{2}=\frac{W}{2}+N\times\mu_{static} \end{gathered}[/tex]

And substituting values, we have:

[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}=50+\frac{P+100\sqrt[]{3}}{2}0.65 \\ \frac{P(\sqrt[]{3}-0.65)}{2}=50+50\sqrt[]{3}\times0.65 \\ P=\frac{2}{\sqrt[]{3}-0.65}\times50(1+\sqrt[]{3}\times0.65)\cong196.46 \end{gathered}[/tex]

From this, we know that the max value for P, where the block will not slide is going to be 196.46 lbf to the right.

Find the average rate of change of
refer to the image please

Answers

The average rate of change of the function f(x) = -2x² - 2 from x = 2 to x = 6 is -16

How to solve an equation

An equation shows the relationship between two or more numbers and variables.

The average rate of change of a function f(x) over the interval x = a to x = b is given by:

A(x) = [f(b) - f(a)]/[b - a]

Given that function f(x) = -2x² - 2 from x = 2 to x = 6, hence:

f(2) = -2(2)² - 2 = -10

f(6) = -2(6)² - 2 = -74

The average rate of change is:

A = [f(b) - f(a)]/[b - a]

Substituting:

A = [-74 - (-10)] / [6 - 2] = -16

The average rate of change is -16

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Cuál es la cantidad de divisores en 2121?

Answers

Answer:

2121 tiene 8 divisores respuesta B

Express your answer in scientific notation.

5.4x10^5 + 6.7x10^4

Answers

Answer:

Step-by-step explanation:

5.4*10*10*10*10*10+6.7* 10*10*10*10

540,000+6.7*10,000

540,000+60,000

114,000=1.14*10^5


That's the value of x, but you need to evaluate the expression x + 26 for
X = 28.5.

Answers

The answer to the expression is 54.6

How to solve variable related problems?

1. Switch the positions of the variables in the equation. Starting with "solving for x" (or any other variable) in one of the equations, this "substitution" approach begins. [2] Say your equations are, respectively, 4x + 2y = 8 and 5x + 3y = 9.

2. To "solve for x," divide both sides of the equation.

3. Reconnect this to the other equation. Don't use the equation you just employed; rather, return to the other one.

When a particular variable's value is given to you

we just have to substitute that value in the required equation.

For instance in this question

x= 28.5

And the given equation is x + 26

Therefore the answer is 28.5 + 26 = 54.6 .

To know more about variable visit:

https://brainly.com/question/10462869

#SPJ13

Other Questions
ken was a very mature looking 17 year old whom everyone always mistook for being much older. pursuing his interest in computers, ken enrolled in compu school, a business and vocational school which taught computer training. on his application and to all school administrators, ken maintained that he was 20 years old which was a very believable lie given his mature appearance. after just two months of training, and before his 18th birthday, ken dropped out of compu school and disaffirmed his contract for enrollment with the school. in response, compu school sued ken for unpaid tuition. If the function h(x)=(x+7)9 is expressed in the form fg with f(x)=x9, find the function g(x). heuristics do not always yield an optimal schedule, but they are very capable of yielding aschedule for very complex networks with many types of resources. ABC has vertices at A(4,1), B(-3,-2), and C(-1,3). what is the perimeter of ABC? The endocrine systems hormones are ____ messengers that travel through the ____A. Chemical;Bodys organs B. Electrical; bloodstream C. Electrical; neural networks D. Chemical; bloodstream Read and choose the option with the correct negative t command to complete the sentence.________ (comer) comida cuando manejas! No comes No comas No enciendesNo enciendas 1936 divided by 8 in long division Andy and Nick went to the amusement park. They each bought a sandwich, and Nick got a small drink. Andy had a $10 gift certificate to put toward the cost, and Nick paid the rest, which came to $44.50. A ticket costs $20.00, and a sandwich costs $6.50. How much does a drink cost at the amusement park? For 10 seconds, Ariana places her finger on her radio artery encounter heartbeats, and 10 seconds to count 15 beats what is Arianas current heart rate based on this measurement Why does the speaker praise these men?A. because they exhibit enormous strengthB. because he is impressed by their muscular strengthC. because they have been around since the beginning of timeD. because they are the ones who we fear, but still admireE. because they don't give up The probability of a student eating at the cafeteria and a student living off campus is 0.07, and the probability of a student eating at the cafeteria given that the student lives off campus is 0.20, what is the probability of a student living off campus? After making your 20th payment of $524.50 on your car loan, you wanted to find out how much is left of your original 5 years loan at 6.2% compounded monthly of $27,000.00. What is the amount of the remaining balance of your car loan? Whats the correct answer answer asap for brainlist Putin says no need for more massive strikes in Ukraine at least for now a basic summary which includes who what What is the place value of the 6-digit in the number 205.876? Calculate the mean height of five men whose weight in kg are 60, 65, 71, 75 and 80 Hey. Can you help me out please? In the computer game World of Warcraft, some of the strikes are critical strikes, which do more damage. Assume that the probability of a critical strike is the same for every attack, and that attacks are independent. During a particular fight, a character has 248 critical strikes out of 598 attacks. Click to correct any capitalization errors.According to the constitution, a person must be at least thirty years old to serveas a senator.Submit Given 4 1/10 -3 5/12 determine the product