Find the value of x.
31°
to
35°

The object's x-coordinate when t = 10.0 s is -70.5 m.

We are given the following information:

Object's acceleration = a x(t) = -0.0320 m/s³ (15.0 s - t)

At t = 0, object's position = x₀ = -14.0 m

Object's initial velocity = v₀x = 4.20 m/s

We are asked to determine the object's x-coordinate when t = 10.0 s.

To solve for the position of the object as a function of time, we integrate the acceleration twice to obtain the position equation:

x(t) = (1/6)a x(t) t³ + v₀x t + x₀

Integrate acceleration w.r.t. time to get the velocity:

v(t) = (1/4)a x(t) t⁴ - (1/2)v₀x t² + x₀t At t = 0,

we have v₀x = 4.20 m/s.

Hence:

v(0) = (1/4)a x(0) (0)⁴ - (1/2)(4.20 m/s)(0)² + (-14.0 m)

      = -14.0 m/s

So the velocity function is:

v(t) = (1/4)a x(t) t⁴ - (1/2)(4.20 m/s) t² - 14.0 m/s

Integrate the velocity function w.r.t. time to get the position function:

x(t) = (1/20)a x(t) t⁵ - (1/6)(4.20 m/s) t³ - 14.0 m t

Since the acceleration function is given as a function of time,

we substitute t = 10.0 s to obtain:

x(10.0 s) = (1/20)(-0.0320 m/s³)(10.0 s)⁵ - (1/6)(4.20 m/s) (10.0 s)³ - 14.0 m (10.0 s)x(10.0 s) = -70.5 m

Hence, the object's x-coordinate when t = 10.0 s is -70.5 m.

Answer: -70.5 m.

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Answer:

6 yd

Step-by-step explanation:

72 ÷ 12 = 6

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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The probability of selecting three red ribbons at random from the basket is approximately 2.27%.

In order to calculate the probability of selecting three red ribbons from a basket containing 9 blue, 7 red, and 6 white ribbons, we need to use the concept of combinations.

A combination represents the number of ways to choose items from a larger set without considering the order.

First, let's determine the total number of ways to choose 3 ribbons from the 22 ribbons in the basket (9 blue + 7 red + 6 white). This can be calculated using the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose. In this case, n = 22 and k = 3. So, C(22, 3) = 22! / (3!(22-3)!) = 22! / (3!19!) = 1540 possible combinations.

Now, let's find the number of ways to choose 3 red ribbons from the 7 red ribbons available. Using the combination formula again, C(7, 3) = 7! / (3!(7-3)!) = 7! / (3!4!) = 35 combinations.

Finally, to calculate the probability of choosing three red ribbons, we'll divide the number of ways to choose 3 red ribbons by the total number of ways to choose any 3 ribbons: Probability = 35/1540 ≈ 0.0227, or approximately 2.27%.

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Answer:

Step-by-step explanation:

To write an estimate of the length of the Nile River, we can round the number 21,832,800 to the nearest power of ten. The nearest power of ten to 21,832,800 is 10,000,000, which is 107 in scientific notation.

To convert 21,832,800 to scientific notation, we move the decimal point seven places to the left to get 2.18328, and then multiply it by 107 to get:

2.18328 x 107

Rounding this to a single digit times an integer power of ten gives:

2 x 107

Therefore, an estimate for the length of the Nile River, in feet, as a single digit times an integer power of ten, is 2 x 107 feet.

Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

\(\implies 6 \times 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

\(\implies (0.06) \cdot (0.154)=0.00924\)

-----------------------------------------------------------------------------------------------

Answer option A

\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)

Therefore, this is a valid answer option.

Answer option B

\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)

Multiply the numbers 6 and 154:

\(\implies 6 \times 154 = 924\)

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)

Therefore, this is a valid answer option.

Answer option C

\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

\(\implies 6 \cdot 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

\(\implies 0.924\)

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

\(\boxed{6 \cdot 154 \cdot (0.00001)}\)

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)

Therefore, this is a valid answer option.

Answer option E

\(\boxed{0.00924}\)

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

Answer:

sin

Step-by-step explanation:

sin is opp/hyp

Answer:

Sine

Step-by-step explanation:

Remember the acronym soh-cah-toa. It stands for sine opposite hypotenuse, cosign adjacent hypotenuse, and tangent opposite adgacent. It's a good way to remember it.

Answer:

i think it's "c" if u check y=6 x= 2

Step-by-step explanation:

so if u insert 2 in the formula c you get 6

Answer:

The base of the second parallelogram is 51cm.

Step-by-step explanation:

If the parallelograms are similar, it means by applying the same scale factor to all the sides in one gives you the other. The question tells us the height of the first shape is 8cm and the height of the second shape is 34cm. That means the scale factor is:

\(\frac{34}{8}=4.25\)

Apply this same scale factor to the base of the first shape to find the base of the second:

\(12 \times 4.25=51\)

Answer: Question # 9: About 17.5 m

Question # 8: 20 m

Step-by-step explanation:

To find the hypotenuse for both figures you have to "add the squares of the other sides, then after that, take their square root.

For # 9 You would add 9² + 15² = 306, √306 = 17.492... so about 14.5

For # 8 the equation would be 16² + 12² = 400, √400 = 20

*Mic Drop*

Answer:

x=10

Step-by-step explanation:

30-10=20

20/2=10

2(10)+10=30

Answer:

x=10

Don’t hold me up on this but, I think this is the answer.

Answer:

The answer is 3, but here’s how I got that answer.

Step-by-step explanation:

As we know the trifle recipe requires 1 ½ cups of sugar, and the chocolate cake requires double the amount of sugar.

You have two options.

Multiply 1½ by 2

1½ x 2 = 3

———————————

Or add 1½ + 1½

1½ + 1½ = 3

———————————-

Wasn’t sure what you were asking for with this this question, but hope it helped.

Answer: 3

Step-by-step explanation:

Since the trifle cake uses 1 ½ cups of sugar and the chocolate twice as much sugar as the trifle cake you should multiply 1 ½ x 2 which would equal 3. So, 3 cups of sugar should go into the cake. (This is my first answer to a question so I'm sorry if I'm confusing)

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Answer:

It means that  the measurments of both angles are equal.

Step-by-step explanation:

Answer:  A) stretched vertically by 2 and shifted up 6 units

Step-by-step explanation:

y = A log(Bx - C) + D    where

Given: f(x) = log x

          g(x) = 2 log x + 6

→ A = 2   vertical stretch by a factor of 2

→ D = +6  vertical shift UP 6 units

Answer: The table that could be the data the student collected is table D.

Step-by-step explanation: What is an electromagnet?

An electromagnet is described as a type of magnet in which the magnetic field is produced by an electric current and usually consist of wire wound into a coil.

If student builds an electromagnet using a variable power source and 40 turns of wire. We have it that the student changes the voltage and counts the number of paper clips that are picked up. The table described below could perfectly described the scenario.

This is Table D

Voltage (V)

3

6

9

12

Number of paper clips

9

18

27

36

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We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.

To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.

Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.

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Answer:

one number is 8 and other is 4

Step-by-step explanation:

So we can say x+y=12.

And 3x+5y=44

For x+y=12, we can subtract x to get: y=12-x

Plug that in to get 3x+5(12-x)=44

3x+60-5x=44

Subtract 44: -2x+16=0

2x=16

x=8

12-8=4.

Answer:

The difference in diameter between the two ends is 1.757''

Step-by-step explanation:

Given;

length of a bar of cast iron, L =  18.125"

initial diameter of the bar, d₁ = 0.983"

final diameter of the bar, d₂ = 2.74"

The difference in diameter between the two ends of the bar is calculated as;

difference in diameter = d₂ - d₁

difference in diameter =  2.74" - 0.983"

difference in diameter = 1.757''

Therefore, the difference in diameter between the two ends is 1.757''

Answer:c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

The values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0

The explanation of the answer is now provided as follows:

Given:

f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0 …………….. (1)

\(R_{3}\) = (x) = (e^z /4!)x^4

Since the aim is \(R_{3}\)(x) < 0.001, this implies that:

(e^z /4!)x^4 < 0.0001 ………………………………….. (2)

Multiply both sided of equation (2) by (1), we have:

e^4x^4 < 0.024 ……………………….......……………. (4)

Taking 4th root of both sided of equation (4), we have:

|xe^(z/4) < 0.3936 ……………………..........…………(5)

Dividing both sides of equation (5) by e^(z/4) gives us:

|x| < 0.3936 / e^(z/4) ……………….................…… (6)

In equation (6), when z > 0, e^(z/4) > 1. Therefore, we have:

|x| < 0.3936 -----> 0 < x < 0.3936

Therefore, the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Answer:

A.) 3 and 5

Step-by-step explanation:

they are on the same side inside

Answer:

b

Step-by-step explanation:

it doesnt

run through the origin

Answer:

No solution

Step-by-step explanation:

Basically the simplified equation is 17 = 0, which is wrong so there is no solution.

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer: the time would be 2:34

Step-by-step explanation:

Answer:

y = 7/2x - 5/2 ; gradient is 7/2

y = 5/3x - 4/3 ; gradient is 5/3

y = -2/3x - 10/3; gradient is -2/3

Step-by-step explanation:

2y = 7x-5

5x - 3y=4

10 - 2x+3y = 0

NOTE: The gradient is the slope

Answer:

yes

Step-by-step explanation: