MATHEMATICS COLLEGE

A 1-kg model airplane has 12.5 joules of kinetic energy and 98 joules of gravitational potential energy. What is its speed? What is its height?

Answers

Answer 1

Answer:

The formula for the kinetic energy is:

Ke = 0.5mv^2

Where ke is the kinetic enrgy

M is the mass

V is the velocity

Ke = 0.5mv^2

12.5 = 0.5(1) v^2

Solve for v

V = 5 m/s

Potential energy, pe = mgh

Where m is mass

G is accelearation due to gravity 9.8 m/s2

H is the height

98 = (1)(9.8) h

H = 10 m

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Use the product rule to answer each of the questions below. Throughout, be sure to carefully label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute.a. Let m (w) = 3 w^17 4^w. Find m ′(w) . b. Let h (t) = ( sin (t) + cos (t)) t 4. Find h ′(t). c. Determine the slope of the tangent line to the curve y = f (x) at the point where a = 1 if f is given by the rule f(x) = e^x sin (x). d. Find the tangent line approximation L(x) to the function y = g (x) at the point where a = − 1 if g is given by the rule g (x) = ( x^2 + x ) 2^x .
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A television station is interested in predicting whether or not voters are in favor of an increase in the state sales tax. It asks its viewers to phone in and indicate whether they support or are opposed to an increase in the state sales tax in order to generate additional revenue for education. Of the 2633 viewers who phone in, 1474 (55.98%) are opposed to the increase. The sample obtained is ____(A) all people who will vote on the sales tax increase on the data of the vote.(B) the 1474 viewers were opposed to the increase.(C) the 2633 viewers who phoned in.(D) all regular viewers of the television station who own a phone and have participated in similar phone surveys in the past.
Compact and oversized tires are produced on two different machines. The table shows the number of each type of tire produced, y, depending on the number of hours, x, the machines work.

Dical and exponent
What is 6
in radical form?

Answers

The square root pf a number can be simplified only if the number is divisible by a perfect square (other than 1).
√
12
can be simplified because
12
is divisible by
4
-- a perfect square.
√
12
=
√
4
×
3
=
√
4
×
√
3
=
2
√
3
√
250
can be simplified because
250
is divisible by
25

√
250
=
√
25
×
10
=
√
25
×
√
10
=
5
√
10
But
6
is not divisible by a perfect square, so
√
6
cannt be simpified further.

Vitamin D is needed for the body to use calcium. An experiment is designed the effects of calcium and vitamin D supplements on the bones of first-year college students. The outcome measure is the total body mineral content (TBBMC), a measure of bone health. Three doses of calcium wil be used: 0, 200, and 400 mg/day. The doses of vitamin D will be 0, 50, and 100 international units (IU) per day. The calcium and vitamin D will be given in a single tablet. Al tablets including those with no calcium and no vitamin D will look identical. Subjects for the study will be 90 men and 90 women.a) What are the factors and the treatments for this experiment?b) Draw a picture explaining how you would randomize the 180 college students to the treatmentsc) Use a spreadsheet to carry out the randomization

Answers

Answer:

(a) The factors are calcium dose, and Vitamin D dose. There are 9 treatments (each calcium/vitamin D combination).

(b) Assign 20 students to each group, with 10 of each gender. The complete diagram would have a total of 18 branches.

SUBJECTS:

Men---> Random Assignment---> Group 1---> Treatment 1---> measure TBBMC

Men---> Random Assignment---> Group 2---> Treatment 2---> measure TBBMC

Men---> Random Assignment---> Group 3---> Treatment 3---> measure TBBMC

Men---> Random Assignment---> Group 4---> Treatment 4---> measure TBBMC

Men---> Random Assignment---> Group 5---> Treatment 5---> measure TBBMC

Men---> Random Assignment---> Group 6---> Treatment 6---> measure TBBMC

Men---> Random Assignment---> Group 7---> Treatment 7---> measure TBBMC

Men---> Random Assignment---> Group 8---> Treatment 8---> measure TBBMC

Men---> Random Assignment---> Group 9---> Treatment 9---> measure TBBMC

Women---> Random Assignment---> Group 1---> Treatment 1---> measure TBBMC

Women---> Random Assignment---> Group 2---> Treatment 2---> measure TBBMC

Women---> Random Assignment---> Group 3---> Treatment 3---> measure TBBMC

Women---> Random Assignment---> Group 4---> Treatment 4---> measure TBBMC

Women---> Random Assignment---> Group 5---> Treatment 5---> measure TBBMC

Women---> Random Assignment---> Group 6---> Treatment 6---> measure TBBMC

Women---> Random Assignment---> Group 7---> Treatment 7---> measure TBBMC

Women---> Random Assignment---> Group 8---> Treatment 8---> measure TBBMC

Women---> Random Assignment---> Group 9---> Treatment 9---> measure TBBMC

(c) Randomization results will vary.

I can't solve this problem: 47 x 98= ( ? x 47)-(2 x 47)

Answers

The equation becomes 4610 = 2115, which is not true.

Let's break down the given equation and the steps to solve it step by step:

Given the equation: 47 × 98

Step 1: Express 98 as a combination of (47)'s and (2)'s. (98) can be written as (47 × 2).

Step 2: Substitute the expression for 98 in terms of 47 and 2 back into the equation:

47 × 98 = (47 × 47) - (2 × 47)

Step 3: Calculate the values on both sides of the equation.

- The left side: 47 × 98 = 4610.

- The right side:

- 47 × 47 = 2209

- 2 × 47 = 94

- Subtracting 94 from 2209 gives 2115.

Explanation:

1. We start with the equation 47 × 98, where 98 is represented as 47 × 2.

2. We substitute 98 in terms of 47 and 2 to get (47 × 47) - (2 × 47).

3. We calculate the values on both sides of the equation to find that they don't match. This indicates that the original equation is not true.

Learn more about Algebraic Equations link is here:

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Answer:

The answer to your question is:

2 and -49

Step-by-step explanation:

2 x -49 = -98

2 + (-49) = -47

x2 - 47x - 98 = 0

The solution to factor the quadratic equation above is:

(X + 2 ) (X - 49)

Since 2 and -49 multiply to -98 and add up -47, you know that the following is true:

x2 - 47x - 98 = (X + 2 ) (X - 49)

I need help with this! thanks

Answers

Answer:

it should be about 6. try measuring the the 3 line with paper or something then put it on the other line

Step-by-step explanation:

Look at the system of equations below.y = {x + 10
y = {x – 10
Which of these statements is correct?
A. The system has no solution.
B. The solution of the system is (-3,8).
C. The solution of the system is (6,-6).
D. The system has an infinite number of
tiang

Answers

Answer:

Step-by-step explanation:

The relationship between a relationship between his life is a stronger understanding and relationship with the revolution and his relationship between his relationship with the union of his life relationship and his life and his father relationship is a stronger understanding and understanding that his life relationship with the union and relationship is stronger understanding of understanding

Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $ L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA $.

Answers

$\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA$

Notice that Given that $R$ is an ellipse, consider a conversion to polar coordinates:

$\begin{cases}x(r,\theta)=\frac r8\cos\theta\ny(r,\theta)=\frac r9\sin\theta\end{cases}$

The Jacobian for this transformation is

$J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\n\frac19\sin\theta&\frac r9\cos t\end{bmatrix}$

with determinant $\det J=\frac r{72}$

Then the integral in polar coordinates is

$\displaystyle\frac1{72}\int_0^(\pi/2)\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^(\pi/2)\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{(\pi\sin^23)/(864)}$

where you can evaluate the remaining integral by substituting $s=6r^2$ and $\mathrm ds=12r\,\mathrm dr$ .

Final answer:

To evaluate the integral, we make a change of variables using the transformation x=u/8 and y=v/9 to transform the region into a unit circle. Then we convert the integral to polar coordinates and evaluate it.

Explanation:

To evaluate the given integral, we can make the appropriate change of variables by using the transformation x = u/8 and y = v/9. This will transform the region R into a unit circle. The determinant of the Jacobian of the transformation is 1/72, which we will use to change the differential area element from dA to du dv. Substituting the new variables and limits of integration, the integral becomes:

L = \iint_{R} 9 \sin (612 u^{2} + 768 v^{2}) \cdot (1/72) \,du \,dv

Next, we can convert the integral from Cartesian coordinates(u, v) to polar coordinates (r, \theta). The integral can be rewritten as:

L = \int_{0}^{2\pi} \int_{0}^{1} 9 \sin (612 r^{2} \cos^{2}(\theta) + 768 r^{2} \sin^{2}(\theta)) \cdot (1/72) \cdot r \,dr \,d\theta

We can then evaluate this integral to find the value of L.

Learn more about Evaluation of Integrals here:

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The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − (x − π/2) + 1/6 (x − π/2)3 + R3(x). Using this, estimate cos(86°) correct to five decimal places.