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1 year ago

What acceleration would that object need to achieve to create a force of 25 Newtons?

Mathematics

1 answer:

Aleks04 [339]1 year ago

8 0

Answer: We want to find the acceleration needed to achieve a force of 25 Newtons.

The acceleration is:

a = 25N/m

By Newton's second law, we know that:

F = m*a

Force equals mass times acceleration.

So if we want to have a force of 25N, we replace F by 25N, so we get:

25N = m*a

Solving this for the acceleration, we get:

25N/m = a

Notice that we can't get the exact acceleration as we do not know the mass of the object, but we got a general formula where we can replace the mass of the object to get the exact acceleration.

Step-by-step explanation:

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Emily has 12 fruits in her bowl. She has 3 apples, 5 bananas, 1 pear and 3 oranges. A fruit is selected at random. What is the p

blsea [12.9K]

Answer: The probability that the fruit is an orange or a pear is $\dfrac{1}{3}$ .

Step-by-step explanation:

Given : Emily has 12 fruits in her bowl.

She has 3 apples, 5 bananas, 1 pear and 3 oranges.

A fruit is selected at random.

P(orange) = $\dfrac{\text{Number of oranges}}{\text{Total fruits}}$

$=\dfrac{3}{12}$

P(pear)= $\dfrac{\text{Number of pears}}{\text{Total fruits}}$

$=\dfrac{1}{12}$

Since both events of selecting orange and pear are mutually exclusive , so

The probability that the fruit is an orange or a pear = P(orange) + P(pear)

$=\dfrac{3}{12}+\dfrac{1}{12}=\dfrac{4}{12}=\dfrac{1}{3}$

Therefore , the probability that the fruit is an orange or a pear is $\dfrac{1}{3}$ .

5 0

3 years ago

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are

alexgriva [62]

Answer:

$P=\left(\begin{array}{ccc}-\frac{2}{3}&-\frac{2}{3}&\frac{1}{3}\\\frac{1}{\sqrt{5}}&0&\frac{2}{\sqrt{5}}\\-\frac{4}{3\sqrt{5}}&\frac{\sqrt{5}}{3}&\frac{2}{3\sqrt{5}}\end{array}\right)$

Step-by-step explanation:

It is a result that a matrix $A$ is orthogonally diagonalizable if and only if $A$ is a symmetric matrix. According with the data you provided the matrix should be

$A=\left(\begin{array}{ccc}-9&-4&2\\ -4&-9&2\\2&2&-6\\\end{array}\right)$

We know that its eigenvalues are $\lambda_{1}=-14, \lambda_{2}=-5$ , where $\lambda_{2}=-5$ has multiplicity two.

So if we calculate the corresponding eigenspaces for each eigenvalue we have

$E_{\lambda_{1}=-14}=\langle(-2,-2,1)\rangle$ , $E_{\lambda_{2}=-5}=\langle(1,0,2),(-1,1,0)\rangle.$ .

With this in mind we can form the matrices $P, D$ that diagonalizes the matrix $A$ so.

$P=\left(\begin{array}{ccc}-2&-2&1\\1&0&2\\-1&1&0\\\end{array}\right)$

and

$D=\left(\begin{array}{ccc}-14&0&0\\0&-5&0\\0&0&-5\\\end{array}\right)$

Observe that the rows of $P$ are the eigenvectors corresponding to the eigen values.

Now you only need to normalize each row of $P$ dividing by its norm, as a row vector.

The matrix you have to obtain is the matrix shown below

3 0

3 years ago

Help me please <br>i need x

kicyunya [14]

Answer:

x=42

Step-by-step explanation:

Just do 24/32 on calculator to get .75

Then multiply .75 by 56, the side you are looking for to get 42

5 0

2 years ago

Can you answer this

Burka [1]

Answer is 2x^+3x-3 with reminder 4

6 0

3 years ago

Find the solution set of this inequality. select the correct graph. |-4x+14|>6

lions [1.4K]

Split the inequality into two:
(-4x+14)>6 & -(-4x+14)>6

solve:
(-4x+14)>6
-4x>-8
x<2
(symbol changes when ÷/× by negative for inequalities.)

-(-4x+14)>6
-4x+14<-6
-4x<-20
x>5

the answers are x<2 and x>5, so you would write your answer like this: (-∞,2) ∪ (5,∞)

5 0

3 years ago