A race car travels 400 km in a time of 2 hours. Determine the speed of<br> the race car

Please help with questions<br> 1d) and 1e)<br><br> Any help is much appreciated thanks

Anestetic [448]

Answer:

1d 6.742 1e 6

Step-by-step explanation: By sketching out the graph you can see the positive x intercept to find 1d

You can also replace h with 25 and isolate t to find 1e

5 0

3 years ago

For the system of equations that follows, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in

Rainbow [258]

Answer:

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Step-by-step explanation:

From the question we are told that

System of equations given as

x₁ + 3x₂ + x₃ + x₄ = 3;

2x₁ - 2x₂ + x₃ + 2x₄ = 8;

x₁ - 5x₂ + x₄ = 5

Matrix form

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$ $\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}$

Generally the echelon reduction is mathematically applied as

$\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -2 times the 1st row to the 2nd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}$

Multiply the 2nd row by -1/8

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}$

Add -1 times the 2nd row to the 3rd row

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}$

Multiply the 3rd row by -8/41

$\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -1/8 times the 3rd row to the 2nd row

Add -1 times the 3rd row to the 1st row

$\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

Add -3 times the 2nd row to the 1st row

$\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}$

3 0

3 years ago

A hot-air balloon rises vertically at a constant rate of 8 m/s. A second hot-air balloon moves past the first hot-air balloon at

Lunna [17]

The second hot-air balloon is moving 5 m/s

8 0

4 years ago

Rewrite this number sentence 50 1/2 divided by 1/4 using multiplication

Shalnov [3]

This division question is asking how many 1/4 you can fit into 50 1/2.

We can fit 4 of them into 1 whole (4 x 1/4 = 1)
We can fit 8 of them into 2 wholes (8 x 1/4 = 2)

and so on.

But we have 50 1/2 wholes, so we would need 50 1/2 x 4.

The new number sentence is 50 1/2 x 4.

3 0

4 years ago

Read 2 more answers

Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool?

adoni [48]

The circumference of the pool is 26.38 meters

<h3>How to determine the circumference?</h3>

The radius, r is given as:

r = 4.2

The circumference, C is calculated using:

$C =2\pi r$

This gives

C =2 * 3.14 * 4.2

Evaluate

C = 26.38

Hence, the circumference of the pool is 26.38 meters

A race car travels 400 km in a time of 2 hours. Determine the speed of the race car