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Arisa [49]
3 years ago
12

Today he ran 3 3/5miles in 33minutes. What is his pace in miles per hour?

Mathematics
1 answer:
zmey [24]3 years ago
5 0

6.54545454545454545454545454545 miles in an hour

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Show that there do not exist scalar c1 c2 and c3 c1(-2,9,6)+c2(-3,2,1)+c3(1,7,5)= (0,5,4)​
fredd [130]

This is the same as showing the following system of equations doesn't have a solution:

\begin{cases}-2c_1-3c_2+c_3 = 0 \\ 9c_1 + 2c_2 + 7c_3 = 5 \\ 6c_1 + c_2 + 5c_3 = 4\end{cases}

or in matrix form,

\begin{bmatrix}-2&9&6\\-3&2&1\\1&7&5\end{bmatrix}\begin{bmatrix}c_1\\c_2\\c_3\end{bmatrix} = \begin{bmatrix}0\\5\\4\end{bmatrix}

The quickest way to check if there is a solution is to check whether the coefficient matrix is invertible. If its determinant is 0, then it is not invertible.

And the quickest way to show that the determinant is 0 is by observing that the third row is a linear combination of the first two rows:

(-2, 9, 6) - (-3, 2, 1) = (-2 + 3, 9 - 2, 6 - 1) = (1, 7, 5)

So there are indeed no such scalars <em>c₁</em>, <em>c₂</em>, and <em>c₃</em>.

5 0
3 years ago
The table shows data that were collected on a hot-air balloon. Which function f(x) best models the data?
slamgirl [31]
For the answer to the question above asking the <span>function f(x) best models the data? The f(x) models are not given but to answer this question</span> just convert the given from meter to kilometer by dividing the number by 1000. this is because 1000 meters is equal to 1 kilometers. The answer is 0.1 km
6 0
3 years ago
(8 -2i)^2 <br>a:60 <br>b:68-32i <br>c:60-32i <br>d:64-32i+4i^2
AURORKA [14]

Answer:

60-32i

Step-by-step explanation:

(8-2i)^2=8^2-2.8.2i+(2i)^2

=64-32i+4i^2

=64-32i-4

=60-32i

8 0
3 years ago
Consider the two functions. F(x)=x^2-8x+7
Tpy6a [65]
(X-7)(x-1)

Minimal x values=7,1
Not the same x value
7 is the greater minimal value
7 0
3 years ago
What is 62.713 rounded to the nearest hundredth?
irina [24]
62.71 would be the answer
8 0
3 years ago
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