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3 years ago

The figure below shows ∠ABC formed by the hands of the clock at 4 o’clock. What is the measure of ∠ABC?

Mathematics

1 answer:

Gre4nikov [31]3 years ago

6 0

Answer:

120°

Step-by-step explanation:

30° x 4 = 120°

Full turn is 360

half is 180

and 180 degree = 6 parts

180÷6=30

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Answer:

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2 years ago

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The fourth-grade students at Harvest School make up 0.3 of all students at the school. Witch fraction is equivalent to 0.3? -Zya

Leni [432]

3/10 or three tenths

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Express a(2) (2a(-1/2)+a) in its simplest form

Soloha48 [4]

First lets simplify the first term and yield (2a)

The second term:
1. 2a * (-1/2) = -a
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3 years ago

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Which matrix equation represents the system of equations?<br><br> {-x+ 2y = 0 <br> y= -2

Snowcat [4.5K]

We are given a system of equations,

$\begin{cases}-x+2y=0\\y=-2\\ \end{cases}$

This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),

$\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}$

The matrix will then be applied to the vector (lower dimensions on top),

$\begin{bmatrix}x\\y\\ \end{bmatrix}$

And the result vector will be whats on the other side of equals sign,

$\begin{bmatrix}0\\-2\\ \end{bmatrix}$

So to put everything together,

$\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\begin{bmatrix}x\\y\\ \end{bmatrix}=\begin{bmatrix}0\\-2\\ \end{bmatrix}$

Hope this helps :)

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2 years ago

Let f(x)=x^2f ( x ) = x 2. Find the Riemann sum for ff on the interval [0,2][ 0 , 2 ], using 4 subintervals of equal width and t

sladkih [1.3K]

Answer:

$A_L=1.75$

Step-by-step explanation:

We are given:

$f(x)=x^2$

$interval = [a,b] = [0,2]$

Since $n = 4$ ⇒ $\Delta x = \frac{b-a}{n} = \frac{2-0}{4}=\frac{1}{2}$

Riemann sum is area under the function given. And it is asked to find Riemann sum for the left endpoint.

$A_L= \sum\limits^{n}_{i=1}\Delta xf(x_i) = \frac{1}{2}(0^2+(\frac{1}{2})^2+1^2+(\frac{3}{2})^2)=\frac{7}{4}=1.75$

Note:

If it will be asked to find right endpoint too,

$A_R=\sum\limits^{n}_{i=1}\Delta xf(x_i) =\frac{1}{2}((\frac{1}{2})^2+1^2+(\frac{3}{2})^2+2^2)=\frac{15}{4}=3.75$

The average of left and right endpoint Riemann sums will give approximate result of the area under $f(x)=x^2$ and it can be compared with the result of integral of the same function in the interval given.

So, $(A_R+A_L)/2 = (1.75+3.75)/2=2.25$

$\int^2_0x^2dx=x^3/3|^2_0=8/3=2.67$

Result are close but not same, since one is approximate and one is exact; however, by increasing sample rates (subintervals), closer result to the exact value can be found.

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3 years ago