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2 years ago

A1.0 kg cart moving right at 5.0 -- on a frictionless track

Mathematics

1 answer:

bulgar [2K]2 years ago

6 0

Answer:

3.0 kg

Step-by-step explanation:

Momentum before collision = momentum after collision

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

(1.0 kg) (5.0 m/s) + m (-2.0 m/s) = (1.0 kg) (-4.0 m/s) + m (1.0 m/s)

5.0 kg m/s + m (-2.0 m/s) = -4.0 kg m/s + m (1.0 m/s)

9.0 kg m/s = m (3.0 m/s)

m = 3.0 kg

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What is the common ratio of 2, 10/3, 50/9

mojhsa [17]

The common ratio of 2, 10/3, 50/9 is $\frac{10}{6}$

<u>Solution:</u>

Given, series of elements are $2, \frac{10}{3}, \frac{50}{9}$

We have to find the common ratio of the above given series.

We know that, common ratio of an G.P is division of any number in that series with the previous number of the series.

So, now take $\frac{10}{3}$ and 2

$\text { Then, common ratio }=\frac{\frac{10}{3}}{2}$

$\begin{array}{l}{\text { Common ratio }=\frac{10}{3} \times \frac{1}{2}} \\\\ {\text { Common ratio }=\frac{10}{3 \times 2}=\frac{10}{6}}\end{array}$

Hence, the common ratio of the given series is $\frac{10}{6}$

6 0

3 years ago

Answer the following question.

Ivenika [448]

Answer:

Step-by-step explanation:

Step 1: equal any two of the three equations together

2x + 3 = 3x - 9

Step 2: isolate the variable

3 = x - 9

6 = x

5 0

3 years ago

Read 2 more answers

Suppose a city with population 300 comma 000 has been growing at a rate of 3% per year. If this rate continues, find the popul

viktelen [127]

Answer:

The population of this city in 13 years is 440,550.

Step-by-step explanation:

Given:

Suppose a city with population 300, 000 has been growing at a rate of 3% per year.

Now, to find the population of this city in 13 years.

Let the population of this city in 13 years be $A.$

Population ( $P$ ) = 300,000.

Rate per year ( $r$ ) = 3%.

Time ( $t$ ) = 13 years.

Now, we put formula to get the population of the city in 13 years:

$A=P(1+r)^t\\\\A=300,000(1+3\%)^{13}\\\\A=300,000(1+0.03)^{13}\\\\A=300,000(1.03)^{13}\\\\A=300,000\times 1.4685\\\\A=440,550.$

Therefore, the population of this city in 13 years is 440,550.

3 0

3 years ago

Determine whether parallelogram JKLM with vertices J(-7, -2), K(0, 4), L(9, 2) and M(2, -4) is a rhombus, square, rectangle or a

White raven [17]

Check the picture below

now, we know is a parallelogram, so the diagonals will bisect

looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason

is it a rhombus? well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal

now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
J&({{-7 }}\quad ,&{{ -2}})\quad 
% (c,d)
K&({{ 0}}\quad ,&{{ 4}})\\\\
K&({{ 0}}\quad ,&{{ 4}})\quad 
% (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
JK=\sqrt{[0-(-7)]^2+[4-(-2)]^2}\implies JK=\sqrt{(0+7)^2+(4+2)^2}
\\\\\\
JK=\sqrt{7^2+6^2}
\\\\\\
KL=\sqrt{(9-0)^2+(2-4)^2}\implies KL=\sqrt{9^2+(-2)^2}$

now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL

and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
K&({{ 0}}\quad ,&{{ 4}})\quad 
% (c,d)
M&({{ 2}}\quad ,&{{ -4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-4}{2-0}$

$\bf -------------------------------\\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
J&({{ -7}}\quad ,&{{ -2}})\quad 
% (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-(-2)}{9-(-7)}\implies \cfrac{2+2}{9+7}$

then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.

7 0

3 years ago

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Which statement must be true according to the dot plot?

astra-53 [7]

Answer: c

Step-by-step explanation:

just did on edg :) got a 100%

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2 years ago

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