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3 years ago

Answer quickly! It very urgent

Mathematics

1 answer:

ra1l [238]3 years ago

6 0

Answer: Because the graphs of the two equations overlap each other

Step-by-step explanation:

Every point on the first line also satisfies the second equation.

This is the same as equivalent fractions

where 1/2 = 2/4 = 3/6 = 4/8

Graphing these on a number line would only show one dot.

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A trough has ends shaped like isosceles triangles, with width 5 m and height 7 m, and the trough is 12 m long. Water is being pu

Svet_ta [14]

Answer:

$\dfrac{dh}{dt}=21 \text{m/min}$

the rate of change of height when the water is 1 meter deep is 21 m/min

Step-by-step explanation:

First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

$V = \dfrac{1}{2}(bh)\times L$

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).

As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

$\dfrac{b}{h} = \dfrac{5}{7}$

$b=\dfrac{5}{7}h$ this can be substituted back in the volume equation

$V = \dfrac{5}{14}h^2L$

the rate of the water flowing in is:

$\dfrac{dV}{dt} = 6$

The question is asking for the rate of change of height (m/min) hence that can be denoted as: $\frac{dh}{dt}$

Using the chainrule:

$\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}$

the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h

$V = \dfrac{5}{14}h^2L$

$\dfrac{dV}{dh} = \dfrac{5}{7}hL$

reciprocating

$\dfrac{dh}{dV} = \dfrac{7}{5hL}$

plugging everything in the chain rule equation:

$\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}$

$\dfrac{dh}{dt}=\dfrac{7}{5hL}\times 6$

$\dfrac{dh}{dt}=\dfrac{42}{5hL}$

L = 12, and h = 1 (when the water is 1m deep)

$\dfrac{dh}{dt}=\dfrac{42}{5(1)(12)}$

$\dfrac{dh}{dt}=21 \text{m/min}$

the rate of change of height when the water is 1 meter deep is 21 m/min

6 0

3 years ago

Read 2 more answers

Describe how you would find the sum of 24,36and 13

Oksi-84 [34.3K]

I would add them together to get 73

Step-wise I would add the ones column together to get 13, carry the one over then add the tens up to get 70 - your answer is 73

3 0

3 years ago

Read 2 more answers

need help, will give Brainly

anastassius [24]

Answer:

$95-$5m

Step-by-step explanation:

after m months the has to pay $5m

so then you just need to subtract 5m from $95

8 0

3 years ago

Read 2 more answers

Homework help, please

Vinvika [58]

Start the line at 3 on the y-axis (vertical). then go down two boxes and to the right three & make a mark at that point. keep going down two and over three until the end of the graph. then just connect the marks.

4 0

2 years ago

Please help! Correct answer only!

bogdanovich [222]

Answer:

<em>Expected Payoff ⇒ $ 1.50 ; Type in 1.50</em>

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

$100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars$

<em>Thus, Solution ; Expected Payoff ⇒ $ 1.50</em>

6 0

3 years ago