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emmainna [20.7K]

3 years ago

7

Find the value of √(6-3√5)

1 answer:

Romashka-Z-Leto [24]3 years ago

4 0

Answer:

There is no answer

Step-by-step explanation:

because 3√5=6,7082039232 > 6

So 6-3√5 < 0

But √x always >0

So there is no answer

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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

Which matrix equation has the solution

leonid [27]

Answer: x=0.6 btw how do you put a picture into a question.

5 0

2 years ago

A dealer sold 500 tennis racquets some were sold at $20 each and the rest were sold at $45 each. The total receipts from these s

arlik [135]

Answer:

He sold 100 rackets for $ 20

Step-by-step explanation:

To start, we have to make 2 equations, one that represents the number of rackets and the other the money

x + y = 500

x * 20 + y * 45 = 20000

we clear x in the first equation

x + y = 500

x = 500 - y

we replace x in the second equation with (500 - y)

x * 20 + y * 45 = 20000

(500 - y) * 20 + y * 45 = 20000

10000 - 20y + 45y = 20000

-20y + 45y = 20000 - 10000

25y = 10000

y = 10000/25

y = 400

we replace x in the first equation with the value obtained

x = 500 - y

x = 500 - 400

x = 100

He sold 100 rackets for $ 20

8 0

3 years ago

Read 2 more answers

2/5(d−10)−2/3(d+6) is

MissTica

Remove parentheses
2/5 • d-10 - 2/3 • d+6

calculate
2/5d-4 - 2/3d-4

the answer
-4/15d-8

3 0

3 years ago

Which of the following expressions represents the solution to the inequality statement? -x ≤ -7

natta225 [31]

Answer:

the answer is -8 or 7

Step-by-step explanation:

Sorry im not good w negatives...

4 0

2 years ago