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3 years ago

8

Dawson rakes leaves in his neighborhood. The equation y = 10x represents the amount of money he earns. What is the constant of p

roportionality?

1 answer:

Dafna11 [192]3 years ago

5 0

Answer:

idk for sure but id say 10x

Step-by-step explanation:

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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

Frank is planting a flower garden. He plants 2 lilies for every 3 rose bushes. If Frank plants 12 lilies, how many rose bushes

Alja [10]

Answer:

17 rose bushes

Step-by-step explanation:

Add all of them together to find the answer. HOPE this helps:> please mark brainliest

7 0

2 years ago

Read 2 more answers

You construct a budget to determine how much money you will need to start your own catering business. You take your savings of $

tatiyna

Answer:

Compound interest is the best.

Step-by-step explanation:

Simple interest is that which is not added to the initial capital once the term of the investment or credit has expired.

Compound interest is that which is added to the initial capital at the end of the investment or credit.

Simple interest:

I= C x i x t

15,000 * 0.05 * 5 = $ 750

Compound interest:

Cf= Ci (1+i)ᵗ

Cf = 15,000 * (1.039)^5 = $ 18,162.22

So, if Cf - Ci = I -> 3,162.22 is the compound interest.

8 0

2 years ago

I need help please and thank you

Art [367]

Answer:

$86.55

Step-by-step explanation:

8.5% x 95 = 8.455

95 - 8.455 = 86.545 = $86.55

8 0

3 years ago

Find the missing dimension of the cylinder. round your answer to the nearest whole number

Ulleksa [173]

Answer:

11 meters

Step-by-step explanation:

Use the formula:

$V = \pi r^{2} h$

V = 7599, h = 20, π = 3.14

Plugin the numbers and solve for r

$7599=3.14(20)r^{2} \\7599=62.8r^{2} \\7599/62.5=62.8r^{2} /62.8\\121=r^{2} \\\sqrt{121}=\sqrt{r^{2} } \\r=11$

8 0

2 years ago