Use systems of linear equations solve x+2y=4<br><br> Must include;<br> Step to solve problem

A pyramid-shaped vat has square cross-section and stands on its tip. The dimensions at the top are 2 m × 2 m, and the depth is 5

Strike441 [17]

Answer:

the water level increases at a rate of 1.718 m/min when the depth is 4 m

Step-by-step explanation:

the volume of the pyramid is

V = (1/3)(height)(area of base) = 1/3 H*L²

For the diagonal in the pyramid

tg Ф = Side Length/ Height = L / H = x / h

where h= depth of water , x= side of the corresponding cross section

therefore x= L *h/H

the volume of the water is

v= 1/3 h*x² = 1/3 (L/H)² h³

in terms of time

v = Q*t

then

Q*t = 1/3 (L/H)² h³

h³ = 3*(H/L)² *Q *t

h = ∛(3*(H/L)² *Q *t) = ∛(3*(H/L)² *Q) *∛t = k* ∛t , where k=∛(3*(H/L)² *Q)

h = k* ∛t

then the rate of increase in depth is dh/dt

dh/dt = 1/3*k* t^(-2/3)

since

t = (h/k)³

dh/dt = 1/3*k* t^(-2/3) = 1/3*k* (h/k)³ ^(-2/3) = 1/3*k* (h/k)^(-2) = 1/3 k³ / h²

= 1/3 (3*(H/L)²*Q) / h² = (H/L)²*Q /h²

dh/dt= [H/(h*L)]²*Q

replacing values, when h=4m

dh/dt= [H/(h*L)]²*Q = [5m/(4m*2m)]² * (3m³/min)= 1.718 m/min

8 0

4 years ago

The actual base of the triangle is 120

konstantin123 [22]

Answer: 18,00 Meters (1.3)

Step-by-step explanation:

Divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle to determine the scale factor for the smaller triangle to the bigger triangle.

1st) 120/90

2nd) Convert

3rd) Factor your half

6 0

4 years ago

There are x number of students at helms. If the number of students increases by 7.8% each year, how many students will be there

vodomira [7]

There will be 1.078x students next year and equation is number of students in next year = x + 7.8% of x

<h3><u>Solution:</u></h3>

Given, There are "x" number of students at helms.

The number of students increases by 7.8% each year which means if there "x" number of students in present year, then the number of students in next year will be x + 7.8% of x

Number of students in next year = number of students in present year + increased number of students.

$\begin{array}{l}{\text { Number of students in next year }=x+7.8 \% \text { of } x} \\\\ {\text { Number of students in next year }=x\left(1+\frac{7.8}{100}\right)} \\\\ {\text { Number of students in next year }=x(1+0.078)=1.078 x}\end{array}$

Thus there will be 1.078x students in next year

3 0

4 years ago

Carlos found the area of the figure. Check his work, and explain any errors. 4 cm TheRectangle:(2)(1.5) = 3 cm 2 cm Triangle:(1)

lesya [120]

Answer:

Your answer is 5.5 cm².

If this helps you, mark me brainliest!!

6 0

2 years ago

I need help and a better explanation for this problem. Urgency on this so please be quick to answer.

Snezhnost [94]

Answer:

48

Step-by-step explanation:

8 0

3 years ago

Use systems of linear equations solve x+2y=4 Must include; Step to solve problem