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nexus9112 [7]
3 years ago
5

At the end of a snow storm, Riley saw there was a lot of snow on her front lawn. The temperature increased and the snow began to

melt at a steady rate. The depth of snow on Riley's lawn, in inches, can be modeled by the equation S = 13 – t, where t is the time, in hours, after the snow stopped falling. What is the x-intercept of the equation and what is its interpretation in the context of the problem?​
Mathematics
1 answer:
9966 [12]3 years ago
4 0

Answer: the x-intercept of the fuction is 13 which represents the number of hours unit

All the snow has melted

Step-by-step explanation:

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A closed box with a square base is to have a volume of 13 comma 500 cm cubed. The material for the top and bottom of the box cos
andrezito [222]

Answer:

x  =  1,5 cm

h  =  6  cm

C(min) = 135 $

Step-by-step explanation:

Volume of the box is :

V(b)  = 13,5 cm³

Aea of the top is equal to area of the base,

Let call  " x " side of the base then as it is square area is A₁ = x²

Sides areas are 4 each one equal to x * h  (where h is the high of the box)

And volume of the box is   13,5 cm³  = x²*h

Then   h  =  13,5/x²

Side area is :  A₂ =  x* 13,5/x²

A(b)  = A₁  + A₂

Total area of the box as functon of x is:

A(x)  = 2*x²  + 4* 13,5 / x

And finally cost of the box is

C(x)  = 10*2*x²   +  2.50*4*13.5/x

C(x)  = 20*x²  +  135/x

Taking derivatives on both sides of the equation:

C´(x)  =  40*x   -  135*/x²

C´(x)  = 0     ⇒      40*x   -  135*/x² = 0    ⇒  40*x³ = 135

x³  = 3.375

x  = 1,5 cm

And   h  =  13,5/x²     ⇒   h  =  13,5/ (1,5)²

h = 6 cm

C(min)  = 20*x²  + 135/x

C(min)  = 45  +  90

C(min)  = 135 $

8 0
3 years ago
Write an equation (any form) for the quadratic graphed below. Y=
Licemer1 [7]

Answer:

y = -2x^2 - 4x - 1

Step-by-step explanation:

We can see that the graph passes through (-2, -1), (-1, 1) and (0, -1).

Let's solve

ax^2 + bx + c = y

a(-2)^2 + b(-2) + c = -1

4a - 2b + c = -1

a(-1)^2 + b(-1) + c = 1

a - b + c = 1

a0^2 + b0 + c = -1

c = -1

we got c = -1 so we input it into the other 2

4a - 2b - 1 = -1

4a - 2b = 0

2a - b = 0

2a = b

a - b - 1 = 1

a - b = 2

a = b + 2

Let's input b = 2a

a = 2a + 2

-a = 2

a = -2

b = 2a = 2*(-2) = -4

c = -1

y = -2x^2 - 4x - 1

4 0
3 years ago
What is trigonometry ​
Vlada [557]

Answer:

the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Choose all the expressions that are equal to 5/9×8. A. 9÷5×8 B. 8/9×5 C. 5÷8×9 D. 5×1/9×8 E. 5×8
Charra [1.4K]
<h2>Problem:</h2>

Choose all the expressions that are equal to 5/9×8.

A. 9÷5×8

B. 8/9×5

C. 5÷8×9

D. 5×1/9×8

E. 5×8

<h2>Solution:</h2>

\purple{ \frac{5}{9}  \times 8 =  \frac{40}{9}  = 4 \:  \frac{4}{9} }

\red{9 \div 5 \times 8 =  \frac{9}{5}  \times 8 =  \frac{72}{5}  = 14 \:  \frac{2}{5} }

\red{ \frac{8}{9}  \times 5 =  \frac{40}{9}  =  \boxed{4 \:  \frac{4}{9} }}

\red{5 \div 8 \times 9 =  \frac{5}{8}  \times 9 =  \frac{45}{8}  = 5 \:  \frac{5}{8} }

\red{5 \times  \frac{1}{9}  \times 8 =  \frac{5}{9}  \times 8 =  \frac{40}{9}  =  \boxed{4 \:  \frac{4}{9} }}

\red{5 \times 8 = 40}

<h2>Answer:</h2>

<u>B</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>D</u>

<h2>=============================</h2>

Hope it helps

<h2>=============================</h2>
5 0
3 years ago
X² + 4x + 3 = 0<br><br>Can someone please help me solve this quadratic equation <br>​
gavmur [86]

Answer:

Step-by-step explanation:

x= -1 and -3

What when multiplied is +3 but when added is 4? 3 and 1. You then get (x+3)(x+1) is the first part of the answer. If you want to find x, set x+3 to 0. x+3=0. Then subtract 3 from both sides to get x by itself. x= -3. Do the same with the x+1.

8 0
3 years ago
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