The temperature was -5 ℉ in Denver and then fell 8 ℉ by the morning.

Find all the polynomials f (t ) of degree ≤ 2 [of the form f (t) = a + bt + ct2] whose graphs run through the points (1, 3) and

Ugo [173]

Answer:

f(t) = 4 - 3t + 2t^2

Step-by-step explanation:

Given:

f(t) = a + bt + ct^2

Differentiate w.r.t. "t"

f'(t) = b + 2ct

1) f(1) = 3

a + b +c = 3...........1)

2) f(2) = 6

a + 2b + 4c = 6.........2)

3) f'(1) = 1

b + 2c = 1 ...............3)

Solving above three simultaneous equations:

a = 4

b = -3

c = 2

Therefore equation becomes:

f(t) = 4 + (-3)t + (2)t^2

3 0

3 years ago

A shipment of sugar fills 2 4/5 containers. If each container holds 2 3/7 tons of sugar, what is the amount of sugar in the enti

Yanka [14]

Answer:

6 4/5 tons

Step-by-step explanation:

Multiply the number of containers by the amount in each to find the total amount of sugar:

2 4/5 * 2 3/7 =
14/5 * 17/7 =
2*17/5 =
34/5 =
6 4/5

8 0

3 years ago

Read 2 more answers

What is the distance between (-5, 2) and (-9, 2)?

ValentinkaMS [17]

Answer:

4

Step-by-step explanation:

use the distace formula:

square root of (x2-x1)^2 + (y2-y1)^2

give brainliest please

6 0

3 years ago

Please help me solve this problem ASAP

DiKsa [7]

$\bold{\huge{\blue{\underline{ Solution }}}}$

<h3>Given :-</h3>

The right angled below is formed by 3 squares A, B and C
The area of square B has an area of 144 inches ²
The area of square C has an of 169 inches ²

We have to find the area of square A?

<h3>Let's Begin :- </h3>

The right angled triangle is formed by 3 squares

We have, 

Area of square B is 144 inches²
Area of square C is 169 inches²

We know that,

$\bold{ Area \: of \: square = Side × Side }$

Let the side of square B be x

Subsitute the required values,

$\sf{ 144 = x × x }$

$\sf{ 144 = x² }$

$\sf{ x = √144}$

$\bold{\red{ x = 12\: inches }}$

Thus, The dimension of square B is 12 inches

Area of square C = 169 inches

Let the side of square C be y

Subsitute the required values,

$\sf{ 169 = y × y }$

$\sf{ 169 = y² }$

$\sf{ y = √169}$

$\bold{\green{ y = 13\: inches }}$

Thus, The dimension of square C is 13 inches.

It is mentioned in the question that, the right angled triangle is formed by 3 squares

The dimensions of square be is x and y

Let the dimensions of square A be z

<h3>Therefore, By using Pythagoras theorem, </h3>

The sum of squares of base and perpendicular height equal to the square of hypotenuse

That is,

$\bold{\pink{ (Perpendicular)² + (Base)² = (Hypotenuse)² }}$

Here, 

Base = x = 12 inches
Perpendicular = z
Hypotenuse = y = 13 inches

Subsitute the required values,

$\sf{ (z)² + (x)² = (y)² }$

$\sf{ (z)² + (12)² = (169)² }$

$\sf{ (z)² + 144 = 169}$

$\sf{ (z)² = 169 - 144 }$

$\sf{ (z)² = 25}$

$\bold{\blue{ z = 5 }}$

Thus, The dimensions of square A is 5 inches

<h3>Therefore,</h3>

Area of square

$\sf{ = Side × Side }$

$\sf{ = 5 × 5 }$

$\bold{\orange{ = 25\: inches }}$

Hence, The area of square A is 25 inches.

6 0

3 years ago

GIVING BRAINLIEST Graphing required Answer ASAP

just olya [345]

Here is the right answer

7 0

3 years ago