Expression will have the LEAST value?

One cold night the temperature was 0 degrees at 8 p.m. The temperature dropped at a constant rate from 8 p.m. to midnight. At mi

Diano4ka-milaya [45]

Let y be the temperature
Let m be the rate of temperature drop in degrees per hour
Let x be the number of hours elapsed since 8PM
The initial temperature (at x = 0) is 0
y = mx
Four hours from 8 PM, the temperature was -16.8 degrees
-16.8 = m(4)
m = -4.2 degrees per hour
At 9PM, one hour will have elapsed.
y = -4.2(1)
y = -4.2 degrees

7 0

2 years ago

Margo used 864 beads to make necklaces for the art club. She made

Anit [1.1K]

Each Necklace Had 36 Beads . 864 / 24 = 36 .

5 0

2 years ago

Read 2 more answers

Given: 2x^2+3x-5, g(x)=x+9. Find: (fg)(3)

Svetradugi [14.3K]

Answer:

264

Step-by-step explanation:

$f(x)=2x^2+3x-5$

$g(x)=x+9$

$(fg)(x)=f(x) \times g(x)$

$\implies (fg)(x)=(2x^2+3x-5)(x+9)$

$(fg)(3)=(2(3)^2+3(3)-5)(3+9)$

$\implies (fg)(3)=22 \times 12$

$\implies (fg)(3)=264$

8 0

2 years ago

The rate of growth of profit (in millions) from an invention is approximated by Upper P prime (x )equals x e Superscript negati

Alecsey [184]

Answer:

The function is $P(x) = \frac{1}{2} e^{-x^2} +0.016$

Step-by-step explanation:

From the question we are told that

The rate of growth is $P'(x) = xe^{x} - x^2$

The total profit is $P(2) =$ $25,000

The time taken to make the profit is $x = 2 \ years$

From the question

$P'(x) = xe^{-x^2}$ is the rate of growth

Now here x represent the time taken

Now the total profit is mathematically represented as

$P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,$

So using substitution method

We have that

$u = - x^2$

$du = 2xdx$

So

$p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du$

$p(x) = {\frac{1}{2} [ e^{-u}} +c ]$

$p(x) = {\frac{1}{2} e^{-x^2}} + \frac{1}{2} c$ recall $u = - x^2$ and let $\frac{1}{2} c = Z$

At x = 2 years

$P(x) =$ $25,000

So

Since the profit rate is in million

$P(x) =$ $25,000 = $\frac{25000}{1000000} =$ $0.025 millon dollars

So

$0.025 = {\frac{1}{2} e^{-2^2}} + Z$

=> $Z = 0.025 - {\frac{1}{2} e^{-2^2}}$

$Z = 0.016$

So the profit function becomes

$P(x) = \frac{1}{2} e^{-x^2} +0.016$

5 0

3 years ago

2 cars c and d started to move to each other car c was 118 miles from Boston car d was 256 miles from Boston car c was going twi

Vadim26 [7]

Answer:

131.3 miles

Step-by-step explanation:

The two cars are moving from different directions. The total distance between the two cars = 118 miles + 256 miles = 374 miles.

Let us assume that the two cars meet at point O, let the distance between car c and O be d₁, the distance between car d and point O be d₂, hence:

d₁ + d₂ = 374 miles (1)

Let speed of car d be x mph, therefore speed of car c = 2x mph (twice of car d). If it take the cars t hours to meet at the same point, hence

For car c:

2x = d₁/t

t = d₁ / 2x

For car d;

x = d₂/t

t = d₂/ x

Since it takes both cars the same time to meet at the same point, therefore:

d₁/2x = d₂ / x

d₁ = 2d₂

d₁ - 2d₂ = 0 (2)

Solving equation 1 and 2 simultaneously gives d₁ = 249.3 miles, d₂ = 124.7 miles

Therefore the distance from point of meet to Boston = 249.3 - 118 = 131.3 miles

7 0

3 years ago