Evaluate the expression for x=6 and y=8 ? 4x^2-3y+12

The area of a rectangle is less than 81 square centimeters. The length of the rectangle is 9 centimeters and the width is x cent

Karo-lina-s [1.5K]

Answer:

Given

The area of a rectangle is less than 81 square centimeters

length 9cm

width =x cm

Step-by-step explanation:

Area of rectangle=length ×width

= 9×X

Area of rectangle is less than 81 cm^2

So 9x-81=0

X=81/9

X=9

So the value of xis 9

4 0

3 years ago

4. A scientist changes the temperature of a solution at a rate of -7°C per minute. How many minutes will it take for

igomit [66]

Answer:

7 minutes

Step-by-step explanation:

The scientist changes the temperature for the solution at a rate of -7°C per minute. We need to find out how long it'll take for the solution's temperature to change from 0°C to -49°C. So, we divide -7 by -49 to find out how long it will take:

-49 / -7 = 7

It will take 7 minutes for the temperature to reach -49°C.

6 0

3 years ago

42 base x +53base x = 125base x. what<br>is the value of x

Finger [1]

Answer:

Step-by-step explanation:

The largest number is 5. Therefore x ≥ 6.

Convert numbers from x system to decimal system:

$42_x=4x+2\\\\53_x=5x+3\\\\125_x=1x^2+2x+5$

Solve the equation for x:

$42_x+53_x=125_x\Rightarrow4x+2+5x+3=x^2+2x+5\qquad\text{combine like terms}\\\\(4x+5x)+(2+3)=x^2+2x+5\\\\9x+5=x^2+2x+5\qquad\text{subtract 5 from both sides}\\\\9x=x^2+2x\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\0=x^2-7x\\\\x^2-7x=0\qquad\text{distributive}\\\\x(x-7)=0\iff x=0\ \vee\ x-7=0\\\\x=0$

7 0

4 years ago

mario walks his dog once every 8 days in the park, while todd walks his dog once every 14 days. today, both mario and todd walke

notsponge [240]

Assuming both Mario and Todd just walked today.

Mario is every 8 days

Todd is every 14 days.

The days that will coincide is the Least Common Multiple (LCM) of 8 and 14

2 / 8 14
2 / 4 7
2 /    2 7
7 /    1    7
    /    1 1

The LCM = 2 * 2* 2* 7 = 56

The will both walk together in the next 56 days.

7 0

3 years ago

A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial pos

jeka57 [31]

Part A - The average value of v(t) over the interval (0, π/2) is 6/π

Part B - The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

<h3>Part A: Find the average value of v(t) on the interval (0, π/2)</h3>

The average value of a function f(t) over the interval (a,b) is

$f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx$

So, since velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval (0, π/2) is given by

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt$

Since v(t) = 3cost, we have

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}$

So, the average value of v(t) over the interval (0, π/2) is 6/π

<h3>Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?</h3>

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

<h3>Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)</h3>

The total distance the yo-yo travels from time t = 0 to time t = π is given by

$x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6$

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

Learn more about average value of a function here:

brainly.com/question/15870615

#SPJ1

4 0

1 year ago