If DE=4x+10, EF= 2x-1, and DF=9x-15, Find DF

Mathematics

1 answer:

djverab [1.8K]3 years ago

6 0

Answer:

Df=9x-15

Step-by-step explanation:

The answer is on the question

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A supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. To do this, the employee plans

Tanzania [10]

Answer: The side of the square will be 3 cm.

Step-by-step explanation:

When squares of equal size of side x, are cut from the four corners, we are left with the following dimensions for the cuboid box.

l= 30-2x

b = 14-2x

h= x

Hence, the volume of the cuboid will be ,

V = lbh

= (30-2x)(14-2x)x

Since this volume should be the largest possible, then differentiating volume with x should be equal to zero.

Therefore, $\frac{dV}{dx} = 0$

$\frac{dV}{dx} =-2(14-2x)x -2(30-2x)x+(30-2x)(14-2x)=0$

solving we get, x = 3, x = $\frac{35}{3}$

We can omit x = $\frac{35}{3}$ because 14 - 2x < 0 , which is not possible.

Therefore, x=3.

7 0

4 years ago

The height H of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 9

mariarad [96]

Answer:

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

Step-by-step explanation:

Statement is incorrect. Correct form is presented below:

The height $h(t)$ of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 90 feet per second is given by equation $h(t) = 3 +90\cdot t -16\cdot t^{2}$ , where $t$ is time in seconds. After how many seconds will the ball be 84 feet above the ground.

We equalize the kinematic formula to 84 feet and solve the resulting second-order polynomial by Quadratic Formula to determine the instants associated with such height:

$3+90\cdot t -16\cdot t^{2} = 84$