Choose the correct way to end the sentence. The lines 2x + 4y = 32 and y =

Simplify cosθ + cosθtan2θ. 1 cscθ secθ sin2θ

motikmotik

Answer:

csc0

Step-by-step explanation:

3 0

3 years ago

Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Vikki [24]

Answer:

Height: 3/2 inches

Length: 12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

The new length of the cardboard = 15 -2x (because we cut from 4 corners)
The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = $4x^3 -44x^2 +105x$

To maximum volume, we use the first derivative of the volume

$\dfrac{dV}{dx} = 0$

<=> $12x^2-88x+105=0$

<=> $\left(2x-3\right)\left(6x-35\right) = 0$

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

$\dfrac{d^2V}{dx^2}$ = 24x -88

If x = 3/2, we have:

$\dfrac{d^2V}{dx^2}$ = 24(3/2) -88 = -52

If x = 35/6, we have:

$\dfrac{d^2V}{dx^2}$ = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0

3 years ago

Solve each absolute value equation and chose The correct answer from the choices provided |x|+5=18

Kamila [148]

Solve the absolute value equation.

First subtract 5 from both sides.

|x|+5=18

|x|=13

If the absolute value of x is 13 that x equals 13 and -13. Absolute value means distance from 0.

x=13,-13

3 0

3 years ago

BELP ME WITH THIS PLZ!!!!!!

kati45 [8]

Answer:

The entire area of the sailboat is 60cm²

Step-by-step explanation:

You can find the area of this shape by breaking it down into simpler shapes and adding up their individual areas.

In this case, the areas we'll use are the rectangle at the bottom, and the pair of triangles at the top.

Because the two triangles can be put together to form a single triangle, we don't need to measure them independently. We can simply take the total length of their bases, multiply it by their height, and divide by two. This follows the rule that the area of a triangle is equal to the area of the square that contains it divided by two.

(2cm + 3cm) × 6cm

= 5cm × 6cm

= 30cm²

The rectangle's area is of course equal to its width times its height, so we can say:

2.5cm × 12cm

= 30cm²

The total area of the shapes then is 30cm² + 30 cm², giving us a total area of 60cm²

3 0

3 years ago

14. You deposit $400 in a savings account that earns 7% interest compounded annually.

oksian1 [2.3K]

Answer:

A=p(1+r/100)^n

=400(1+7/100)^2

=400*1.14

=456

4 0

2 years ago

Choose the correct way to end the sentence. The lines 2x + 4y = 32 and y = –1/2x + 16 are