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3 years ago

13

Solve for x. The problem is in the picture!

1 answer:

Harrizon [31]3 years ago

4 0

<h2>Question:- Solve for X </h2>

<h3>Given:- </h3>

According to the diagram:-

Angle D = (6x+ 8)°
Angle E = (5X+8)°
Exterior angle C = 82°

<h2>Answer:- </h2>

<h3>Exterior angle property:- </h3>

Exterior angle is equal to the sum of two opposite interior angle

<h3>ATQ :- </h3>

$\angle D + \angle \: E = ext \angle C \\ 6x + 8 + 5x + 8 = 82 \\ 11x + 16 = 82 \\ 11x = 82 - 16 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = \frac{ \cancel{66}^{ \: \: 6} }{ \cancel{11} } \\ x = 6$

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

Please help me I will mark brain-list

kozerog [31]

Answer:

q12 is 8

q13 is 81

Step-by-step explanation:

100*6 =600 / 75 = 8

90*72 = 6480 / 80 = 81

6 0

3 years ago

Read 2 more answers

The function f(t)= 5 tan 2 t, does not have an amplitude and has a period of π.

trasher [3.6K]

ANSWER

False

EXPLANATION

The tangent function has no amplitude because it is not bounded.

The given tangent function is

$f(t) = 5 \tan(2t)$

This is of the form

f(t)=a tan(bt)

The period is given by

$T = \frac{\pi}{ |b| }$

$T = \frac{\pi}{ |2| } = \frac{\pi}{2}$

The first statement is true but the second is false.

Hence the whole statement is false.

8 0

3 years ago

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One Step Equations<br> solve for x <br><br> 2.4+x=9.8

Simora [160]

Answer:

x=7.4

Step-by-step explanation:

2.4+x=9.8

(x=9.8-2.4)

x=7.4

7 0

3 years ago

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The polynomial p(x)=(3-2x)(x^2-5) is graphed in a coordinate plane. Which statement about the graph is correct?

satela [25.4K]

Answer:

0 = (3-2x) x (x x 2 -5)

(3-2x) x ( x x 2 - 5) = 0

(3-2x) x (2x - 5) = 0

3 - 2x = 0

2x - 5 = 0

x = 3/2

x = 5/2

x1 = 3/2 or x2 = 5/2

7 0

3 years ago