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3 years ago

Between what 2 consecutive integers does /35 lie

1 answer:

7 0

The correct question is
Between what two consecutive integers does Square Root Of 35 lie?

we know that

I need to find two numbers n and m such that
n < (√35)< m ---------> n² < 35 < m²

list the first squares
1²=1;
2²=4;
3²=9;
4²=16;
5²=25;
6²=36...

So,
you can see that n=5 and m=6 satisfy the request

the answer is
5 and 6

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A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the

Stells [14]

Answer:

$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box= $L\times B\times H$

Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

$V(x)=120x-30x^2-16x^2+4x^3$

$V(x)=4x^3-46x^2+120x$

Differentiate w.r.t x

$V'(x)=12x^2-92x+120$

$V'(x)=0$

$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

$3x-5=0\implies x=\frac{5}{3}$

Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

$V''(6)=24(6)-92=52>0$

Substitute x=5/3

$V''(5/3)=24(5/3)-92=-52$

Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

5 0

2 years ago

Arianna invests $2,000 into an ETE which earns 2% per year. In 10 years, how much will Arianna's investment be worth if interest

Alchen [17]

Answer:

$2040

Step-by-step explanation:

3 0

1 year ago

Question 4 (1 point)

Nostrana [21]

Answer:

The ball will hit the ground at 10 seconds and its maximum height is 1024 feet.

Step-by-step explanation:

Height of a mountain, h = 90 feet

Upward velocity of a ball, u = 64 ft/s

Its height as a function of time can be written by using the second equation of motion as follows :

$f(x) = -16t^2 + 64t + 960$ .....(1)

When it will hit the ground, f(x) = 0

$-16t^2 + 64t + 960=0\\\\16(-t^2+4t+60)=0\\\\-t^2+4t+60=0$

It is quadratic equation.

t = -6 s and t = 10 s

Neglecting -6 seconds, the ball will hit the ground at 10 seconds.

For maximum height,

Put f'(x) = 0

$-32t+64=0\\\\\\t=\dfrac{64}{32}\\\\t=2\ s$

Put t = 2 in equation (1)

$f(2) = -16(2)^2 + 64(2) + 960\\\\=1024\ \text{feet}$

Hence, the ball will hit the ground at 10 seconds and its maximum height is 1024 feet.

5 0

2 years ago

Use the Law of Sines to find the missing angle of the triangle. Find m<b to the nearest tenth.

defon

1. By the Law of Sines, you have:

SinA/a=SinB/b=SinC/c

2. You don't need the fraction SinC/c, so you can eliminate it. Then:

SinA/a=SinB/b

A=40°
a=19
B=m∠b
b=13

3. When you substitute this values into SinA/a=SinB/b, you obtain:

SinA/a=SinB/b
Sin(40°)/19=SinB/13
SinB=13xSin(40°)/19
m∠b=SinB^-1(13xSin(40°)/19)
m∠b=26.1°

Therefore, the answer is: 26.1 degrees.

6 0

2 years ago

Please help!! I only have half an hour to do this or I fail math !!!

netineya [11]

Answer:

8+6-10+2+15-3-7-5+2-15-8+10 = 5

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers