All categories

3 years ago

Can you please help me with question number 14

Mathematics

2 answers:

Nutka1998 [239]3 years ago

8 0

The answer should be C, if my math is correct!

Hope I could help :)

elena-14-01-66 [18.8K]3 years ago

3 0

Remember
√(ab)=(√a)(√b)
and
√x²=x
so

note: x⁴=(x²)(x²)
and y³=(y²)(y)
√(18x⁴y³)=
(√18)(√x⁴)(√y³)=
(√9)(√2)(√x²)(√x²)(√y²)(√y)=
(3)(√2)(x)(x)(y)(√y)=
3x²y√(2y)

C is the answer

You might be interested in

Find the value of X and the value of Y. (10 POINTS)

Ganezh [65]

sin 45 = opp/hyp

sin 45 = 4 / y

y = 4/sin 45

y = 4 /((sqrt2)/2)=4* sqrt(2)

tan 45 =opp/adj

tan 45 = 4/(x-3)

1 = 4/(x-3)

x-3 = 4

x=7

3 0

3 years ago

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat

tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

Step 1:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane. Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

Step( ii):

By using Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ y z + λ ( 1) = 0

⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ x z + λ ( 9) = 0

⇒ $\frac{xz}{9}$ = - λ .......(b)

Obtain the equations are δ F / δ z = 0

δ f / δ x +λ δ Ф / δ z =0

x y + λ ( 4) = 0

⇒ $\frac{xy}{4}$ = - λ .......(c)

Step (iii):-

Equating (a) and (b) equations

we get $y z = \frac{xz}{9}$

cancel 'z' value we get x = 9y .......(d)

Equating (b) and (c) equations

we get $\frac{xy}{4} = \frac{xz}{9}$

cancel 'x' value on both sides , we get

4z =9y ......(e)

substitute (d) (e) values in equation (1) we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

therefore the dimensions are x =9 , y=1 and z = 9 /4

Conclusion:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

9 + 9 + 4(9/4) = 27

27 =27

so satisfied equation

3 0

3 years ago

The population of New York City is 23,945. Eastdale has a population of 12,774 What is the total population of the two communiti

serious [3.7K]

No.d
37,619

I hope that this helps you and please mark me as the brainliest.

3 0

3 years ago

In a race, there are 20 runners. Trophies for the race are awarded to the runners finishing in first and second place. In how ma

andrew11 [14]

Answer:

There are 380 ways that 1st and 2nd place can be determined in the race

Step-by-step explanation:

There are 20 possibilities for determine the 1st place

There are 19 possibilities for determine the 2nd place

Number of ways that 1st and 2nd place can be determined = 20 * 19

Number of ways that 1st and 2nd place can be determined = 380

7 0

3 years ago

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?

kompoz [17]

Answer:

5.9 years

Step-by-step explanation:

We believe a better representation of the compound interest formula is ...

$V(t)=P(1+\dfrac{r}{n})^{nt}$

We want to find the value of t for P=1 and V(t)=2. We are told n=4, so the formula becomes ...

$2=(1+\dfrac{.12}{4})^{4t}\\\\\log{(2)}=4t\log{(1.03)}\quad\text{take logs}\\\\t=\dfrac{\log{2}}{4\log{1.03}}\approx\boxed{5.9\quad\text{years}}$

8 0

4 years ago