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2 years ago

50 POINTS !! PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.

Mathematics

2 answers:

valentina_108 [34]2 years ago

5 0

Answer:

a=18.7 or 19 rounded up

Step-by-step explanation:

Use Pythagoras Thereom

a^2=8^2+17^2

a^2=64+289

a^2=353

√353

a=18

ValentinkaMS [17]2 years ago

4 0

Answer:

The length of missing leg is 15 cm.

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Find two numbers such that the sum of their squares is 100. The square of the larger number is equal to the sum of the product o

Shtirlitz [24]

Answer with Step-by-step explanation:

Let x and y are two numbers

According to question

$x^2+y^2=100$ ....(1)

Suppose x is larger than y

$x^2=x(4y+8x)$

$x=4y+8x$

$x-8x=4y$

$-7x=4y$

$y=-\frac{7}{4}x$

Substitute the value of y

$x^2+(-\frac{7}{4}x)^2=100$

$x^2+\frac{49}{16}x^2=100$

$\frac{16x^2+49x^2}{16}=100$

$\frac{65}{16}x^2=100$

$x^2=\frac{16\times 100}{65}$

$x=\sqrt{\frac{1600}{65}}=\frac{40}{\sqrt{65}}=\frac{40}{65}\sqrt{65}=\frac{8}{13}\sqrt{65}$

$y=-\frac{7}{4}\times \frac{8}{13}\sqrt{65}=-\frac{14}{13}\sqrt{65}$

3 0

2 years ago

This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

velikii [3]

Answer:

The maximum value= 36

Minimum value = - 36

Step-by-step explanation:

Given that

f(x, y, z) = 8 x + 8 y + 4 z

h(x,y,z)=4 x² + 4 y² + 4 z² - 36

From Lagrange multipliers

Δf = λ Δh

Δf = < 8 ,8 , 4>

Δh = < 8 x ,8 y , 8 z>

Δf = λ Δh

< 8 ,8 , 4> = < 8 λ x ,8 λ y , 8 λ z>

8 = 8 λ x -------------1

8 = 8 λ y ---- ------2

4 = 8 λ z ----------------3

From equation 1 ,2 and 3

Now by putting the value of x,y and z in the following equation

4 x² + 4 y² + 4 z² = 36

$4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{\lambda^2 }+4\times \dfrac{1}{(2\lambda)^2 }=36$

$\dfrac{4}{\lambda^2 }+ \dfrac{4}{\lambda^2 }+ \dfrac{1}{\lambda^2 }=36$

So the value of λ is

$\lambda =\pm \dfrac{1}{2}$

When λ = 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= 2 , y = 2 , z=1

f(x, y, z) = 8 x + 8 y + 4 z

f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1

f(2, 2, 1) =36

When λ = - 1/2

x = 1 / λ , y=1 / λ , z= 1 /2 λ

x= - 2 , y = - 2 , z= - 1

f(x, y, z) = 8 x + 8 y + 4 z

f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)

f(-2, -2, -1) = - 36

The maximum value= 36

Minimum value = - 36

7 0

2 years ago

Read 2 more answers

A rectangular box with a square base contains 24 cubic feet. if the height of the box is 18 inches, how many feet are there in e

Romashka-Z-Leto [24]

Answer:

Step-by-step explanation:

V = Lwh

the volume (given) = 24 ft^3

the height (given) = 18" = 1.5'

24 = L*w*1.5

divide both sides by 1.5

16 = Lw

You need to find the number of feet in each side of the base

since the box has a square base

L = W

AND, found above, L*w = 16

so 4*4= 16

Answer - 4

3 0

2 years ago

Can u help with 8 and 10? And check the rest??

Hoochie [10]

7.) 4x greater because 8*8=64 and 4*4=16 64/16=4
8.) 22 because 70-13-13=44/2=22
9.) 32 because the square root of 64 is 8 so each side is 8 square feet
10.) The rectangle is an 8 by 5 and the perimeter is 26

3 0

2 years ago

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Help plssss!!! Giving. 10 pointsssssss

gayaneshka [121]

Answer:

its 34

Step-by-step explanation:

8 0

2 years ago