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3 years ago

Free Brainliest! PLEASE HELP

Mathematics

2 answers:

Arturiano [62]3 years ago

8 0

$a^2+16^2=20^2$

$a^2+256=400$

Subtracting 256 from both sides

$a^2=144$

Taking squareroot both sides

$a= \sqrt144$

$a = \sqrt2.2.3.2.2.3$

$a=12$

Therefore length of missing leg is

$a = 12 units$

tresset_1 [31]3 years ago

5 0

a^2+16^2=20^2

a^2+256=400

Subtracting 256 from both sides

a^2=144

Taking squareroot both sides

a= \sqrt144

a = \sqrt2.2.3.2.2.3

a=12

Therefore length of missing leg is

a = 12 units

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The movie theater in town has 4 rooms. Each room has 58 seats on the left side and 32 seats on the right side. Which equation co

saveliy_v [14]

Answer:

The right option is (C) (58 + 32)×4

Step-by-step explanation:

Total number of rooms = 4

Number of seats on left = 58 seats in each room

Number of seats on right = 32 seats in each room

Total number of seats in a room = 58 + 32 seats

Total number of seats in the movie theater = Number of rooms × Number of seats in each room

Total number of seats in the movie theater = 4 × (58 + 32) = 360 seats

Hence the right option is (C) (58 + 32)×4

7 0

3 years ago

Help it’s easy math but still

I am Lyosha [343]

I think the way that you do is 5/5+3=5/8

5/8*4=2.5 so 2.5 is the answer

7 0

3 years ago

Read 2 more answers

sumalee won 40 super bouncy balls playing horseshoes at her school's game night. later, she gave two to each of her friends. she

slavikrds [6]

sumalee has 16 friends because she gave away 32, if you divide 32 by 2 its 16 cuz thats how many she gave away to each person

6 0

3 years ago

Prove: <img src="https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D" id="TexFormula1" title="\frac{a}{b}" alt="\frac{a}{b}" align="ab

Masteriza [31]

Step-by-step explanation:

$\dfrac{a}{b} = \dfrac{c}{d}$

Add 1 to both sides of the equation:

$\dfrac{a}{b} + 1 = \dfrac{c}{d} + 1$

Note that

$\dfrac{a}{b} + 1 = \dfrac{a + b}{b}$

Likewise,

$\dfrac{c}{d} + 1 = \dfrac{c + d}{d}$

Therefore,

$\dfrac{a + b}{b} = \dfrac{c + d}{d}$

8 0

3 years ago

Solve the following differential equations using classical methods. Assume zero initial conditions.

MA_775_DIABLO [31]

I'll use the integrating factor method for the first DE, and undetermined coefficients for the second one.

(a) Multiply both sides by exp(7t ):

exp(7t ) dx/dt + 7 exp(7t ) x = 5 exp(7t ) cos(2t )

The left side is now the derivative of a product:

d/dt [exp(7t ) x] = 5 exp(7t ) cos(2t )

Integrate both sides:

exp(7t ) x = 10/53 exp(7t ) sin(2t ) + 35/53 exp(7t ) cos(2t ) + C

Solve for x :

x = 10/53 sin(2t ) + 35/53 cos(2t ) + C exp(-7t )

(b) Solve the corresonding homogeneous DE:

d²x/dt ² + 6 dx/dt + 8x = 0

has characteristic equation

r ² + 6r + 8 = (r + 4) (r + 2) = 0

with roots at r = -4 and r = -2. So the characteristic solution is

x (char.) = C₁ exp(-4t ) + C₂ exp(-2t )

For the particular solution, assume an ansatz of the form

x (part.) = a cos(3t ) + b sin(3t )

with derivatives

dx/dt = -3a sin(3t ) + 3b cos(3t )

d²x/dt ² = -9a cos(3t ) - 9b sin(3t )

Substitute these into the non-homogeneous DE and solve for the coefficients:

(-9a cos(3t ) - 9b sin(3t ))

… + 6 (-3a sin(3t ) + 3b cos(3t ))

… + 8 (a cos(3t ) + b sin(3t ))

= (-a + 18b) cos(3t ) + (-18a - b) sin(3t ) = 5 sin(3t )

So we have

-a + 18b = 0

-18a - b = 5

==> a = -18/65 and b = -1/65

so that the particular solution is

x (part.) = -18/65 cos(3t ) - 1/65 sin(3t )

and thus the general solution is

x (gen.) = x (char.) + x (part.)

x = C₁ exp(-4t ) + C₂ exp(-2t ) - 18/65 cos(3t ) - 1/65 sin(3t )

7 0

3 years ago

Free Brainliest! **PLEASE HELP**

Free Brainliest! PLEASE HELP