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2 years ago

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A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b

elow is equal to the measure of the exterior angle. In which step did the student first make a mistake and how can it be corrected?

1 answer:

fredd [130]2 years ago

8 0

Answer:

first one is your answer option a) hope it helps

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First-order linear differential equations

kkurt [141]

Answer:

$(1)\ logy\ =\ -sint\ +\ c$

$(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Step-by-step explanation:

1. Given differential equation is

$\dfrac{dy}{dt}+ycost = 0$

$=>\ \dfrac{dy}{dt}\ =\ -ycost$

$=>\ \dfrac{dy}{y}\ =\ -cost dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}$

$=>\ logy\ =\ -sint\ +\ c$

Hence, the solution of given differential equation can be given by

$logy\ =\ -sint\ +\ c.$

2. Given differential equation,

$\dfrac{dy}{dt}\ -\ 2ty\ =\ t$

$=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty$

$=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})$

$=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}$

$=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c$

$=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Hence, the solution of given differential equation is

$log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

8 0

3 years ago

Someone please help me with my homework please please help please help me with my homework

densk [106]

C=2x Pi x R so 2x3.14x17.5 = 109.9

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4 years ago

Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house. The length

podryga [215]

Answer:

The length of the patio is 32 ft and the width is 13 ft

Step-by-step explanation:

see the attached figure to better understand the problem

Let

L ----> the length of his patio

W ---> the width of his patio

we know that

$L+2W=58$ ----> equation A

$L=2W+6$ ----> equation B

substitute equation B in equation A and solve for W

$2W+6+2W=58$

$4W+6=58$

$4W=58-6$

$4W=52$

$W=13\ ft$

Find the value of L

$L=2W+6$ ----> $L=2(13)+6=32\ ft$

therefore

The length of the patio is 32 ft and the width is 13 ft

3 0

3 years ago

Solve the inequality and enter your solution as an inequality comparing the

avanturin [10]

Answer: x > 20

Step-by-step explanation:

x + 10 > 30

-10 -10

x > 20

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3 years ago

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Write an equation to match each graph:

Makovka662 [10]

Answer:

y=-|x+1|+1

Step-by-step explanation:

It's an absolute value function vertically flipped and shifted 1 unit to the left, 1 unit to the the top.

8 0

3 years ago