Different ways to show subtraction for a problem like 32

Inessa [10]

This is a quadrilateral, so the sum of interior angle measures, like a rectangle or square ( who’s interior angle measures are4 x 90) —— is 360

So ...
E + 89 + 130 + 90 = 360
E + 309 = 360
- 309 - 309
E = 51 degrees

7 0

3 years ago

The length of the sides of a triangle are three consecutive integers. If the perimeter is 87, find the dimensions of the triangl

nadezda [96]

You can divide 87 by 3 which is 29, so each angle will be 29 degrees.
Since they are consecutive, that means they will all measure the same.

Hope this helps! :)

8 0

3 years ago

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Solve the following differential equations or initial value problems. In part (a), leave your answer in implicit form. For parts

shepuryov [24]

Answer:

(a) (y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) y = arctan(t(lnt - 1) + C)

(c) y = -1/ln|0.09(t + 1)²/t|

Step-by-step explanation:

(a) dy/dt = (t^2 + 7)/(y^4 - 4y^3)

Separate the variables

(y^4 - 4y^3)dy = (t^2 + 7)dt

Integrate both sides

(y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) dy/dt = (cos²y)lnt

Separate the variables

dy/cos²y = lnt dt

Integrate both sides

tany = t(lnt - 1) + C

y = arctan(t(lnt - 1) + C)

(c) (t² + t) dy/dt + y² = ty², y(1) = -1

(t² + t) dy/dt = ty² - y²

(t² + t) dy/dt = y²(t - 1)

(t² + t)/(t - 1)dy/dt = y²

Separating the variables

(t - 1)dt/(t² + t) = dy/y²

tdt/(t² + t) - dt/(t² + t) = dy/y²

dt/(t + 1) - dt/(t(t + 1)) = dy/y²

dt/(t + 1) - dt/t + dt/(t + 1) = dy/y²

Integrate both sides

ln(t + 1) - lnt + ln(t + 1) + lnC = -1/y

2ln(t + 1) - lnt + lnC = -1/y

ln|C(t + 1)²/t| = -1/y

y = -1/ln|C(t + 1)²/t|

Apply y(1) = -1

-1 = ln|C(1 + 1)²/1|

-1 = ln(4C)

4C = e^(-1)

C = (1/4)e^(-1) ≈ 0.09

y = -1/ln|0.09(t + 1)²/t|

8 0

3 years ago

8. In right triangle LMN shown below, altitude MK is drawn to LN from M. IF LM = 12 and LK =10, then

Elena-2011 [213]

The length of the KN is 4.4

Step-by-step explanation:

We know from Pythagoras theorem

In a right angle ΔLMN

Base² + perpendicular² = hypotenuse ²

From the properties of triangle we also know that altitudes are ⊥ on the sides they fall.

Hence ∠LKM = ∠NKM = 90 °

Given values-

LM=12

LK=10

Let KN be “s”

⇒LN= LK + KN

⇒LN= 10+x eq 1

Coming to the Δ LKM

⇒LK²+MK²= LM²

⇒MK²= 12²-10²

⇒MK²= 44 eq 2

Now in Δ MKN

⇒MK²+ KN²= MN²

⇒44+s²= MN² eq 3

In Δ LMN

⇒LM²+MN²= LN²

Using the values of MN² and LN² from the previous equations

⇒12² + 44+s²= (10+s) ²

⇒144+44+s²= 100+s²+20s

⇒188+s²= 100+s²+20s cancelling the common term “s²”

⇒20s= 188-100

∴ s= 4.4

Hence the value of KN is 4.4

8 0

4 years ago

Simplify the radical below. √x^13 A. 13√x B. 6x√x C. x√x^12 D. x^6√x

olga nikolaevna [1]

D, think as 13 dividing 2, you get 6 and have one left

7 0

3 years ago

Read 2 more answers

Different ways to show subtraction for a problem like 32 - 15