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2 years ago

If triangle STU is congruent to triangle VWX, which statement is not true?

1 answer:

4 0

If triangles are congruent then, their corresponding sides and angles should have the same measurement. From the given, STU is congruent to VWX, angle S, T, U should be congruent to angles V, W, and X, respectively. From the choices, the answer should be letter D. because U and V do not appear in the same order from both names.

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Show that (2xy3 + cos x)dx + (3x2 y2 − sin y)dy = 0 is exact, and find the solution. Find c if y(0) = π

Licemer1 [7]

We're looking for a solution of the form $F(x,y)=C$ . By the chain rule, this solution should have total differential

$\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

and the equation is exact if the mixed second-order partial derivatives of $F$ are equal, i.e. $\frac{\partial^2F}{\partial x\partial y}=\dfrac{\partial^2F}{\partial y\partial x}$ .

The given ODE is exact, since

$\dfrac{\partial(2xy^3+\cos x)}{\partial y}=6xy^2$

$\dfrac{\partial(3x^2y^2-\sin y)}{\partial x}=6xy^2$

Then

$\dfrac{\partial F}{\partial x}=2xy^3+\cos x\implies F(x,y)=x^2y^3+\sin x+f(y)$

$\dfrac{\partial F}{\partial y}=3x^2y^2-\sin y=3x^2y^2+\dfrac{\mathrm df}{\mathrm dy}$

$\dfrac{\mathrm df}{\mathrm dy}=-\sin y\implies f(y)=\cos y+C$

$\implies x^2y^3+\sin x+\cos y=C$

With $y(0)=\pi$ , we get

$\cos\pi=C\implies C=-1$

$\implies\boxed{x^2y^3+\sin x+\cos y=-1}$

6 0

3 years ago

A manufacturing process produces integrated circuit chips. Over the long run the fraction of bad chips produced by the process i

Vitek1552 [10]

Answer:

0.0244 (2.44%)

Step-by-step explanation:

defining the event T= the chips passes the tests , then

P(T)= probability that the chip is not defective * probability that it passes the test given that is not defective + probability that the chip is defective * probability that it passes the test given that is defective = 0.80 * 1 + 0.20 * 0.10 = 0.82

for conditional probability we can use the theorem of Bayes. If we define the event D=the chip was defective , then

P(D/T)=P(D∩T)/P(T) = 0.20 * 0.10/0.82= 0.0244 (2.44%)

where

P(D∩T)=probability that the chip is defective and passes the test

P(D/T)=probability that the chip is defective given that it passes the test

5 0

3 years ago

Answers: 3x + 26 5x + 15 x + 30 10x - 7 please answer fast!

pentagon [3]

Answer: I think it's A. 3x + 26 but im not completely sure

Step-by-step explanation:

5 0

3 years ago

PLEASE HELP ASAP A. 300 ft2 B.150 ft2 C.45 ft2 D.75 ft2

Kaylis [27]

Answer:

75 ft^2

Step-by-step explanation:

Area of trapezoid = 1/2({b1+b}*h)

1/2(25x6) =

150 / 2 =75

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

4 0

2 years ago

Read 2 more answers

Solve the equation.

djverab [1.8K]

(y - 5)/3 = 1
y - 5 = 3 x 1 = 3
y = 3 + 5 = 8

6x + 29 = 5
6x = 5 - 29 = -24
x = -24/6 = -4

7 0

3 years ago

Read 2 more answers