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1 year ago

Write two conditionals from each biconditional

Mathematics

1 answer:

bearhunter [10]1 year ago

3 0

Two conditionals from each biconditional are

(1) A month has exactly 28 days (2) It is February
(1)Two angels are complementary (2) The measures of the angles add up to 90
(1) The area of square s^2 (2) The perimeter of the square is 4s

<h3>How to write two conditionals from each biconditional?</h3>

A biconditional statement is represented as:

if and only if p, then q

From the above biconditional statement, we have the following conditional statements

Conditional statement 1: p

Conditional statement 2: q

Using the above as a guide, the conditional statements from the biconditional statements are:

<u>Biconditional statement 30</u>

A month has exactly 28 days
It is February

<u>Biconditional statement 31</u>

Two angels are complementary
The measures of the angles add up to 90

<u>Biconditional statement 32</u>

The area of square s^2
The perimeter of the square is 4s

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Suppose a change of coordinates T:R2→R2 from the uv-plane to the xy-plane is given by x=e−2ucos(5v), y=e−2usin(5v). Find the abs

anzhelika [568]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The solution is $\frac{\delta (x,y)}{\delta (u, v)} | = 10e^{-4u}$

Step-by-step explanation:

From the question we are told that

$x = e^{-2a} cos (5v)$

and $y = e^{-2a} sin(5v)$

Generally the absolute value of the determinant of the Jacobian for this change of coordinates is mathematically evaluated as

$| \frac{\delta (x,y)}{\delta (u, v)} | = | \ det \left[\begin{array}{ccc}{\frac{\delta x}{\delta u} }&{\frac{\delta x}{\delta v} }\\\frac{\delta y}{\delta u}&\frac{\delta y}{\delta v}\end{array}\right] |$

$= |\ det\ \left[\begin{array}{ccc}{-2e^{-2u} cos(5v)}&{-5e^{-2u} sin(5v)}\\{-2e^{-2u} sin(5v)}&{-2e^{-2u} cos(5v)}\end{array}\right] |$

$Let \ a = -2e^{-2u} cos(5v), \\ b=-2e^{-2u} sin(5v),\\c =-2e^{-2u} sin(5v),\\d=-2e^{-2u} cos(5v)$

$\frac{\delta (x,y)}{\delta (u, v)} | = |det \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] |$

=> $\frac{\delta (x,y)}{\delta (u, v)} | = | a * b - c* d |$

substituting for a, b, c,d

=> $\frac{\delta (x,y)}{\delta (u, v)} | = | -10 (e^{-2u})^2 cos^2 (5v) - 10 e^{-4u} sin^2(5v)|$

=> $\frac{\delta (x,y)}{\delta (u, v)} | = | -10 e^{-4u} (cos^2 (5v) + sin^2 (5v))|$

=> $\frac{\delta (x,y)}{\delta (u, v)} | = 10e^{-4u}$

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3 years ago

The composite figure shown has a surface area of 844 square centimeters.

kolezko [41]

Given the surface area of the composite figure, the height of the rectangular prism is approximately 8 centimeters.

<h3>What is the height of the rectangular prism?</h3>

First we calculate the surface area of the rectangular pyramid;

S.A = lw + (1/2)w√(4h²+l²) + (1/2)l√(4h²+w²)

Given that;

w = 10cm
l = 18cm
h = 12cm

S.A = lw + (1/2)w√(4h²+l²) + (1/2)l√(4h²+w²)

S.A = (18cm×10cm) + (1/2)10cm√(4(12cm)²+18cm²) + (1/2)18cm√(4(12cm)²+(10cm)²)

S.A = (180cm²) + 5cm√(576cm² + 324cm²) + 9cm√(576² + 100cm²)

S.A = (180cm²) + 5cm(30cm) + 9cm(26cm)

S.A = 180cm² + 150cm² + 234cm²

S.A = 564cm²

Now, surface Area of the rectangular prism will be;

= Area of composite figure - surface area of the rectangular pyramid

= 1844cm² - 564cm²

= 1280cm²

Now surface area of rectangular prism is expressed as;

SA = 2lw + 2lh + 2hw

w = 10cm
l = 18cm
h = x

SA=2lw + 2lh + 2hw

SA - 2lw = h( 2l + 2w)

h = (SA - 2lw) / ( 2l + 2w)

h = (1280cm² - ( 2×18cm×10cm)) / ( 2×18cm + 2×10cm)

h = (1280cm² - 360cm²) / ( 36cm + 20cm)

h = 1020cm² / 56cm

h = 8cm

Given the surface area of the composite figure, the height of the rectangular prism is approximately 8 centimeters.

Learn more about Prism and Pyramid here: brainly.com/question/9796090

#SPJ1

8 0

1 year ago