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anzhelika [568]

4 years ago

8

A solid oblique pyramid has a square base with an edge length of 2 cm. Angle BAC measures 45°.What is the volume of the pyramid?

2.4 cm33.6 cm34.8 cm37.2 cm3

2 answers:

nirvana33 [79]4 years ago

7 0

Answer:

It's 4.8 cm ^3

Step-by-step explanation:

I took the test and got 100% right

Aloiza [94]4 years ago

3 0

I think it's 4.8 .... I'm not 100% sure though

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A graphing calculator is recommended. A function is given. g(x) = x4 − 5x3 − 14x2 (a) Find all the local maximum and minimum val

Taya2010 [7]

Answer:

The local maximum and minimum values are:

Local maximum

$g(0) = 0$

Local minima

$g(5.118) = -350.90$

$g(-1.368) = -9.90$

Step-by-step explanation:

Let be $g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}$ . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:

$g(x) = x^{2}\cdot (x^{2}-5\cdot x -14)$

Then, first and second derivatives of the function are, respectively:

First derivative

$g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)$

$g'(x) = 2\cdot x^{3}-10\cdot x^{2}-28\cdot x +2\cdot x^{3}-5\cdot x^{2}$

$g'(x) = 4\cdot x^{3}-15\cdot x^{2}-28\cdot x$

$g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)$

Second derivative

$g''(x) = 12\cdot x^{2}-30\cdot x -28$

Now, let equalize the first derivative to solve and solve the resulting equation:

$x\cdot (4\cdot x^{2}-15\cdot x -28) = 0$

The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:

$x\cdot (x-5.118)\cdot (x+1.368) = 0$

The critical points are 0, 5.118 and -1.368.

Each critical point is evaluated at the second derivative expression:

x = 0

$g''(0) = 12\cdot (0)^{2}-30\cdot (0) -28$

$g''(0) = -28$

This value leads to a local maximum.

x = 5.118

$g''(5.118) = 12\cdot (5.118)^{2}-30\cdot (5.118) -28$

$g''(5.118) = 132.787$

This value leads to a local minimum.

x = -1.368

$g''(-1.368) = 12\cdot (-1.368)^{2}-30\cdot (-1.368) -28$

$g''(-1.368) = 35.497$

This value leads to a local minimum.

Therefore, the local maximum and minimum values are:

Local maximum

$g(0) = (0)^{4}-5\cdot (0)^{3}-14\cdot (0)^{2}$

$g(0) = 0$

Local minima

$g(5.118) = (5.118)^{4}-5\cdot (5.118)^{3}-14\cdot (5.118)^{2}$

$g(5.118) = -350.90$

$g(-1.368) = (-1.368)^{4}-5\cdot (-1.368)^{3}-14\cdot (-1.368)^{2}$

$g(-1.368) = -9.90$

7 0

4 years ago

A small airplane can carry less than 1,050 pounds of luggage and mail. The mail for the day weighs 490 pounds. If each passenger

Soloha48 [4]

70x + 490=1050
-490 -490\
70x= 560

divide both sides by 70

x = 8

8 passengers

3 0

3 years ago

Can you help meSolve for X pretty please 4+x=7

oksano4ka [1.4K]

Answer:

use a calculator / solve for x calculator

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What does an equal sign mean mathematically?

DIA [1.3K]

Answer:

It means that the both sides of the expression in the given equation must be/are congruent.

Hope this helps!

3 0

3 years ago

The 7th grade has 159 students. There are twice as many boys in the grade as there are girls.

aleksklad [387]

Answer:

106 boys

Step-by-step explanation:

7th grade = 159 students

Boys to girls ratio:

2:1

Find two thirds of 159:

2/3*159 = 106 boys

159-106= 53 girls

Check:

53*2 = 106

3 0

3 years ago

Read 2 more answers