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3 years ago

Find the surface area of the triangular pyramid. The side lengths of the base are equal.

Mathematics

1 answer:

Sliva [168]3 years ago

3 0

Answer:

Step-by-step explanation:

We have

three triangles with the base b = 10cm and the height h₁ = 6cm

one triangle with the base b = 10cm and the height h₂ = 8.7cm.

The formula of an area of a triangle:

$A=\dfrac{b\cdot h}{2}$

b - base

h - height

Substitute:

$A_1=\dfrac{(10)(6)}{2}=\dfrac{60}{2}=30\ cm^2$

$A_2=\dfrac{(10)(8.7)}{2}=\dfrac{87}{2}=43.5\ cm^2$

$S.A.=3A_1+A_2\\\\S.A.=3(30)+43.5=90+43.5=133.5\ cm^2$

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Convert the complex number z = 4 - 10i from rectangular form to polar form.

mrs_skeptik [129]

ANSWER

$r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree))$

EXPLANATION

The polar form of a complex number ,

$z = x + yi$

is given by:

$z = r( \cos( \theta) + i \sin( \theta) )$

where

$r = \sqrt{ {x}^{2} + {y}^{2} }$

The given complex number is:

$z = 4 - 10i$

$r = \sqrt{ {4}^{2} + {( - 10)}^{2} }$

$r = \sqrt{16 + 100}$

$r = \sqrt{116} = 2 \sqrt{29}$

And

$\theta= \tan^{ - 1}(\frac{ y}{x} )$

$\theta= \tan^{ - 1}(\frac{ - 10}{4} )$

$\theta= 292 \degree$

Hence the polar form is :

$r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree))$

6 0

3 years ago

What is the mode for 2103 and 623m

lions [1.4K]

there is no mode

no number repeats

3 0

3 years ago

the sum of the perimeter of two squares is 40cm while the sum of the area is 58cm². Find length the side of the square.

tia_tia [17]

$a,\ b-the\ length\ of\ sides\\\\(1)\qquad4a+4b=40\qquad\text{divide both sides by 4}\\\\a+b=10\to a=10-b\\\\(2)\qquad a^2+b^2=58\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\(10-b)^2+b^2=58\qquad\text{Use}\ (x-y)^2=x^2-2xy+y^2\\\\10^2-2(10)(b)+b^2+b^2=58\\\\100-20b+2b^2=58\qquad\text{subtract 58 from both sides}\\\\42-20b+2b^2=0\\\\2b^2-20b+42=0\qquad\text{divide both sides by 2}\\\\b^2-10b+21=0\\\\b^2-7b-3b+21=0\\\\b(b-7)-3(b-7)=0\\\\(b-7)(b-3)=0\iff b-7=0\ \vee\ b-3=0\\\\\boxed{b=7\ \vee\ b=3}$

$\text{Put the values of b to }\ (1):\\\\for\ b=7\to a=10-7=3\\\\for\ b=3\to a=10-3=7\\\\Answer:\ \boxed{7cm\ and\ 3cm.}$

8 0

4 years ago

The point (-2,3) is the solution to a system of two linear equations. Which of the following can be one of the

Fynjy0 [20]

Answer:

We conclude that The point (-2, 3) satisfies the equation y = -x+1.

Hence, option B i.e. y = -x+1 is one of the equations of a system of two linear equations.

Step-by-step explanation:

Given

The point (-2, 3)

Checking option A

Given the equation

y = 3x-2

substitute x = -2 and y = 3

3 = 3(-2) - 2

3 = -6 - 2

3 = -8

FALSE!

L.H.S ≠ R.H.S

Thus,

The point (-2, 3) does not satisfy the equation y = 3x-2.

Checking option B

Given the equation

y = -x+1

substitute x = -2 and y = 3

3 = -(-2)+1

3 = 2+1

3 = 3

TRUE!

L.H.S = R.H.S

Thus,

The point (-2, 3) satisfies the equation y = -x+1.

Checking option C

Given the equation

y=x-1

substitute x = -2 and y = 3

3 = -2-1

3 = -3

FALSE!

L.H.S ≠ R.H.S

Thus,

The point (-2, 3) does not satisfy the equation y=x-1.

Checking option D

Given the equation

y=2x+3

substitute x = -2 and y = 3

3 = 2(-2)+3

3 = -4+3

3 = -1

FALSE!

L.H.S ≠ R.H.S

Thus,

The point (-2, 3) does not satisfy the equation y=2x+3.

Conclusion:

Thus, we conclude that The point (-2, 3) satisfies the equation y = -x+1.

Hence, option B i.e. y = -x+1 is one of the equations of a system of two linear equations.

4 0

3 years ago

The angles of a triangle are 2x , 3x ,and 4x degrees . find the value of x

BigorU [14]

Answer:

Step-by-step explanation:

2;3;4;x

2x 3x =6x

six is equal to the x an. four

4 0

4 years ago