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Dmitrij [34]
3 years ago
14

A hemispherical depression is cut out from one face of a cuboidal wooden block of edge 21cm such that the diameter of the hemisp

here is equal to the edge of the cube. Determine the total surface area of the remaining block
Mathematics
2 answers:
Mandarinka [93]3 years ago
4 0

Answer:

  (2646 +110.25π) cm² ≈ 2992.4 cm²

Step-by-step explanation:

The area of a sphere is 4 times the area of a circle with the same radius. Hence the area of a hemisphere will be 2 times the area of that circle. This means carving a hemispherical depression in the face of the cube will add an area that is equal to the area of the circular hole.

Of course the total surface area of a cube is 6 times the area of one square face. The area of a circle is ...

  A = πr² = π(d/2)² = (π/4)d²

The total surface area of the carved cube is ...

  S = 6·(21 cm)² + (π/4)·(21 cm)² = (441 cm²)(6 +π/4)

  S ≈ 2992.36 cm²

The total surface area of the remaining block is about 2992.4 cm².

joja [24]3 years ago
4 0

Answer:

(2646 +110.25π) cm² ≈ 2992.4 cm²

Step-by-step explanation:

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Which expression are equal to the value of 3 in the number 14,397
Irina-Kira [14]

Answer:

300

Step-by-step explanation:

This is a place value problem.

 The given figure is;

                14, 397:

Pronounced as;

Fourteen thousand, three hundred and ninety seven:

          14, 397;

                     10 000     ten thousand

                       4000      four thousand

                          300      three hundred

                            90       ninety

                              7         seven

The place value of 3 is hundreds.

6 0
3 years ago
Evaluate when a=15:2(a-5)+2
sasho [114]

Answer:

22

Step-by-step explanation:

if a=15

then, 2(a-5)+2= 2(15-5)+2 = 2(10)+2= 20+2=22

7 0
3 years ago
Difference between mafic intermediate and felsic magmas
Inga [223]

Both are indicators of the chemical composition of silicate minerals, magmas and rocks.

Mafic is used for silicate minerals, magmas and rocks that are composed of heavier elements, like magnesium, iron, calcium and sodium. They are dark and have high specific gravities.

<span>Opposite to the this, felsic silicate minerals, magmas and rocks in their composition have less from these heavy elements. They are composed from silicon, oxygen, aluminium and potassium, are light in color and have lower specific gravities.</span>

8 0
3 years ago
For a school fundraiser mai will make school spirit bracelets. She will order bead wiring and alphabet beads to create the schoo
Andreas93 [3]

Answer:

235 bracelets

Step-by-step explanation:

Mai must spend $250 on wire and $5.30 per bracelet beads. Mai creates the expression.

We are given the equation:

5.3n+ 250 to represent the cost of making n bracelets.

The maximum number of bracelets Mai can make with a budget of $1500 Is calculated as:

$1500 = 5.3n+ 250

Collect like terms

1500 - 250 = 5.3n

1250 = 5.3n

n = 1250/5.3

n = 235.8490566 bracelets.

Bracelets are created as whole numbers and they can't be in decimal form.

Therefore, the maximum number of bracelets Mai can make with a budget of $1500 is 235 bracelets.

6 0
2 years ago
1. Find the domain of the given function. (1 point)
Vika [28.1K]
1) Find the domain of the given function. f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.
 using a graphical tool    see the attachment  
the answer is C) x ≥ -3, x ≠ 2  
 2. Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 2 - (x - 7)2
 using a graphical tool     
see the attachment
 the answer is  C) Increasing: x < 7; decreasing: x > 7
3. Perform the requested operation or operations.
f(x) = 4x + 7, g(x) = 3x2
Find (f + g)(x).
 (f + g)(x) = f(x) + g(x) 
(f + g)(x) = 4x + 7 + 3x^2 
(f + g)(x) = 3x^2 + 4x + 7
 The answer is  C) 4x + 7 + 3x2
 4. Perform the requested operation or operations.
f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)).
 f(x)=(x-5)/8    g(x)=8x+5
g(f(x))=8((x-5)/8)+5=x-5+5=x
the answer is  B) g(f(x)) = x   
5. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five. 
 y=f(g(x))=9/((5x+5) ^1/2)
let do
g(x)=5x+5...........so
f(x)= 9/( x^1/2)
the answer is  A) f(x) = nine divided by square root of x. , g(x) = 5x + 5

6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?
Original size- >4km*4km=16 km2
4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km
Therefore
3km----------------------------- 1 sec
(8km-4km)---------------------x
X=4/3=1.33 sec
The answer is D) 1.33 sec

7. Find the inverse of the function.
f(x) = the cube root of quantity x divided by seven. - 9
to solve, replace f(x) with y , switch x and y, solve for y and replace y with f⁻¹(x)

f(x)=((x/7)-9) ^(1/3)
replace f(x) with y
y=((x/7)-9) ^(1/3)
switch x and y
x=((y/7)-9) ^(1/3)
solve for y
x^3=((y/7)-9)
x^3+9=y/7
y=7(x^3+9)
the answer is C) f-1(x) = 7(x3 + 9)  

8. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 – 9

using a graphical tool     see the attachment  the answer is C) Shift the graph of y = x2 right 14 units and then down 9 units  

9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. '

f(x)=(x-9) ^1/2  g(x)=(x+5) ^1/2 
using a graphical tool     see the attachment

the answer is C) Shift the graph of f left 14 units

10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = -16x5 - 7x4 – 6
The answer is B) Degree: 5; leading coefficient: -16

11. Write the quadratic function in vertex form.y = x2 + 4x + 7 

Complete the square on the right side of the equation
Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.
a=1,b=4,c=7
Consider the vertex form of a parabola.
a(x+d)2+e
Find the value of dd using the formula d=b/2a
d=4/(2*1)=2
Find the value of e using the formula e=c−b2/4a
e=7−4=3
Substitute the values of a, d, and e into the vertex form a(x+d)2+e
(x+2)2+3
The answer is A) y = (x + 2)2+ 3

12. Find the zeros of the function.
f(x) = 3x3 - 12x2 - 15x
using a graphical tool   (see the attachment)x1=-1
x2=0
x3=5
The answer is C) 0, -1, and 5

13. Find a cubic function with the given zeros.7, -3, 2
X1=7
X2=-3
X3=2
f(x)=(x-7)(x+3)(x-2)=(x2-4x-21)(x-2)=x3-6x2-13x+42
the answer is C) f(x) = x3 - 6x2 - 13x + 42  

14. Find the remainder when f(x) is divided by (x - k).f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3 
 f(x)=7(3)4+12(3)3+6(3)2-5(3)+16=946
  The answer is the B) 946

15.  Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24

The constant term of () is -24

 The leading coefficient is 1.

We have to only consider the factors of the constant (leading coefficient = 1)

The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24

The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

6 0
3 years ago
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