If f(x) = 2x - 1, find f'(x).
Answer:
f'(x)=2
Step-by-step explanation:
[tex]if~y=ax^n\\where~a~is~constant.\\\frac{dy}{dx} =a nx^{n-1}\\f(x)=2x-1\\f'(x)=2*1x^{1-1}-0\\=2x^0\\=2*1\\=2[/tex]
If 45 crackers will serve 15 students, how many crackers are needed for 30 students? Please help I'm not smart enough to solve this-
A silo consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal. The diameter of the cylindrical base of the silo is 12 ft and the height of the cylinder is 10 ft, while the height of the cone is 8 ft. Calculate the surface area of the silo. Leave your answer in terms of π.
480π sq. ft.
276π sq. ft.
216π sq. ft.
204π sq. ft.
Answer:
216π sq ft
Step-by-step explanation:
given that :
d = 12 ft => r = 12/2 = 6ft
h(cyl) = 10 ft
h(cone) = 8 ft
the surface area = ?
the solution :
the slant of cone = √r²+h²
= √6²+8²= √100 = 10 ft
the surface area of silo =
the lateral area of cone + the lateral area of cylinder + the base area
= π×r×slant + 2×π×r×h(cyl) + π×r²
= π×6×10 + 2×π×6×10 + π×6²
= 60π + 120π + 36π
= 216π sq ft
The surface area of the silo will be 216π square feet. Then the correct option is C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A silo consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal.
The surface area is the sum of the surface area of the cone and cylinder. Then we have
The diameter of the cylindrical base of the silo is 12 ft and the height of the cylinder is 10 ft, while the height of the cone is 8 ft.
Surface area = πrl + 2πrh + πr²
The length of the radius will be
r = d /2
r = 12 / 2
r = 6 ft
The length of slant height will be
l² = 6² + 8²
l² = 100
l = 10 ft
Then the surface area of the silo will be
SA = π × 6 × 10 + 2π × 6 × 10 + π6²
SA = 60π + 120π + 36π
SA = 216π square feet
The surface area of the silo will be 216π square feet.
Then the correct option is C.
More about the geometry link is given below.
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A rectangle with an area of 81 cm² has a length that is 3 times the width. How long is the width of the rectangle? Round to the nearest tenth.
Answer:
W ≈ 5.2 cm
Step-by-step explanation:
Represent the length and width by L and W respectively.
Then L * W = 81 cm^2, and L = 3W.
Substituting 3W for L in the first equation, we get:
3W * W - 81 = 0, or 3W^2 - 81 = 0.
To make it easier to find the final answer, rewrite 3W^2 - 81 = 0 as
81
W^2 = ------- = 27
3
Then W (the width) is the positive square root of 27, or W ≈ 5.2 cm
Answer:
60.75 ≈ 60.8
Step-by-step explanation:
4u-> 81
1u -> 20.25 (width)
3u-> 60.75 (length)
URGENT!!!!!!
500 sheets of paper is 6.5 cm thick. How thick is a pile of 350 sheets of the same paper?
Answer:
4.55
Step-by-step explanation:
step 1. 6.5 / 500 = .013
step 2. .013 X 350 = 4.55
Hope this helps
What is the slope of the line
Answer:
slope = -3/4
Step-by-step explanation:
y(1)-y(2)/x(1)-x(2)
Plug in coordinates (0,4) and (4,1)
1-4/4-0
-3/4 is the slope
what is the value of 64 2/3?
Answer:
[tex] \frac{194}{3} [/tex]
Step-by-step explanation:
[tex]64 \frac{2}{3} [/tex]
[tex]64 + \frac{2}{3} [/tex]
[tex]64 \times \frac{3}{3} + \frac{2}{3} [/tex]
[tex] \frac{64 \times 3}{3} + \frac{2}{3} [/tex]
[tex] \frac{64 \times 3 + 2}{3} [/tex]
[tex] \frac{192 + 2}{3} [/tex]
[tex] \frac{194}{3} [/tex]
Hope it is helpful...Pls help I need this RN
Answer:
3.2 , Edgar , Liam
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
Help plz
1) __ × 4 = -20
2) __-7 = - 2
3) __ × - 5= 20
4) __- 9 = - 2
5) __+ 17 = 20
Answer:
1) -5
2) 5
3) -4
4) 7
5) 3
Step-by-step explanation:
1) -20 divided by -4
2) -2 plus 7
3) 20 divided by 5
4) -2 plus 9
5) 20 minus 17
Which expression is equivalent to (3x2 – 2x + 6 ) + ( 3x - 4)?
Answer:
3×2-2x + 6 + 3x - 4
-2x +3x + 3 × 2 +6-4
x + 8can anyone help me solve ...
Answer:
a) x= 34°
b) x = 51°
Step-by-step explanation:
Points to keep in mind when solving triangle problems.
An isosceles triangle has two equal sides and the angles opposite to those sides are also equal angles.
A triangle with all sides equal is called an equilateral triangle, which is also called equiangular triangle.
HELP PLSSSSSSSZzzzzzzzzzzzz
Answer:
w equal to 9z
or z equals to w/9
A scatter plot with a line is shown below.
Which statement is most likely correct about the line.
A hiker is descending 152m every 8 minutes what will be hikers change in elevation in half an hour? what as an integers
Answer:
570 meters
Step-by-step explanation:
[tex]\frac{8}{152} :\frac{30}{y}[/tex]
y × 8 = 152 × 30
8y = 4560
8y ÷ 8 = 4560 ÷ 8
y = 570
can the angles with measures 80o , 55o and 65o form angles on a line
Answer:
Nope, this is because the angles in a triangle add up to 180, whereas these values added are equal to 200 degrees
No, the angles with measures 80°, 55°, and 65° cannot form angles on a line.
In geometry, angles on a line are also known as "linear angles" or "straight angles." A straight angle measures 180°, and it is formed by two rays that point in opposite directions and share a common endpoint, creating a straight line. To determine if the given angles can form a straight angle, we need to add their measures.
Let's calculate the sum of the given angles:
Sum = 80° + 55° + 65°
= 200°
Since the sum of the given angles (200°) is not equal to 180°, it means that the angles cannot form a straight line. Instead, they form a shape that is not a straight angle, such as a triangle or a polygon.
In this case, the given angles form a triangle since they satisfy the triangle inequality theorem. The sum of any two sides of a triangle is always greater than the third side. Mathematically, for a triangle with sides of lengths a, b, and c, the inequality holds: a + b > c, b + c > a, and c + a > b.
Therefore, the angles with measures 80°, 55°, and 65° cannot form angles on a line but rather form a triangle with a sum of 180°, satisfying the triangle inequality.
To know more about Linear Angles here
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Solve the equation. Then check your solution. StartFraction x Over 90 EndFraction = StartFraction 7 Over 9 EndFraction
Answer:
Step-by-step explanation:
x = 7
Symbolically, this equation is:
x 7
----- = -----
90 9
Cross multiplying yields 9x = 9(7), and so x must be 7.
Answer:
its b!!
Step-by-step explanation:
Pythagoras
1.if the radius of the smaller circle is 3, find it’s area
2. Find the area of the yellow ring
3. Find the area of the white ring
Answer:
1. [tex]Area = 28.26[/tex]
2 and 3: See explanation
Step-by-step explanation:
Solving (1)
[tex]r = 3[/tex] --- radius
The area is:
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14* 3^2[/tex]
[tex]Area = 28.26[/tex]
There are no enough information to solve (2) and (3) as the radius and/or diameter are not provided.
However, the following formula will be used to calculate the required areas.
[tex]Area = \pi r^2[/tex] --- same process as (1)
8. The pyramid shown below has a square base and a vertex that lies
directly above the center of the square. Which of the following most
closely describes horizontal cross sections of this solid?
Answer:
They are all squares similar to the base.
Step-by-step explanation:
They are not congruent to the base but are similar.
if you are at (0,0) on a coordinate grid, what direction do you go to plot point (-2,6)
Answer:
go left 2 and up 6
Step-by-step explanation:
(x,y)
(x,y) --> (-2,6)
0 = x 0 = y
0 - 2 = -2 = x
0 + 6 = 6 = y
(-2,6)
When making the X negative, you want to go left on the grid. When making Y positive, you want to go up on the grid.
Answer: you would go to the left side horizontally (aka quadrant 3), then go down until 6 vertically
Step-by-step explanation: if you don't get it, here's a visual explanation
Which of the following does not represent a function?
Write the general polynomial p(x) if its only zeros are 1,4, and -3, with multiplicities 3,2, and 1, respectively. What is its degree? Find p(x) precisely if p(0)=16.
Answer:
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- General polynomial
The degree is 6
[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- The polynomial precisely
Step-by-step explanation:
Given
[tex](a,b,c)= (1,4,-3)[/tex] --- zeros
[tex](m_1,m_2,m_3) =(3,2,1)[/tex] --- multiplicities
Solving (a): The polynomial
The polynomial is represented as:
[tex]p(x) = (x -a)^{m_1} * (x -b)^{m_2} * (x -c)^{m_3}[/tex]
So, we have:
[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)^{1}[/tex]
[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
Include constant k; So, the polynomial becomes
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
Solving (b): The degree (d)
To do this, add up the multiplicities
[tex]d = m_1 +m_2 +m_3[/tex]
[tex]d = 3+2+1[/tex]
[tex]d = 6[/tex]
The degree is 6
Solving (c): The actual polynomial
In (a), we have:
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
[tex]p(0)=16[/tex] means:
[tex](x,p(x)) = (0,16)[/tex]
This gives:
[tex]16 = k(0 -1)^{3} * (0 -4)^{2} * (0 +3)[/tex]
[tex]16 = k(-1)^{3} * (-4)^{2} * (3)[/tex]
[tex]16 = k*-48[/tex]
Solve for k
[tex]k = \frac{16}{-48}[/tex]
[tex]k = -\frac{1}{3}[/tex]
So:
[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]
PLEASE HELP ASAP, giving brainlist t anyone who answers <3
50 points. I am stuck on this question, Please help!
Line AB is the diameter of circle E. The measure of < CBD = 63 degrees and the measure of Arc CA is 36 degrees. Find angles ADB, angles ABD, angles BAD and arc BD.
Thank you
Step-by-step explanation:
arc CAD = 2×63= 126°
< ADB = ½×180 = 90°
arc AD = 126-36 = 90°
< ABD = ½×90° = 45°
< BAD = 180-90-45 = 45°
arc BD = 2×45 = 90°
Q. If 5 (3x-1) =40, then x = *
a-3
b-9
Answer: 3
Step-by-step explanation:
Distribute the 5: 15x-5=40
Add 5 from both sides: 15x=45
Divide 15 by both sides: 3
Answer:
a-3
Step-by-step explanation:
5(3x-1)=40
15x-5=40
15x=40+5
15x=45
x=45/15
x=3
if sin A-cos B then A+B=
Answer:
sinA=sin(90-B)
sinA=90_B
now,A+B
=90
6. A tank can hold 50 litres of water. At present, it is only 30% full. How many litres of water shall I put in the tank so that it is 50% full?
Answer:
10 litres
Step-by-step explanation:
50 litres - 100%
x litres - 30%
x=(50*30)/100=15 litres - that's 30% of the tank (this amount of water is already added)
50 litres - 100%
x litres - 50%
x=(50*50)/100=25 litres - that's 50% of the tank (this amount of water will be in the tank)
To find what amount of water should be added we must subtract the amount of water that is already added from the amount of water that will be in the tank.
25 - 15=10 litres should be added
A computer store bought a program at a cost of $40 and sold it at a selling price of $32.5. Find the percent markdown (Rounded to a whole number) .
Answer:
The percentage markdown is approximately 19%
Step-by-step explanation:
The cost at which the computer store bought the program = $40
The selling price at which the store sold the program = $32.5
The percentage markdown is given as follows;
Let CP represent the cost at which the computer store bought the program, and let SP represent the selling price of the program, we can find the percentage markdown as follows;
[tex]Percentage \ markdown = \dfrac{CP- SP}{CP } \times 100[/tex]
CP = $40, SP = 32.5
Therefore, we get;
[tex]Percentage \ markdown = \dfrac{40- 32.5}{40} \times 100 = 18.75\% \approx 19\%[/tex]
The percentage markdown ≈ 19%.
CAN SOMEONE PLEASE HELP ME??!!
Answer:
RO = 17.9
Step-by-step explanation:
If they're similar, the fraction between their sides need to be equal, so do this:
NK/NM = RO/RQ
71.6/64 = RO/16
71.6•16/64 = RO
RO = 17.9
Express 4x + 3y - 8 = 0 in slope and y-intercept form.
Step-by-step explanation:
Given equation :-
4x + 3y - 8 = 0Slope intercept form :-
y = mx + c→ 4x + 3y - 8 = 0
→ 3y = -4x + 8
→ y = (-4x + 8)/3
→ y = -4/3x + 8/3
Answer:
y = -4/3x + 8/3.
Step-by-step explanation:
4x + 3y - 8 = 0
3y - 8 = -4x
3y = -4x + 8
Divide through by 3:
y = -4/3x + 8/3.
Write the expression in complete factored form.
p(y+ 9) + u(y + 9) =
Answer:
(p+u)(y+9)
Step-by-step explanation:
p(y+9)+u(y+9)
Multiply them out
py+uy+9p+9u
y(p+u)+9(p+u)
=(p+u)(y+9)