Answer:
2-and-a-half pounds
10 / 4 = 2.5
Find the derivative of In( x + a) by using first principle.
Answer:
slide for von
Step-by-step explanation:
Prove: (sin α + cos β)^2 + (cos β + sin α)(cos β − sin α) = 2 cos β(sin α + cos β)
The two terms on the left side both have a common factor of (sin(α) + cos(β)), so we can pull it out like so:
(sin(α) + cos(β))² + (cos(β) + sin(α)) (cos(β) - sin(α))
= (sin(α) + cos(β)) [(sin(α) + cos(β)) + (cos(β) - sin(α))]
= (sin(α) + cos(β)) (sin(α) + cos(β) + cos(β) - sin(α))
= 2 cos(β) (sin(α) + cos(β))
Use the coordinate grid below to draw a square the has one vertex in each quadrant, and has an area of 16 square units. Prove that your figure has the correct area using distance and area calculations.
PLEASE HELP AND NO LINKS!
The area of the cube using the distance formula is 16 square units and each side measure is 4 units.
What is a cube?It is defined as three-dimensional geometry that has six square faces and eight vertices.
We have a cube shown in the picture.
Area of the cube = 16 square units
Area of cube = side²
Side = √16 = 4 units
Each side of the cube = 4 units.
From the attached figure, we can see each side lies on each quadrant.
Using the distance formula, we can calculate the distance between two
points:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The area of the cube = 4×4 = 16 square units
Thus, the area of the cube using the distance formula is 16 square units and each side measure is 4 units.
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PLEASE HELP!!!!! IMA DESPRATE!!!!!! ach side of a telescope lens can be described by the equation f(x) = x2/58, where x is the width of the lens and f(x) is half its thickness.
If the lens is 2.9 inches wide, what is the total thickness (rounded to the nearest hundredth)?
Since the lens is 2.9 inches wide, the total thickness of the lens is 0.29 in
To answer the question, we need to know what equations are.
What are equations?Equations are mathematical expressions which show the relationship between two variables.
The total thickness of the lensSince f(x) = x²/58 describes half the thickness of the lens where x = width of lens.
So, the total thickness of the lens is y = 2f(x)
= 2 × x²/58
= x²/29
Since x = 2.9 in, substituting x into the equation, y, we have
y = x²/29
y = (2.9)²/2
y = 8.41/29
y 0.29 in
So, the total thickness of the lens is 0.29 in
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What is the ratio for the volumes of two similar spheres, given that the ratio of their radii is 5:6?
Answer:
125 : 216
Step-by-step explanation:
Let the volumes of the spheres be V₁ and V₂ respectively.
Volume (Sphere radius = 5) :
V₁ = 4/3π(5)³V₁ = 4/3π x 125V₁ = 500/3πVolume (Sphere radius = 6) :
V₂ = 4/3π(6)³V₂ = 4/3π x 216V₂ = 864/3πTaking the ratio of V₁ and V₂ :
V₁/V₂500/3π x 3π/864500/864125 : 216Given ratio: [tex](\text{Radius of Sphere}_1 : \text{Radius of Sphere}_2) = (5 :6)[/tex]
Step-1) Multiply both sides of the ratio by x:
[tex]\implies (\text{Radius of Sphere}_1 : \text{Radius of Sphere}_2) = (5x :6x)[/tex]
[tex]\implies \text{Radius of Sphere}_1 = 5x;\ \text{Radius of Sphere}_2 = 6x[/tex]
Step-2) Substitute the radiuses of each sphere into the "Volume formula"
Volume of sphere₁ Volume of sphere₂
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi r^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi r^{3}[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (5x)^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (6x)^{3}[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (5x)(5x)(5x) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (6x)(6x)(6x)[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (125x^{3} ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4 \pi (2x)(6x)(6x)[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{500x^{3} }{3} \pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 288x^{3} \pi[/tex]
Step-3) Plug the volume of both spheres in ratio form:
The ratio for the volumes of the two spheres must be in the respective place of the ratio for the radiuses of the two similar spheres. Therefore,
Ratio form: [tex]\underline{(\small\text{Volume of sphere}_1 : \text{Volume of sphere}_2)}[/tex]
[tex]\implies \dfrac{500x^{3} }{3} \pi: 288x^{3} \pi[/tex]
Step-4) Simplify both sides of the ratio:
[tex]\implies \dfrac{500x^{3} }{3}: 288x^{3}[/tex]
[tex]\implies \dfrac{500 }{3}: 288[/tex]
[tex]\implies \dfrac{500 }{3}} \div{\dfrac{288}{1} } \implies \dfrac{500}{3} \times \dfrac{1}{288} \implies \dfrac{500}{864} \implies \boxed{\dfrac{125}{216}}[/tex]
Therefore, the ratio for the volumes of two similar spheres is 125 : 216.
Which data set is more likely to produce a histogram with a symmetric distribution? Explain your reasoning.
Data on the number of seconds on a track of music in a pop album.
Data on the number of seconds spent talking on the phone yesterday by everyone in the school.
The data set that is more likely to produce a histogram with a symmetric distribution is data on the number of seconds on a track of music in a pop album.
Which data set would produce a a histogram with a symmetric distribution?Data on a histogram have a symmetric distribution if the left side and the right side of the histogram are mirror images of each other.
It is likely that the number of seconds on a track of music in a pop album would be relatively uniform. Thus, it is likely to have a symmetric distribution. The number of seconds spent talking on the phone varies greatly.
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P(q) = 1/4
P(R) = 2/3
If Q and Rare independent events, find the P(Q and R).
Answer:
P(Q ∩ R) = 1/6
Step-by-step explanation:
Given:
P(Q) = 1/4P(R) = 2/3For independent events Q and R,
P(Q ∩ R) = P(Q)P(R)
Therefore,
P(Q ∩ R) = (1/4)(2/3)
= 2/12
= 1/6
What is the volume, in cubic feet, of a cylinder with a height of 20 feet and a base radius of 4 feet, to the nearest tenths place?
Answer:
about 1,005.3 cubic feet
Step-by-step explanation:
V = π(4^2)(20) = π(16)(20) = 320π = 1,005.3 cubic feet
Diego was trying to write (5^2)^4 with a single exponent and wrote (5^2)^4=5^2+^4=5^6. What should the answer be? Explain Diego's error in complete sentences and thoughts.
Answer:
5^8
Step-by-step explanation:
Diego added the exponents. This was an error. If he was simplifying
5^2 × 5^4, then he could add the exponents and get a correct answer. But his problem had a power raised to a power. In this case, you multiply the exponents to simplify.
(5^2)^4 means
5^2×5^2×5^2×5^2
which is
5×5×5×5×5×5×5×5
which is 5^8.
keith has a debt of $145.50 at the beginning of the summer. he wants to have at least 200 in the account at the end on the summer if he plans to save 75.50 each week what is the minimum number of weeks he’ll have to work in order to meet his goal?
Total amount he needs to save = 200 + 145.50 = 345.50
Number of weeks = total needed / weekly savings
345.50 / 75.50 = 4.57
He will need to work 5 weeks.
Students graphed the growth rate over several weeks of two plants in their classroom. The equations of both plants are given where x represents the time in weeks and y represents the heights of the plants in inches.
Plant A: y = 1.8x + 3.1
Plant B: y = 2.3x + 1.9
Approximately how many weeks will it take for both plants to reach the same height? Round your answer to the nearest tenth.
What is the solution to the system of linear equations? Round to the nearest tenth as needed.
(
,
)
Answer:
A i think
Step-by-step explanation:
[50 POINTS] What is the volume of the cylindrical stack of pennies?
Radius of base=19.05/2=9.525
Volume
πr²hπ(9.525)²(38)3447.57π10825.3698 mm³Look at circle B below. The circumference of the circle is approximately 157 units. Which best represents the area of circle B?
Answer:
area of circle B=1964 square unit
Wite a differential equation in which y^2= 4(t + 1) is a solution.
Can someone help me please?
Answer:
128 Layers
Step-by-step explanation:
1*2*2*2*2*2*2*2 = 128
What is the area of a circle with a radius of 35 inches?
in²
(Use 3.14 for Pi.)
Answer:
[tex] \boxed{ \tt{Area \: \: of \: a \: circle = \pi \: {r}^{2} }}[/tex]
Plug the values and then solve :[tex] \longrightarrow \tt \: 3.14 \times 35^{2} [/tex]
[tex] \longrightarrow \tt \: 3846.5\: in ^{2} [/tex]
Our final answer is 3846.5 in ^2--------- HappY LearninG <3 --------
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
What is the area of a circle with a radius of 35 inches?
[tex]\rule{50}{1}\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
We're asked to find the area of a circle, which we can find using the following formula:-
[tex]\Large\textsf{$A=\pi r^2$}[/tex]
Where:-
A=area[tex]\pi[/tex] = pi [3.14...]r = radius (we're given that it's equal to 35 inches)Replace r with 35 and π with 3.14:-
[tex]\Large\text{$A=3.14\times35^2$}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\Large\text{$A=3.14\times1,225$}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\Large\text{$A=3846,5 in^2$}[/tex]
Good luck with your studies! :-)[tex]\rule{50}{1}\smile\smile\smile\smile\smile\rule{50}{1}[/tex]
What is the general form of the equation of the line shown?
Y-2=0
y+2=0
X-2 = 0
Answer:Option A is correct.
y-2=0
Step-by-step explanation:
Option A is correct.
General form of the equation of the line: y-2 = 0
Step-by-step explanation:
The general form of the equation is given by:
y = mx +b where m is the slope and b is the y-intercept.
y-intercepts of the line is the value of y at the point where the line crosses the y-axis(i.e x= 0)
From the given figure;
we can see that the line crosses the y-axis at y =2 and also here the slope is , m= 0
therefore, by definition of y-intercepts
y-intercept (b) = 2
Therefore, the equation of line as shoen in figure is:
y = (0)x + 2
or
y = 2
y-2 = 0
Therefore, the general form of the equation line as shown in the figure is:
y-2 =0
Hello Please Find The Answer To This Question (easy)
The equation of the line that is perpendicular to y = -5/2 x + 1 and passing through (10, 3) will be y = 2/5 x + 1.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the perpendicular line will be given as
y = mx + c
The given equation is y = -5/2 x + 1.
The slope of the line is -5/2.
Then the product of the slope of the perpendicular lines is a negative one.
-5/2 × m = - 1
m = 2/5
Then the equation will be
y = 2/5 x + c
Then the equation is passing through (10, 3). Then we have
3 = 2/5 × 10 + c
3 = 2 + c
c = 1
Then the equation is y = 2/5 x + 1.
More about the linear system link is given below.
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PLEASEEEEE HURRRYYYY
Based on the given inequality statement, which statement correctly describes where the values are located on a number line relative
to each other?
-5 < 2
O -5 is located to the right of 2.
O 2 is located to the left of -5.
• -5 is located to the left of 2.
O 2 is located at the same position as -5.
Hi!~
Answer:
C) -5 is located to the LEFT of 2
Step-by-step explanation:
On a number line, of course the negatives (-) are to the left while the positives (+) are to the right, so since -5 is negative, and 2 is positive, -5 is located to the LEFT of 2.
Hope this helps! :)
Lucy spent $165 in December using a new credit card. In January, she began paying between $15 and $25 each month towards her account balance. The equation f(x) = 165(0.8)x describes the curve of best fit for Lucy's account balance f(x). Let x represent the number of months since December.
Month Account Balance
December $165.00
January $132.00
February $105.60
March $84.48
Using the equation for the curve of best fit, what will Lucy's account balance be in June? Round to the nearest cent.
A.
$28.25
B.
$53.95
C.
$43.25
D.
$33.25
Answer: 43 c
Step-by-step explanation: adding and multiplecation
Which of the following is the best example of a definition?
All right angles are congruent.
All right triangles have two congruent angles.
The base angles of an isosceles triangle are congruent.
An isosceles triangle is a triangle with two congruent sides.
Answer:
all right angels are congruent
Step-by-step explanation:
Hello, this is the question:
Look at the table below.
X y
1 5
2 7
3 9
4 11
5 13
Which equation represents the relationship of x to y?
A y = 3x + 1
B y = 2x + 3
C y = 3x
D Y =3x-1
Answer:
y = 2x + 3
Step-by-step explanation:
x = 1 , y = 2(1) + 3 = 5
x = 2, y = 2(2) + 3 = 7
x = 3, y = 2(3) + 3 = 9
x = 4, y = 2(4) + 3 = 11
x = 5, y = 2(5) + 3 = 13.
A number between 1 and O is multiplied by 1,000.
The answer has to be:
Answer:
1,000
Step-by-step explanation:
uhhhh haha
Use the given information to determine which lines if any are parallel state The postulate or theorem that justifies
Answer: 13 and 14
Step-by-step explanation: algbra
List all of the factors of the number 30
50 points! answer ASAP!! Which of the following is the graph of y = negative (x minus 2) cubed minus 5?
On a coordinate plane, a cubic root function approaches the negative y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then increases and approaches x = 4. On a coordinate plane, a cubic root function approaches x = negative 5 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then approaches the y-axis in quadrant 3. On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4. On a coordinate plane, a cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then decreases and approaches the negative y-axis in quadrant 3.
Answer: The second image you attached (I also attached the picture of the right answer)
Step-by-step explanation:
In this equation A is negative so you know it is going downward.
the shift is down 5 units and to the right 2.
You can see this shift in the graph I attached
it is also 1 to 1
Answer:
b
Step-by-step explanation:
What is 2+2? Does 2+2 have anything to do with the number 21? Do the Mayans and the Sons have a answer?
Answer:
i dont know what this means
Step-by-step explanation:
please explain in a further and better format to underline the question son.
3/4 divied be 8/14. please give me answer
Answer:
1 5/16
Step-by-step explanation:
3/4 / 8/14 is the same as
3/4 * 14/8 = 42 /32 1 5/16
A fair coin is flipped two times. Which diagram shows all of the possible outcomes?
Answer:
A
Step-by-step explanation:
It is the only one that has both heads and tails equally on all options, instead of heads heads or tails tails. There aren't any fair coins that are like that
hope this helps :)
Giving brainliest please help
Answer:
[tex](x, \: y) --->\: (x - 3, \: \: y - 5)[/tex]
