a) the maximum error in surface area and the relative error is 25.4 cm² and 1.25%
b) the maximum error in the volume and the the relative error is 162.1 cm³ and 1.875%
As we know the formula for surface area is
Surface Area , S= 4*π*r^2.
So differentiating both sides we get
dS/dr = 8*π*r .....1
and the formula for the circumference is :2*π*r
, so the error on the circumference will be respect to radius
=> Δc = 2*π*Δr
=> Δr = ΔC / (2*π)
substituing the value ofΔr in the equation 1, we get
The maximum error in surface area which is :
ΔS = 8*π*r*Δr = 4*r*Δc
= (2/π)*c*Δc.
= 25.4
where for the relative error
ΔS/S = 4*r*Δc/(4*π*r^2)
= Δc/(π*r)
= 2*Δc/c
= 1.25%
Now Since the formula for the volume of a sphere is :
V = 4/3*π*r^3
dofferentiating both sides we get ,
=> dV/dr = 4*π*r^2.
So, the the maximum error in the calculated volume will be :
ΔV = 4*π*r^2*Δr
= 2*r^2*Δc
= 1/(2*π^2)*c^2*Δc
=162.1
Where as the relative error for the volume will be
ΔV/V = 3*Δr / r = 3*ΔC/C = 1.875%
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Consider the density curve plotted below:1.63.24.86.480.050.10.150.20.25XPDF(X)Density CurveFind P(X<1.6) : Find P(X>4.8) :
Given:
There is a density curve given in the question
Required:
We need to find for
[tex]\begin{gathered} P(X<1.6) \\ P(X>4.8) \end{gathered}[/tex]Explanation:
Part a
We want to find P(X<1.6)
For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:
[tex]P(X<1.6)=\frac{1}{2}*1.6*0.05=0.04[/tex]Part b
For this case we want to find this probability:
P(X>4.8)
and we can complement rule and we got
[tex]P(X>4.8)=1-P(X<4.8)=1-\frac{1}{2}*4.8*0.15=0.64[/tex]Final answer:
0.04
0.64
a standard poker deck of cards contains 52 cards, of which four are kings. suppose two cards are drawn sequentially, so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. find the probability that the first card is a king and the second card is not a king. (round your answer to four decimal places.)
The probability that the first card is a king and the second card is not a king is 0.0045
Suppose two cards are drawn sequentially so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. To find the probability that the first card is a king and the second card is not a king.
In the first case let's find the probability of drawing a king from the deck of cards,
A = ( 4/52 )
In the second case the probability of drawing a card that is not a king from the deck is,
B = ( 3/51 )
At last, to get the final probability to draw that the first card is a king and the second card is not a king we need to multiply the above two cases as,
A x B = ( 4/52 ) ( 3/51 )
= 1/221
= 0.0045
The probability that the first card is a king and the second card is not a king is 0.0045
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Find the area of 2x-9 + x+5
Answer: 3x-4
Step-by-step explanation: First Simplify, add the numbers 2x-9+x+5=2x-4+x Then combine like terms, 2x-4+x= 3x-4
Find all possible values of the expression 1/a
1/2
__<1/a<__
The possible values of the expression 1/a = 1/2 is 2
The expression is the simple fraction form = 1/a
The expression is the defined as the a sentence with a minimum of two variables and at least one math operation.
The simple fraction is fraction that contains the numerator and denominator as whole number. The term one the top of the simple fraction called as the numerator and bottom term is called as the denominator.
Here it is given that
1/a = 1/2
Therefore the value of a = 2
Hence, the possible values of the expression 1/a = 1/2 is 2
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10. Evaluate (14-2)÷3(2-3) - 2²Mark only one oval.A. OB. 2C. 20D. 22
Order of the operations: parentheses, exponentials, division and multiplication, addition and subtraction.
1. Solve operations in parentheses:
[tex]=12\div3\cdot6-2^2[/tex]2. Solve exponentials:
[tex]=12\div3\cdot6-4[/tex]3. Solve division:
[tex]=4\cdot6-4[/tex]4. Solve multiplication:
[tex]=24-4[/tex]5. Solve subtraction:
[tex]=20[/tex]Then, the solution for the given expression is 20Answer: Answer is 20( please make me brainliest i just did this all in my head)
Step-by-step explanation: soo (14-2) =12 12divided by 3=4 so (2*3)= 6 so 4x6=24 24-2*2 =20 (2*2)=4 so 24-4=20 well this is confusing but i tried my best so hope my answer wasn't toooo confusing lol :)
For each set of points below, determine the distance between them using the distance formula. each answer in this problem will be an integer
Distance between two coordinates:
[tex]\text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given point: b) (10, -5) and ( -6, 7)
[tex]x_1=10,y_1=-5,x_2=-6,y_2=7[/tex]Substitute the value in the expression of distance formula
[tex]\begin{gathered} \text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Distance}=\sqrt[]{(-6-10)^2+(7-(-5))^2} \\ \text{Distance}=\sqrt[]{(-16)^2+(12)^2} \\ \text{Distance}=\sqrt[]{256+144} \\ \text{Distance}=\sqrt[]{400} \\ \text{Distance = 20 unit} \end{gathered}[/tex]The distance between coordinates (10,-5) & (-6,7) is 20 unit
State if there appears to be a positive correlation, negative correlation, or no correlation. When there is a correlation, identify the relationship as linear or nonlinear.
Answer:
Negative Correlation:
Linear relationship
Explanation:
We can draw the line of best fit through the points given, and this indicates that the relationship is linear. Furthermore, the line of best fit has a negative slope (which tells us that if one variable increases, the other decreases); therefore, the data set has a negative correlation
Solve the inequality for x. Show each step of the solution.
12(x+3)>4x-8
Answer:
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
12x+36>4x−8
Step 2: Subtract 4x from both sides.
12x+36−4x>4x−8−4x
8x+36>−8
Step 3: Subtract 36 from both sides.
8x+36−36>−8−36
8x>−44
Step 4: Divide both sides by 8.
8x/8 > -44/8
Therefore your answer will now equal [tex]x > \frac{-11}{2}[/tex]
[tex]{ \boxed{ \pink{ \sf{x > - \frac{11}{2}}}}}[/tex]
Step-by-step explanation:
The given inequality is, [tex]{ \green{ \sf{12(x + 3) > 4x - 8}}}[/tex]
[tex]{ \star}[/tex]Step 1: Simplify both the sides of inequality.
[tex]{ \green{ \sf{12x + 36 > 4x - 8}}}[/tex]
[tex]{ \star}[/tex]Step 2: Now Subtract 4x from both sides.
[tex]{ \purple{ \sf{12x+36−4x> { \cancel{4x}−8{ \cancel{−4x}}}}}}[/tex]
[tex]{ \purple{ \sf{8x+36>−8}}}[/tex]
[tex]{ \star}[/tex]Step 3: Subtract 36 from both sides.
[tex]{ \blue{ \sf{8x+{ \cancel{36}{ \cancel{−36}}}>−8−36}}}[/tex]
[tex]{ \blue{ \sf{8x>−44}}}[/tex]
[tex]{ \star}[/tex]Step 4: Divide both sides by 8.
[tex]{ \orange{ \sf{ \frac{ \cancel8}{ \cancel8} x > - \frac{ \cancel{44^{ \blue{ \tt{11}}}} }{ \cancel8_{ \blue{ \tt{2}}} }}}} [/tex]
[tex]{ \boxed{ \red{ \sf{x > - \frac{11}{2}}}}} [/tex]
The coordinates of rhombus abcd are a(-4,-2) b(-2,6) c(6,8) d(4,0). What is the area of the rhombus
First, graph the rhombus:
Area of a rhombus = Product of diagonals / 2
Find the length of the diagonals:
Distance between points:
[tex]\sqrt[\placeholder{⬚}]{(x2-x1)^2+(y2-y1)2^}[/tex]Diagonal AC
[tex]AC=\sqrt[\placeholder{⬚}]{(6-(-4))^2+(8-(-2))^2}[/tex]AC= 10√2
Diagonal BD
[tex]BD=\sqrt[\placeholder{⬚}]{(4-(-2))^2+(0-6)^{^2}}[/tex]BD=6√2
Area= AC x BD / 2
Area = [(10√2) x (6√2)]/2
Area = 60
I REALLLY would like to ACTUALLY understand how to solve this. Please tell me how you got the steps. So far, this was my thinking:
[tex]\frac{4x+2}{x^{2} -9+8} = \frac{2(x+1)}{(x-1)(x-8)}[/tex]
Please let me know what comes next?????
The empty boxes of the numerators for the given rational expression is to be filled with 4x and 2 respectively.
What is a rational expression?Rational expression is a division of two polynomials. Which implies that the numerator and denominator of the fraction consists of polynomials.
To solve this, we will first factorise the expression of the denominator as follows;
x² - 9x + 8 = x² - 8x - x + 8
x² - 9x + 8 = x(x - 8) -1(x - 8)
x² - 9x + 8 = (x - 1)(x - 8)
Hence, we can rewrite the rational expression as:
(4x + 2)/[(x - 1)(x - 8)]
we can break the expression further by dividing each term of the numerator with the expression (x - 1)(x - 8) as follows;
(4x + 2)/[(x - 1)(x - 8] = [4x/(x - 1)(x - 8)] + [2/(x - 1)(x - 8)]
Therefore, 4x and 2 will be the appropriate values to be filled in the empty boxes equated to the rational expression.
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what is the difference written in scientific notion?0.00067 - 2.3 * 10^-5
Answer:
[tex]6.47\times10^{-4}[/tex]Explanation:
To evaluate the difference:
[tex]0.00067-2.3\times10^{-5}[/tex]First, rewrite the expression in the form below:
[tex]=67\times10^{-5}-2.3\times10^{-5}[/tex]Next, factor out the powers of 10.
[tex]\begin{gathered} =10^{-5}(67-2.3) \\ =10^{-5}(64.7) \\ =64.7\times10^{-5} \\ =6.47\times10^1\times10^{-5} \\ =6.47\times10^1^{-5} \\ =6.47\times10^{-4} \end{gathered}[/tex]Thus, the difference written in scientific notation is:
[tex]6.47\times10^{-4}[/tex]Note: A number is in scientific notation if it is expressed as a product of a number (between 1 and 10) and a power of 10.
A. 2x-1+3x=0 B. 5x-1=0 How can we get Equation B from Equation A ?
By taking x as a common factor we get:
2x - 1 + 3x = 0
(2 + 3)*x - 1 = 0
5x - 1 = 0
How to get equation B from equation A?Let's start with equation A, it is:
2x - 1 + 3x = 0
If we group like terms, we will get:
(2x + 3x) - 1 = 0
Now we can take x as a common factor in the left term, so we get:
(2x + 3x) - 1 = 0
(2 + 3)*x - 1 = 0
Now we simplify the sum in the left term:
(2 + 3)*x - 1 = 0
5x - 1 = 0
This is equation B.
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The Beta club is selling chocolate to raise money for Beta convention. Chocolate bars sell for $1.25 each and chocolate covered almonds sell for $2.00 each. The Beta club needs to raise more than $375 for all members to attend the convention. The students can sell up to 500 bars and covered almonds altogether.
1. Write a system of inequalities that can be used to represent this situation.
2. The club sells 100 chocolate bars. What is the least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention? Justify your answer.
(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
In the question ,
Part(1)
let the number of chocolates be "x" .
let the number of chocolates with covered almonds be "y"
price of each chocolate bar = $1.25
price of each chocolate covered almonds = $2
Beta club needs more than $375
So , according to the question
1.25x + 2y > 375
and also the students can sell up to 500 bars and covered almonds altogether.
So , x+y ≤ 500 .
Part(2)
Given , the club sells 100 chocolate bars.
substituting x= 100 in the inequality 1.25x + 2y > 375 , we get
1.25(100) + 2y > 375
125 + 2y > 375
2y > 375-125
2y > 250
y > 125
least number of chocolate covered almonds to be sold is 126 .
Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375 and x+y ≤ 500 .
(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .
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Working alone, it takes Kristen 10.2 hours to harvest a field. Kayla can harvest the same field in 16.5 hours. Find how long it would take them if they worked together.
ANSWER:
13.35 hours
EXPLANATION:
Given:
Time Kristen takes to harvest = 10.2 hours
Time Kayla takes to harvest = 16. 5 hours
Let X represent the time it would take them to work together.
Here, to find the time it would take them if they worked together, let's find their mean time, using the formula below:
[tex]X\text{ = }\frac{Time\text{ taken by kristen + Time taken by Kayla}}{2}[/tex][tex]\begin{gathered} X\text{ = }\frac{10.2\text{ + 16.5}}{2} \\ \\ X\text{ = }\frac{26.7}{2} \\ \\ X\text{ = }13.35\text{ hours} \end{gathered}[/tex]It would take them 13.35 hours if they worked together.
If the measures of two angles of a triangle are 96° and 29°, what is the measure of the third angle?
Answer: measure of the third angle is 55 degrees
Step-by-step explanation: the sum of all interior angles in a triangle is always 180 so, 96+29+x=180.
125+x=180
x=55
Graph the Linear equation: y = - 3/4x + 5
Based on the given linear equation of y = - 3/4x + 5, the graph is shown attached.
How to graph an equation?When given a linear equation, you graph it by coming up with x values and then using the equation to find the corresponding y values.
The linear equation is y = - 3/4x + 5.
If the value x = -1, then y would be:
y = - 3/4x + 5
= -3/4(-1) + 5
= 5.75
If the value x = 0, then y would be:
y = -3/4(0) + 5
= 5
If the value x = 1, then y would be:
= -3/4(1) + 5
= 4.25
If the value x = 2, then y would be:
= -3/4(2) + 5
= 3.5
If the value x = 3, then y would be:
= -3/4(3) + 5
= 2.75
The points would be:
(-1, -5.75) (0, 5) (1, 4.25) (2, 3.5) (3, 2.75)
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|x + 6| < or equal to 1
8
x < or equal to 2
x < or equal to ?
Answer: -14
Step-by-step explanation:
[tex]\frac{1}{8}|x+6| \leq 1\\\\|x+6| \leq 8\\\\-8 \leq x+6 \leq 8\\\\-14 \leq x \leq 2[/tex]
The table shows deshawna's science grade during four grading periods. How much greater was the percentage change in her grade from grading period 1 to 2 than from grading period 2 to 3. round to nearest tenth
Since the percent grade in period 1 was 92% and in period 2 was 96%, then the percent change from period 1 to 2 was 4%.
Since the percent grade in period 2 was 96% and in period 3 was 99%, then the percent change from period 2 to 3 was 3%.
Since 4% is 1% greater than 3%, then the percent change from grading period 1 to 2 was 1% greater than the percent change from grading period 2 to 3.
Therefore, the answer is: 1.0%.
Please help ASAP starting to fall behind! This equation really confuses me and if someone could help that would be amazing!
Given the function:
f(x) = x² - 4x - 2
Find the following values.
a) f(2)
f(2)=
b) f(4)
f(4)=
c) f(-3)
f(-3)=
The values of the functions is ,
(a) f(2) = -6
(b) f(4) = -2
(c) f(-3) = 19
In the question ,
it is given that the function is f(x) = x² - 4x - 2
we have to find the value of f(2) , f(4) , f(-3)
Part(a)
to find f(2) , we substitute x = 2 in the function
On substituting , we get
f(2) = 2² - 4*2 - 2
= 4 - 8 - 2
= 4 - 10
= -6
Part(b)
to find f(4) , we substitute x = 4 in the function f(x)
On substituting , we get
f(4) = 4² - 4*4 - 2
= 16 - 16 -2
= 0 - 2
= -2
Part(c)
to find f(-3) , we substitute x = -3 in the function
On substituting , we get
f(2) = (-3)² - 4*(-3) - 2
= 9 + 12 -2
= 9 + 10
= 19
Therefore , The values of the functions is , (a) f(2) = -6 , (b) f(4) = -2 , (c) f(-3) = 19
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This math question please
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. if beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars? if segment ad ≅ segment cd, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad ≅ segment cd, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if m∠acd = 90° then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if m∠acd = 90° then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.
A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.
Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.
The answer is that point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.
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Astronomers use a light year to measure distance. a light year is the distance light travels in one year. The speed is approximately 300,00km/sec. how long will it take a rocket traveling 63,000km/hr to reach Alpha Centauri (the ⭐ closest to Earth other than the ). Note: Alpha Centauri is approximately 4.34 light years from Earth. which is 4.11 x 10^13 km away (when using scientific notation). one light year is 9.46 x 10^12 km.
Speed of light = 300,000 km/sec
Rocket's speed = 63,000 km/hr or 6.3 x 10⁴ km/hr
Alpha Centauri distance from Earth = 4.11 x 10¹³ km
One light year (distance) = 9.46 x 10¹² km
To solve for the time it takes it travel, we can manipulate the speed formula.
[tex]\begin{gathered} \text{speed}=\frac{dis\tan ce}{\text{time}} \\ \text{time}=\frac{dis\tan ce\text{ }}{\text{speed}} \end{gathered}[/tex]We already have the distance of Alpha Centauri from Earth written above. We also have the speed of the rocket written above too. We will substitute those values to the formula.
[tex]\begin{gathered} \text{time}=\frac{4.11\times10^{13}\operatorname{km}}{6.3\times10^4\operatorname{km}\text{ /hr}} \\ \text{time}=0.6523809524\times10^9 \\ \text{time}=6.52\times10^8\text{ hr} \end{gathered}[/tex]Please be quick!
Clare has been working to save money and wants to have an equation to model the amount of money in
her bank account.
She has been depositing $175 a month consistently. She doesn't remember how much money she
deposited initially; however, on her last statement she saw that her account has been open for 10 months
and currently has $2475 in it.
Write an equation for the amount of money in Clare's bank account after x months. Which equation form
did you choose?
The initial amount that was deposited by Clare is $725.
The equation for the amount of money in Clare's bank account after x months will be 725 + 175x
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let the amount deposited initially be x.
Based on the information, this will be illustrated as:
x + 175(10) = 2475
x + 1750 = 2475
Collect like terms
x = 2475 - 1750
x = 725
The initial amount is $725.
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What sets does -√3,1 and 0 belong to
√2 and -√3 belong to the set of Irrational Numbers.
1 belong to the following sets:
• Rational
,• Whole
,• Natural
,• Integers
0 belongs to the following sets:
• Rational
,• Whole
,• Integers
3|y|+(y-x²)
if x = -1 and y = -5
Which equation has the solution x = 5? Select each correct answer. Responses
A) 11 + 6x = 22
B) 3x + 1 = 9
C) 18−2x=9
D) 25/x+4=9
E) x/5 + 5 = 6
F) 32−4x=12
The equation that has the same solution as x = 5 are as follows:
25 / x + 4 = 9x / 5 + 5 = 6 32 - 4x = 12 How to solve equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
In other words, an equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The equation can be solved as follows:
The equation will have the same solution as x = 5.
Therefore,
25 / x + 4 = 9
subtract 4 from both sides of the equation
25 / x + 4 = 9
25 / x + 4 - 4 = 9 - 4
25 / x = 5
cross multiply
5x = 25
divide both sides by 5
x = 25 / 5
x = 5
x / 5 + 5 = 6
x / 5 = 6 - 5
x / 5 = 1
cross multiply
x = 5
32 - 4x = 12
- 4x = 12 - 32
- 4x = - 20
divide both sides of the equations by - 4
x = -20 / - 4
x = 5
Therefore, the equation with same solution are 25 / x + 4 = 9, x / 5 + 5 = 6 and 32 - 4x = 12
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Will and Sarah are racing across the playground. Instead of running, they are hopping. During the race, they must both hop at the same time. In one hop, Will can travel 5 feet, and Sarah can travel 4 feet.
The playground is 200 feet wide. Will wins the race after hopping 40 times. How far had Sarah hopped when Will finished the race?
I know the answer i just need explanation.
Sarah has hopped for 160ft when Will finished the race.
What is basic arithmetic?
Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.
For Will
5 × 40
= 200 feet
For Sarah
4 × 40
= 160 ft
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Simplify using the properties of exponents: (x^4 y^-3)^4/x^0y^2
Answer:
Rewrite using the commutative property of multiplication.
2
(
2
x
0
y
2
)
−
3
y
x
3
Anything raised to
0
is
1
.
2
(
2
⋅
1
y
2
)
−
3
y
x
3
Multiply
2
by
1
.
2
(
2
y
2
)
−
3
y
x
3
Rewrite the expression using the negative exponent rule
b
−
n
=
1
b
n
.
2
1
(
2
y
2
)
3
y
x
3
Simplify the denominator.
Tap for more steps...
2
1
8
y
6
y
x
3
Simplify terms.
x
3
4
y
5
(8.59×10 4 )−(3.2×10 3 )
Answer:
The answer is 8.27×10^4
Answer: 8.27×10^4
Step-by-step explanation:
30. Solve for x: 7^/10 = 2, approximate to 4 digitsa. 6.325 b. 3.256 c. 3.265 d. 3.652 e. 3.562
• Solution
[tex]7^{\frac{x}{10}}=2[/tex]
To solve for x, we take the logarithm of both sides.
[tex]\log 7^{\frac{x}{10}}=\log 2[/tex]Applying the law of logarithm to the equation above;
[tex]\log a^b=b\log a[/tex][tex]\begin{gathered} \log 7^{\frac{x}{10}}=\log 2 \\ \frac{x}{10}\log 7=\log 2 \\ \text{Dividing both sides by log 7;} \\ \frac{x}{10}=\frac{\log 2}{\log 7} \\ \frac{x}{10}=\frac{0.3010}{0.8451} \\ \frac{x}{10}=0.3562 \\ \text{Cross multiplying the equation;} \\ x=0.3562\times10 \\ x=3.562 \end{gathered}[/tex]Therefore, the approximate value of x is 3.562
The correct option is E.