3.22 approx. is the value of x in equation [tex]e^{\frac{x}{2}[/tex] = 5 solved by using natural logarithms
We have been asked to find x in [tex]e^{\frac{x}{2}[/tex] = 5 using natural logarithms
⇒ [tex]e^{\frac{x}{2}[/tex] = 5
⇒ [tex]\frac{x}{2}[/tex] = ㏑(5)
⇒ x = ㏑(25)
= 3.22 approx.
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
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Correct questionUse natural logarithms to solve each equation.
[tex]e^{\frac{x}{2}[/tex] = 5
please help as soon as possible
The value of g (7) is 16.
What is Piecewise function?
A piecewise function is a function which built from pieces of different functions over different intervals.
The given function is;
g (x) = x² - 5 , x ∈ (-∞, -7)
= 9x - 17 , x ∈ [-7, 2]
= (x + 1) (x - 5) , x ∈ (2, ∞)
Now, Find the value of g (7) as;
Since, Number 7 is belong in interval (2, ∞).
Hence, To find the value of g (7) we use the function,
g (x) = (x + 1) (x - 5) , x ∈ (2, ∞)
Substitute x = 7 we get;
g (x) = (7 + 1) (7 - 5)
g (7) = 8 * 2
g (7) = 16
Hence, The value of g (7) is 16.
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Simplify [tex]\sqrt{18[/tex]
Answer:
3√2
Step-by-step explanation:
Square root of 18 is equal to 3√2 in radical form and 4.24264068712 in decimal form.
ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Answer:
the slope would be -3 because it takes the place of the m in y=mx+b
Step-by-step explanation:
Ari and Jeremiah both work at vet clinics. Ari gets paid $8.50 per hour. Jere works at another vet clinic getting paid $6.50 per hour plus $15 for dog walking. Write an equation for the number of hours, h, that Ari and Jere would need to work to earn the same amount of money in a week
Answer:
[tex]8.50h = 6.50h + 15[/tex]
can any body help me with this
Answer:
BRO I TRIED THIS BEFORE
YOU JUST NEED TO SEARCH IT IN gogle
A bicyclist brakes from 21 m/s to stop in 32.3 m. what is the acceleration of the bicyclist
The acceleration of the bicyclist is 6.83 m/s².
The given parameters;
Initial velocity of the bicycle (u) = 21 m/s
Distance travel by the bicycle (s) = 32.3 m
We have to find the acceleration of the bicyclist.
How to calculate the acceleration?
If the initial velocity is u, final velocity is v and distance travel by object is s then we can calculate acceleration as;
v² = u² + 2as
Initial velocity of the bicycle (u) = 21 m/s
Distance travel by the bicycle (s) = 32.3 m
Final velocity of the bicycle (v) = 0
Hence, The acceleration of the bicycle is calculated as follows;
v² = u² + 2as
Where, v is the final velocity of the bicycle.
0 = u² + 2as
2as = - u²
a = - u²/2s
a = - (21)²/2*32.3
a = - (21)²/64.6
a = -441/64.6
a = -6.83
| a | = 6.83 m/s²
The acceleration of the bicyclist is 6.83 m/s².
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The height of a box is 7 inches. The length is three inches more than the width. Find the width if the volume is 910.
The width of the box whose height is given as 7 inches and length is three inches more than the width given a volume of 910 is; 10 inches.
What is the width of the box in discuss whose height, length and width are as described in the task content?It follows from the task content that the height of the box is; 7 inches.
Let, x = width of the box and;
x+ 3 = length of the box.
Therefore, since the volume of a box is given by the formula;
V = l × b × h
Therefore, we have;
910 = 7 (x) (x+3)
Divide both sides by; 7
130 = x² + 3x
x² + 3x -130 = 0.
(x+13) (x-10) = 0
Therefore, x = -13 or x = 10.
Ultimately, the possible values of the width are; -13 or 10.
Since the width cannot be a negative number, it follows that the width of the box in discuss is; 10 inches.
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A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, how many servings can be made from two gallons?
A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, Two gallons of milk will make 192 servings
How to find the how many servings can be made from two gallons of milkGiven data
2 cups of milk to make 6 servings.
Assuming
1 gallon 4 quarts
1 quart 2 pints
1 pint 2 cups
1 cup = 8 fluid ounces
if 1 quart 2 pints, then 4 quarts will be
= 4 * 2 = 8 pints
if 1 pint 2 cups, then 8 pints will be
= 8 * 2 = 16 cups
if 1 gallon is 16 cups, the 2 gallons will be
= 16 * 2 = 32 cups
If 1 cup is 6 servings, then 32 cups will be
= 32 * 6 = 192 servings
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I do not understand this please help
Answer:
9 edges. All triangular prisms have 9 edges.5 faces. 2 identical faces and 3 rectangular faces.12 edges. A cuboid/rectangular prism has 12 edges.Hope this helps!
A group of friends were working on a student film that had a budget of $900. They used 53% of their budget on equipment. How much money did they spend on equipment?
The $53 money they spend on equipment if the group of friends was working on a student film that had a budget of $900. They used 53% of their budget on equipment.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
A group of friends was working on a student film that had a budget of $900. They used 53% of their budget on equipment.
The money spend on equipment = 53% of $900
The money spend on equipment = (53/100)900
= 0.53x100
= $53
Thus, the $53 money they spend on equipment if the group of friends was working on a student film that had a budget of $900. They used 53% of their budget on equipment.
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Evaluate ab + c for a = 2, b = 3, and c = 4.
Answer:
10
Step-by-step explanation:
substitute the given values into the expression
ab + c
= 2(3) + 4
= 6 + 4 = 10
Hey there!
ab + c
= 2(3) + 4
= 6 + 4
= 10
Therefore, your answer should be:
10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
extract square roots
x2 = 16
r2 - 100 = 0
2s2 = 50
(k - 4)2 = 169
(2s - 1)2 - 225 = 0
Help quick please thanks
Answer:
d=12.5
hope this helps :)
Solve 4.3t + 6.8 = 8.4t – 7.55 for t.
Question 1 options:
A)
3.5
B)
–0.18
C)
–3.5
D)
–1.13
Answer:
A) 3.5
Step-by-step explanation:
Solving the equation: First bring all the terms with variable 't' to one side of the equation.4.3t + 6.8 = 8.4t - 7.55
Subtract 8.4t from both sides,
4.3t - 8.4t +6.8 = -7.55
Combine like terms,
-4.1t + 6.8 = -7.55
Now isolate 't'To isolate 't' first subtract 6.8 from both sides.
-4.1t = -7.55 - 6.8
-4.1t = -14.35
Divide both sides by (-4.1)
t = -14.35 ÷ (-4.1)
t = 3.5
5x-4y > 10
3x-2y < -7
Answer:
[tex]x > \frac{2(5 + 2y)}{5} \\ \\ x < \frac{2y - 7}{3} [/tex]
Step-by-step explanation:
[tex]1. \: 5x > 10 + 4y \\ 2. \: x > \frac{10 + 4y}{5} \\ 3. \: x > \frac{2(5 + 2y)}{5} \\ \\ \\ 1. \: 3x < - 7 + 2y \\ 2. \: 3x < 2y - 7 \\ 3. \: x < \frac{2y - 7}{3} [/tex]
DRU MIZEL MAINTAINS THE RECORDS OF THE AMOUNT OF A COAL DELIVERED TO HIS DEPARTMENT IN THE STEEL MILL. IN JANUARY, 3 tons 1,500 lbs WERE DELIVERED. IN FEBRUARY, 2 tons 1,200 lbs WERE DELIVERED. FIND THE TOTAL AMOUNT DELIVERED IN THESE TWO MONTHS.
The total amount of coal delivered in these two months is equal to 6.35 tons.
What is a conversion factor?A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.
Conversion:
1 lbs = 0.0005 tons
1500 lbs = 0.75 tons
1200 lbs = 0.6 tons.
Now, we can determine the total amount of coal delivered in these two months:
Total amount of coal = 3 tons + 0.75 tons + 2 tons + 0.6 tons
Total amount of coal = 6.35 tons.
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PLEASE HELP!!!!!
At the scene of a traffic accident, a police investigator must determine the speed of both vehicles. The investigator uses the formula s=2 square root 51 where s represents speed, measured in miles per hour, and l represents the length of the skid marks, measured in feet. Approximately how long are the skid marks of the car that is going 65 miles per hour?
The length of skid marks of a car that is going 65 miles per hour is approximately equal to 211 feet.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this scenario, the formula (expression) which is being used by this investigator is given by:
S = 2√(5L)
Where:
S represents speed, measured in miles per hour.L represents the length of the skid marks, measured in feet.Making L the subject of formula, we have:
S²/4 = 5L
L = S²/20
Substituting the given parameters into the formula, we have;
L = 65²/20
L = 4,225/20
Length of skid marks, L = 211.25 ≈ 211 feet.
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If BT = 10, TO = 2x and BO = 4x-14, Find the length of TO & BO.
The length of TO is 6.66 and of BO is 3.32
In the problem we are given that BT=10 TO=2x amd BO=4x-10
We have to find the value of x in order to find the values of length of BO and TO.
BT=BO+TO
4x-10+2x=10
6x=20
x=3.33
The length of TO is 6.66
and of BO is 3.32
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A seat on a ferris wheel is level with the center of the wheel. the diameter of the wheel is 200 feet. suppose the wheel rotates 60°, causing the height of the seat to decrease. how much closer to the ground is the seat after the rotation? 50 feet 50 startroot 3 endroot feet 100 feet 100 startroot 3 endroot feet
Using sine formula, the seat on a Ferris wheel is 50√3 feet closer to the ground after rotating 60°.
One of the 6 trigonometric functions is the sine function. Sine function can be described as the ratio of the length of the opposite side of the triangle to its hypotenuse.
sin x = (opposite side) / (hypotenuse)
where "opposite side" is the length of the side opposite to angle x
If the wheel rotates 60°, causing the height of the seat to decrease, using sin formula, solve for the vertical distance between the positions before and after the rotation.
sin x° = (opposite side) / (hypotenuse)
where x = 60
opposite side = vertical distance between the positions before and after the rotation
hypotenuse = radius = 200 feet/2 = 100 feet
sin 60° = opposite side / 100 feet
opposite side = 50√3 feet
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3. El resultado de restarle 13 a la suma de dos
números consecutivos, es 18. ¿Cuáles son esos
números consecutivos?
(1) 6 y 7
(2)9 y 10
(3) 10 y 11
(4) 15 y 16
(5) 31 y 32
When the result of subtracting 13 from the sum of two consecutive numbers is 18. The numbers are 15 and 16. The correct option is d.
How to illustrate the information?From the information, the result of subtracting 13 from the sum of two consecutive numbers is 18.
Let the numbers be x and x+1.
Therefore, (x + x + 1) - 13 = 18
2x + 1 - 13 = 18
2x - 12 = 18
2x = 18 + 12
2x = 30
Divide
x = 30/2
x = 15
Therefore, when the result of subtracting 13 from the sum of two consecutive numbers is 18. The numbers are 15 and 16. The correct option is d.
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what gradient?
pls help giving brainliest answers!! :)
Answer: 2
Step-by-step explanation:
4x-2y=6
Divide both parts of the equation by 2:
2x-y=3
2x-y+y=3+y
2x=3+y
2x-3=3+y-3
2x-3=y
y=2x-3
simplify |8-40/4^3| 4^2 - 8 A.0 B.10 C.20 D.30
The required answer for the given expression is 0.
What is simplification?Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.
Now the given expression is,
|8-40/4^3| 4^2 - 8
Solving the mod first,
Since 4^3 = 64 ; 4^2 = 16,
and 8 - 40 = -32
Therefore,
|8-40/4^3| 4^2 - 8 = |-32/64|16 - 8
Now solving
⇒ 32/64 = 1/2
Therefore we get,
|8-40/4^3| 4^2 - 8 = |-31/2| 16 - 8
Now since, |-a| = a
therefore, |-1/2| = 1/2
Therefore we get,
|8-40/4^3| 4^2 - 8 = (1/2) 16 - 8
Now, since (1/2) 16 = 8
Therefore we get
|8-40/4^3| 4^2 - 8 = 8 - 8
solving we get,
|8-40/4^3| 4^2 - 8 = 0
this is the required answer for the given expression.
Thus, the required answer for the given expression is 0.
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What is the exact value of sin 120° ? Use a double-angle identity.
Answer:
[tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Sine is positive in the second quadrant, so:
[tex]\sin \frac{240^{\circ}}{2}=\sqrt{\frac{1-\cos 240^{\circ}}{2}} \\ \\ =\sqrt{\frac{1.5}{2}} \\ \\ =\sqrt{3/4} \\ \\ =\frac{\sqrt{3}}{2}[/tex]
At a little-known vacation spot, taxi fares are a bargain. A 18-mile taxi ride takes 24 minutes and costs $7.20. You want to find the cost of a 34-mile taxi ride. What unit price do you need?
The unit price is $2.5
34 mile taxi ride will cost $85
How to calculate the unit price ?18 mile taxi ride costs $7.20
The cost of 1 mile is
= 18/7.20
= 2.5
The unit price is $2.5 for 1 mile
The cost of 34 mile taxi ride can be calculated as follows
= 2.5 × 34
= 85
Hence the 34 mile taxi ride will cost $85
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3-5 At the fair, Kate found a strange machine with a sign on it labeled, "Enter a number. When she pushed the number 15, the machine displayed 9. When she entered 23, the machine displayed 17. Perplexed, she tried 100, and the machine displayed 94. what would the machine display if she entered 77.
The machine will display the digit 71 if she pressed a 77 number.
According to the statement
We have to find that the digit shown by the machine.
So, For this purpose, we know that the
Digits are the single numbers used to represent values in math
From the given information:
At the fair, Kate found a strange machine with a sign on it labeled, "Enter a number. When she pushed the number 15, the machine displayed 9. When she entered 23, the machine displayed 17. Perplexed, she tried 100, and the machine displayed 94.
From this
we find that the machine displayed a number after subtracting 6 from the pressing digit in the machine.
For example, When she pushed the number 15, the machine displayed 9.
Displaying digit = 15-9
6 = 6.
If she pressed a 77 number then machine will display
77 -6 = 71.
So, The machine will display the digit 71 if she pressed a 77 number.
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How many solutions are there to the equation below?
4x-9(x + 1) = 20 - 5x
Ο Α. 0
OB. 1
C. Infinitely many
Answer: the correct answer is B.0. Step-by-step explanation: there is no value for x.
Add or subtract if possible. 3√20x + 8√45x -4√5x
The subtraction of the expression 10√27 - 4√12 is 22√3.
Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together.
In mathematics, subtraction involves removing anything from a group or a number of objects. What is left in the group gets smaller when you subtract.
Consider the expression,
y = 3√20x + 8√45x - 4√5x
Now, the number in the root can also be written as:
20 = 2 × 2 × 5
45 = 5 × 3 × 3
Therefore,
y = 3√20x + 8√45x - 4√5x
y = 3( √[2 × 2 × 5] )x + 8( √[5 × 3 × 3] )x - 4√5x
y = 3 × 2√5x + 8 × 3√5x - 4√5x
y = √5x ( 3 × 2 + 8 × 3 - 4 )
y = √5x ( 6 + 24 - 4 )
y = 26√5x
The value of the expression 3√20x + 8√45x -4√5x is 26√5x.
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How many packages of diapers (d) can you buy with $40 if one package costs $8?
Answer:
5
Step-by-step explanation:
because 8+8+8+8+8=40 or 8*5
and theres 8 five times
>
Question 2
Name the slope and one point that is on the line represented by the equation:
y+ 3 =
(x+7)
=-- and point (-7, -3)
m=
and point (7,3)
Om= and point (-7, -3)
and point (-7, -3)
The slope of the line is equal to 1 and a point lying on the line with the given equation is (7, 3).
The equation of the line is given as y + 3 = x + 7. First, we write the equation of the line in proper form. It can be written in slope-intercept form as y = mx + c where m is known as the slope of the line and c is the intercept made by the line.
Now, according to the equation given in question.
y = x + 7 - 3
y = x + 4
If we compare this equation with the slope-intercept form of line, we get the slope equal to one.
y = mx + c
y = x + 4
=> m = 1 and c = 4.
A point which satisfies the equation y = x + 4 can be (7, 3) as
7 = 3 + 4
=> 7 = 7 (L.H.S. = R.H.S.)
Thus, slope of the line is equal to 1 and a point lying on the line with the given equation is (7, 3).
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Please solve thanks!!
The function according to the rigid transformation g(k + 3) = - 4 · f(k + 3), where f(x) = x² - x - 1, is equal to the quadratic equation g(k + 3) = - 4 · k² - 20 · k - 44.
How to evaluate a quadratic equation
In this problem we find the definition of a quadratic equation and besides we are asked to find the result of horizontal translation, a reflection about the x-axis and a dilation, all of them rigid transformations. In other words, we must look for the resulting expression according to this definition:
g(k + 3) = - 4 · f(k + 3)
g(k + 3) = - 4 · [(k + 3)² - (k + 3) - 1]
g(k + 3) = - 4 · [(k² + 6 · k + 9) - (k + 3) - 1]
g(k + 3) = - 4 · (k² + 5 · k + 11)
g(k + 3) = - 4 · k² - 20 · k - 44
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