Answers
Answer:
7.5 -ln(0.25)
Step-by-step explanation:
We can first graph this function. Looking at the graph, we can separate this into two ranges -- from x=0.25 to x=1 and from x=1 to x=4.
From x=0.25 to x=1, we want to find the area above y=1/x and below y=4. To do this, we can take the integral of y=4 from x=0.25 to x=1 to encompass the whole area under y=4 from that range. Then, we subtract the area under y=1/x as we don't need that (we only want what's above it). Therefore, we have
[tex]\int\limits^{1}_{0.25}{4} \, dx - \int\limits^{1}_{0.25} {1/x} \, dx \\= 4(1) - 4 (0.25) - (ln(1) - ln(0.25))\\= 4 - 1 - ln(1) + ln(0.25)\\= 3 - ln(1) + ln(0.25)[/tex]
Next, we know that ln(x/y) = ln(x) - ln(y), so ln(0.25) - ln(1) = ln(0.25/1) = ln(0.25), so we have
3 - ln(0.25)
For x=1 to x=4, we want to find the area above y=x and below y=4. We can apply a similar strategy, subtracting the area below y=x from the area below y=4 to get
[tex]\int\limits^{4}_{1}{4} \, dx - \int\limits^{4}_{1} {x} \, dx \\ \\= 4(4) - 4(1) - (4^{2} /2 - 1^2/2)\\= 16 - 4 - 8 + 0.5\\= 4.5[/tex]
Add these two areas up to get
3-ln(0.25) + 4.5 = 7.5 -ln(0.25)
Related Questions
What is -1,098 3/20 minus -895.9
Answers
Answer:
the answer is -1445.05.
Answer:
Step-by-step explanation:
the answer is -1445.05.
how do you simplify this question x^3z^7/x^5z
Answers
Answer:
go to symbolab and it will simplify for you, brainly is useless with these kinds of questions. Symbolab.com very easy to use and gives you answer right away instead of have to wait for some oaf like me to solve your problems.
Step-by-step explanation:
-ek 4 - Assessment - C12000: X --- 2.com/le/content/9122/viewContent/279438/View puma 5 Drive Safely | Dash... BUMA ment e Left:0:23:21 Jennifer Glenn: Attempt 1 Question 19 (2.5 points) In the formula =(G15-G14)*$M$3/4, which mathematical operation is performed first?
Answers
Answer:
yes
Step-by-step explanation:
Find the y-intercept
of the line on the
graph?
Answers
9514 1404 393
Answer:
(0, -3)
Step-by-step explanation:
The y-intercept is the point where the graph crosses the (vertical) y-axis. That point is halfway between grid lines marked -2 and -4, so is at the grid line with the value -3. The x-coordinate there is 0, so the y-intercept point is ...
(x, y) = (0, -3)
_____
Since the y-intercept always has an x-coordinate of 0, we sometimes refer to the y-intercept using only the y-value: -3.
A triangle has a perimeter of 75 inches. Find the length of three sides
if one side is 15 inches larger than the smallest side, and the third
side is twice the smallest
Answers
Answer:
The side lengths are:
15, 30, and 30
Step-by-step explanation:
Let x determine the length of the smallest side length then
the other one is said to be 15 in larger so it's x + 15
finally the third size is said to be twice as the smallest one so it's 2x
The perimeter is the sum of all three sides added up
x + 2x + x + 15 = 75 add like terms
4x + 15 = 75 subtract 15 from both sides
4x = 60 divide both sides by 4
x = 15
PLZZ HELP I NEED HELP
write a 2 step equation and solve:
1. four more than six times a number is 22.
2. five less than eleven times a number is 50.
3. seven less than nine times a number is -16.
Answers
Step-by-step explanation:
1) let the number=x
six times a number=6x
Condition:
6x+4=22
2) eleven times a number=11x
Condition:
11x-5=50
3) 9 times a number=9x
Condition:
9x-7=-16
Note:if you need to ask any question please let me know.
How do I solve this
Answers
Answer:
i dont know
Step-by-step explanation:
brainiest to whoever right.
Answers
Answer:
The problems listed are all the formulas for 2d figures:
Area of a Triangle: 1/2 B*H
Area of a Square: S^2
Area of a Rectangle: l*w
Perimeter of a Square: 4s
Perimeter of a Triangle: a+b+c
Perimeter of a Rectangle: 2l+2w
773 centimeters to meters
Answers
Answer:
7.73
Step-by-step explanation:
How much water should be added to 12mL of 11% alcohol solution to reduce the concentration to 6%
Answers
Answer:
We have 12 mL of 11% alcohol.
How much water do we add to make it a 6% solution?
We have 1.32 mL alcohol and 10.68 mL water
x is the water to add
(1.32) / (12 + x) = .06
1.32 = .72 + .06x
.6 = .06x
x = 10 mL
Step-by-step explanation:
Answer with explanation please?
Answers
Answer:
x=136°
bcs they are parallel and they are congruent
................
1. Simplify the expression. –12 ÷ (–2) 24 –24 6 –6
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\dfrac{-12}{-2} \times24-24(6)-6}\\\\\\\boxed{\rightarrow 6(24) - 24(6) - 6}\\\\\\\huge\boxed{\rightarrow{144 - 144 - 6}}\\\\\\\huge\boxed{\rightarrow 0 -6}\\\\\\\huge\boxed{= -6}\\\\\\\\\huge\boxed{\textsf{Therefore, your answer is: \mathsf{-6 }}}\huge\checkmark[/tex]
Good luck on your assignment and enjoy your day!~[tex]\frak{Amphitrite1040:)}[/tex]Is 3.6 a natural/counting
Number
Answers
Answer:
It’s a rational number
Step-by-step explanation:
Given H = f(t) where H is the height in meters of an object and t is the time in seconds since it was launched, which of the following is the best interpretation of f(8) = 12?
Answers
Answer:
Recall that the height of the object, in meters, is a function of elapsed time, in seconds. Thus what [tex]f(8)=12[/tex] means is that the object is at a height of 8 meters when 12 seconds have passed since its launch.
Best interpretation of the given f(8) = 12 is 8 seconds after the object is launched it is at a height of 12meters.
What is interpretation?
" Interpretation is defined as the explanation of something in your own words or as per your understanding."
According to the question,
Given,
H = f(t)
H represents the height in meters of an object
t represents the time in seconds
Interpretation of the given situation,
f(8) = 12
time = 8seconds
height of the object = 12meters
Hence, interpretation of the given situation is 8 seconds after the object is launched it is at a height of 12meters.
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2. An electronic watch is sold for Rs 840 at a profit of Rs 90. Find its cost price and the profit per cent.
Answers
Answer:
750 CP AND PROFIT%=12%
Step-by-step explanation:
SP=rs 840
profit=90
CP=SP-profit
=840-90
=750
profit %=profit/CP*100%
=90/750*100%
=12%
Help please due tomorrow
Answers
Answer:
Angle BAD corresponds to Angle FEH in the scaled copy.
Angle ABC corresponds to Angle EFG in the scaled copy.
Angle BCD corresponds to Angle FGH in the scaled copy.
Angle ADC corresponds to Angle EHG in the scaled copy.
The calculation for the correlation, r, for this set of five students is __________. Answer choices are rounded to the hundredths place.
Answers
Answer:
im not sure
Step-by-step explanation:
Answer:
0.32
Step-by-step explanation:
A summer camp has 372 campers who will be going on an outing. Estimate the number of vans needed to accommodate the entire camp if each van can comfortably hold 12 passengers. Then calculate the actual number of vans that will be needed
Answers
Answer:
31
Step-by-step explanation:
You divide, 372 divided by 12
the actual number of vans needed is 31 vans to accommodate the entire camp. To estimate the number of vans needed to accommodate the entire camp, we can use the concept of rounding up to the nearest whole number.
The number of vans required will be the total number of campers divided by the capacity of each van (12 passengers), rounded up to the nearest whole number.
Estimate:
Number of vans needed =[tex]\(\frac{372}{12}\)[/tex](rounded up to the nearest whole number)
[tex]\(\frac{372}{12} \approx 31\)[/tex]
So, the estimate suggests that around 31 vans will be needed to accommodate the entire camp.
To calculate the actual number of vans needed, we can use the exact division without rounding up.
Actual number:
Number of vans needed = [tex]\(\frac{372}{12} = 31\)[/tex] vans
Thus, the actual number of vans needed is 31 vans to accommodate the entire camp.
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10% + 20% + 70% divided by 250 milliion
Answers
Answer: 8.16e-10
I think idrk
Answer:
[tex] \frac{10\% +20\% + 70\% }{250 \: million} \\ \\ \\ \frac{ \frac{10}{100} + \frac{20}{100} + \frac{70}{100} }{250 \times 10 ^{6} } = \frac{ \frac{100}{100} }{250 \times {10}^{6} } \\ \\ \frac{1}{250 \times {10}^{6} } = 4 \times {10}^{ - 9} [/tex]
I hope I helped you^_^
Solve for r -2r+4 < -9r-6
Answers
Answer:
r < -5/4
Step-by-step explanation:
r -2r+4 < -9r-6
Combine like terms
-r +4 < -9r-6
Add 9r to each side
-r + 9r+4 < -9r-6+9r
8r+4 < -6
Subtract 4 from each side
8r +4-4 < -6-4
8r < -10
Divide by 8
8r/8 < -10/8
r < -5/4
Answer:
[tex]r = \frac{ - 10}{8} [/tex]
Step-by-step explanation:
[tex]r - 2r + 4 < - 9r - 6 \\ r - 2r + 9r < - 4 - 6 \\ - r + 9r< - 10 \\ 8r < - 10 \\ r = \frac{ - 10}{8} [/tex]
Write the equation of the line that is parallel to the line y=-7/4x-2 through the point (4,-2)
Answers
Answer: D
Step-by-step explanation:
m = - 7/4
Point (4, -2)
y - - 2= -7/4(x-4)
y + 2 = - 7/4x + 7
y = - 7/4x +7-2
y = - 7/4 x + 5
The equation of the line that is parallel to the given line is option (D) [tex]y=-\frac{7}{4}x+5[/tex] is the correct answer.
What is equation of a line?The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.
For the given situation,
The line is [tex]y=-\frac{7}{4} x-2[/tex] ------ (1)
The general equation of line in slope intercept form is
[tex]y = mx + c[/tex] ------ (2)
On comparing the equation 1 and 2, we get the slope as
⇒ [tex]m=-\frac{7}{4}[/tex] and
When two lines are parallel, then the slope of the parallel line is equal to the slope of the given line.
So, the slope of the parallel line is [tex]m = -\frac{7}{4}[/tex]
Thus the equation of the parallel line passing through the point (x1,y1) is (4,-2) as,
⇒ [tex]y-y1=m(x-x1)[/tex]
⇒ [tex]y-(-2)=-\frac{7}{4} (x-4)[/tex]
⇒ [tex]y+2=-\frac{7}{4} (x-4)[/tex]
⇒ [tex]y=-\frac{7}{4}x+\frac{7}{4} (4)-2[/tex]
⇒ [tex]y=-\frac{7}{4}x+7-2[/tex]
⇒ [tex]y=-\frac{7}{4}x+5[/tex]
Hence we can conclude that the equation of the line that is parallel to the given line is option (D) [tex]y=-\frac{7}{4}x+5[/tex] is the correct answer.
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If AED is 95°, find
the measure of
CEB.
Reason:
Answers
Answer:
Angle AED = Angle CEB —> Opposite angles
So; Angle CEB = 95°
I hope I helped you^_^
∠AED and ∠CEB are opposite angles so they will be the same so ∠CEB will also 95°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
Two opposite angles become by the intersection of two lines will always same.
Since E is the intersection point so ∠AED and ∠CEB are opposite angles.
So,
∠AED = ∠CEB
∠CEB = 95°.
Hence "∠AED and ∠CEB are opposite angles so they will be the same so ∠CEB will also be 95°".
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Help please due today
Answers
Answer: Base = 3 Height = 8
Step-by-step explanation:
Base
9 to 1/3 = 3
Height
24 to 1/3 = 8
how to find endpoint? please give good explanation
Answers
Answer:
(-11 , -16)
Step-by-step explanation:
The midpoint will always be, as the term suggests, in the middle of the line segment. You simply need to find the distance for both x & y, and to apply that to the midpoint. In this case:
Endpoint (x₁ , y₁): (5 , 10)
Midpoint (x₂ , y₂): (-3 , -3)
Note that when finding distance, you will subtract the point₂ from point₁:
x: 5 - (-3) = 8
y: 10 - (-3) = 13
Therefore, each time you plot another point, you will be subtracting 8 from the x value, and 13 from the y value:
Endpoint (x₃ , y₃) = Midpoint (-3 , -3) + (_ - 8 , _ - 13) = (-11 , -16)
(-11 , -16) is your answer.
~
Using midpoint formula
[tex]\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]
[tex]\\ \rm\longmapsto (-3,-3)=\left(\dfrac{5+x_2}{2},\dfrac{10+y_2}{2}\right)[/tex]
Firstly
[tex]\\ \rm\longmapsto \dfrac{5+x_2}{2}=-3[/tex]
[tex]\\ \rm\longmapsto 5+x_2=2(-3)=-6[/tex]
[tex]\\ \rm\longmapsto x_2=-6-5[/tex]
[tex]\\ \rm\longmapsto x_2=-11[/tex]
Now
.[tex]\\ \rm\longmapsto \dfrac{10+y_2}{2}=-3[/tex]
[tex]\\ \rm\longmapsto 10+y_2==2(-3)[/tex]
[tex]\\ \rm\longmapsto 10+y_2=-6[/tex]
[tex]\\ \rm\longmapsto y_2=-6-10[/tex]
[tex]\\ \rm\longmapsto y_2=-16[/tex]
Hence the coordinates are
(x2,y2=(-11,-16)Help please! Find the area of the shape below. (Show work)
Answers
Answer:
292 yd²
Step-by-step explanation:
First you split the composite shape into two rectangle.
a) Horizontal rectangle - L × W
7 × 26 = 182 yd²
b) Vertical rectangle - L × W
5 × 22 = 110 yd²
Therefore 182 + 110 = 292 yd²
6 x 3 1/2.
Please help
Answers
Answer:
21
Step-by-step explanation:
6*3 = 18
1/2 = 0.5
6*0.5 = 3
18 + 3 = 21
Answer:
21
Step-by-step explanation:
6. Solve for x: 23x+1 = 210
Please please give detailed steps!! thank you
Answers
Answer:
x = 3
Step-by-step explanation:
Given
[tex]2^{3x+1}[/tex] = [tex]2^{10}[/tex]
Since bases on both sides are equal, both 2, then equate the exponents
3x + 1 = 10 ( subtract 1 from both sides )
3x = 9 ( divide both sides by 3 )
x = 3
linear equation 4x-1=9
Answers
Answer:
5/2 or 2.5
Step-by-step explanation:
4x-1=9
4x=9+1
4x=10
x=10/4
x=5/2 or 2.5
Answer:
x = 5/2
Step-by-step explanation:
4x - 1 = 9
4x - 1 + 1 = 9 + 1
4x = 10
4x/4 = 10/4
x= 5/2
Can someone help with this question?
Answers
Which would be used to solve this equation? Check all that apply.
р
=12
3
-
subtracting 3 from both sides of the equation
ОО
multiplying both sides of the equation by 3
dividing both sides of the equation by 3
substituting 4 for p to check the solution
O substituting 36 for p to check the solution
U
Answers
Answer:
Multply both side by 3
Step-by-step explanation: