Answer:
The total amount of pollution discharged during the first 7 years of operation is 1.955 tons
Step-by-step explanation:
Given
[tex]r(t) = \frac{t}{t^2 + 1}[/tex]
Required
The total amount in the first 7 years
This implies that:
[tex]r(t) = \frac{t}{t^2 + 1}; [0,7][/tex]
The total amount is calculated by integrating r(t) i.e.
[tex]v = \int\limits^a_b {r(t)} \, dt[/tex]
So:
[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]
--------------------------------------------------------------
We have:
[tex]t^2 + 1[/tex]
Differentiate
[tex]d(t^2 + 1) = 2t[/tex]
Rewrite as:
[tex]2t = d(t^2 + 1)[/tex]
Solve for t
[tex]t = \frac{1}{2}d(t^2 + 1)[/tex]
---------------------------------------------------------------------------
So:
Make t the subject
[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]
[tex]v = \int\limits^7_0\frac{1}{2}* {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]
[tex]v = \frac{1}{2}\int\limits^7_0 {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]
Integrate
[tex]v = \frac{1}{2}\ln(t^2 +1)|\limits^7_0[/tex]
Expand
[tex]v = \frac{1}{2}[\ln(7^2 +1) - \ln(0^2 +1)][/tex]
[tex]v = \frac{1}{2}[\ln(50) - \ln(1)][/tex]
[tex]v = \frac{1}{2}[3.91 - 0][/tex]
[tex]v = \frac{1}{2}[3.91][/tex]
[tex]v = 1.955[/tex]
I need the answer HELP HELP HELP HELP
Answer:
A; TDC Inc., has 40 salespeople
B; Exactly half of the salespeople took fewer than 6 flights last year
F; Exactly half of the salespeople took at least 7 flights last year
The cost of making a shirt is half of what the shirt normally sells for. Today, however, the shirt is 15% discount feom it’s normal price. What is the current price of the shirt.
marks)
9 (b). The first two terms of an arithmetic progression are shown.
р
5p
The sum of the first three terms is 90
Work out the value of p.
9514 1404 393
Answer:
p = 6
Step-by-step explanation:
The difference between the first two terms is ...
5p -p = 4p
Since this is an arithmetic sequence, the next term will be 4p more than the last term:
5p +4p = 9p
Then the sum of the first three terms is ...
p + 5p + 9p = 90
15p = 90 . . . . . . . . . . collect terms
p = 6 . . . . . . . . . . . . divide by 15
_____
The first three terms are 6, 30, 54.
Estimate the sum of the decimals below by rounding to the nearest whole number.
6.802
6 1844
+ 6.318
Answer:
19
Step-by-step explanation:
6.802 = 7
6.1844 = 6
6.318 = 6
7 + 6 + 6 = 19
I hope this helps!
Find the volume of the cone. Round your answer to the nearest hundredth.
Answer:
I believe the answer is 1.36
Find the length of the arc in terms of pi A 144° 10 AB = [?]
Answer:
arc AB = 144°/360° x 2π x 10
= 2/5 × 20π = 8π
Solve the Exponential Equation:
[tex]5 { }^{66} = {3}^{42} [/tex]
find the length of the missing side
help!
Answer:
B would be 72 using a^2+b^2=c^2
Step-by-step explanation:
30^2 + x =78^2
in other words
900 + x =6084
6084-900= 5184
The square root of 5184 is 72
round to the nearest thousand 83,243 answer
Answer:
83,000
Step-by-step explanation:
Thousand = 1,000s place
1,000s place of 83,243 is the 3 (3,000)
The number right before 3 is the 2 (200)
2 is closer to zero than 10 so it rounds down
83,243 then becomes 83,000 since the other numbers before the (2) round down with it.
los trabajadores de una mina se encuentran a 20 metros bajo tierra .Si excavan 3 metros desde alli suben otros 8 metros para coger una caretilla a que altura estaba la carretilla
Answer:
carretilla
Step-by-step explanation:
la carretilla se encontraba a unos 18 metros de altura
Sarah's vegetable soup recipe uses 2
cups of vegetables to make one pot of soup. She wants to triple the recipe.
How many cups of vegetables does she need?
Answer:
No.of cups for one soup : 2 cups
No.of cup for 3 soups: 2×3
=6
So , 6 cups of vegetable
HOPE IT HELPS U :)
Find the equation of the line that contains the points (-4,3) and (4,3).
Answer:
yes
Step-by-step explanation:
PLEASE ANSWER ASAP!!! I WILL MAKE YOU BRAINLIST Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
15
Step-by-step explanation:
a^2 + b^2 = c^2
20^2 +b^2 = 25^2
400 + b^2 = 625
-400 -400
b^2 = 225
b = √225
b = 15
The formula distance =rate x time (d = ) tells how far an object travels at a certain rate (speed) over a certain time
How long will it take a train to travel 765 miles at 85 tniles per hour?
Answer:
42.05 HRS
Step-by-step explanation:
D = R x T ..... D=765 MILES R= 95 MILES/HR WE HAVE TO SOLVE FOR T BECAUSE THE QUESTIONS ASKS "HOW LONG.." T = D/R AND THEN SUBSTITUTE THE DISTANCE AND RATE ;)
If h(x) = x - 7 and g(x) = x², which expression is equivalent to (gºf)(5?
O (5-7)2
(5)²-7
O (5)? (5 – 7)
O (5-7) x²
Answer:
(5^2)(5-7)
Step-by-step explanation:
So we know h(x)=x-7.
We also know g(x)=x^2
We need to plug in these values for (g*h)(5)
This would equal:
((x-7)*x^2)(5)
Since parthese can also be considered multipcation symbols, we can think of this as:
(x-7)(x^2)(5)
Lets distrubute the 5 to all the x's:
(5-7)(5^2)
Which is:
([tex]5^{2}[/tex])(5-7)
This looks like answer C.
Hope this helps!
Solve the proportion: 144/a = 9/4
a=?
Step-by-step explanation:
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A baseball pitching coach charges $90 for 2.5 hours of training. If you train for 9 hours in one week, how much will that cost for the week, in dollars?
Answe$324
Step-by-step explanation:
First you divide 9 by 2.5 to get 3.6 which is how many times you practiced for 2.5 hours
Next you multiply 3.6 by 90 to get 324
Fabric is stretched over the wooden frame below What is the total area of the fabric? Round to the nearest square inch
Answer:
72 in²
Step-by-step explanation:
We obtain the value of EC:
From Pythagoras :
EC = √CD² - DE²
EC = √10² - 6²
EC = √100 - 36
EC = √64
EC = 8
To obtain AE:
AE = √AB² - BE²
AE = √(√52)² - 6²
AE = √52 - 36
AE = √16
AE = 4
Hence, we can obtain the areas of each triangle :
△ABE = △ADE
△BCE = △CDE
AREA OF △ABE = 1/2 * base * height
= 1/2 * 4 * 6 = 12 in²
AREA OF △BCE = 1/2 * base * height
= 1/2 * 6 * 8 = 24 in²
HENCE, total area of fabric :
(2 * 12) + (2 * 24)
24 in² + 48 in²
= 72 in²
My exam, does any one know the answer
Answer:
D) 7
Step-by-step explanation:
Five times a number=5x
added to 4= 5x+4
[tex]5x+4=39[/tex]
[tex]5x=35[/tex]
[tex]x=7[/tex]
So, the number is 7.
Write the inverse function for the function, ƒ(x) =1/2 x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) =
ƒ -1(4) =
Answer:
0
Step-by-step explanation:
Given that f(x) = 1/2x + 4
Let y = f(x)
y = 1/2 x + 4
Replace y with x
x = 1/2 y + 4
Make y the subject of the formula
1/2y = x - 4
y = 2(x-4)
If x = 3
y = 2(4-4)
y = 2(0)
y = 0
Hence ƒ -1(4) is 0
A line passes through (-3,-2) and is perpendicular to 3x - 2y = 7.
What is the equation of the line in slope-intercept form?
Answer:
y=-2/3x
Step-by-step explanation:
Perpendicular gradients(slopes) are negative reciprocals so first rearrange the given equation to find the gradient. y=3/2x-7/2
the gradient of the new line will be m=-2/3 then use the point (-3,-2) to find the equation of the line
y=mx+b
-2=(-2/3)(-3)+b
-2=2+b
b=0
y=-2/3x
The graph shows the relationship between tablespoons and teaspoons. Determine a rule that relates the number of tablespoons by writing the correct term or value from the tiles in each blank.
Answer:
Multiply
1/3
Step-by-step explanation:
You can divide by 3 or multiply by 1/3. Since it looks like 3 is grayed out, I guess you have to use the latter.
Jeff and Eric roommates and enjoy talking about sports. They mainly discuss their favorite professional soccer teams. Jeff enjoys European soccer whereas Eric prefers American teams. Outside soccer they do not discuss much. Their lack of range of talking to it fall into which category?
0°
EXPLANATION:In each figure below find m∠1 and m∠2, if a||b. Show your work with statements.
====================================
If you have any questions feel free to ask me^^
Have a nice and great day!
Cayler#PilipinasAngBayanKo
0°
Sana Maka help ako tnx
I’m back again :( Please anybody help me
Welcome back....♡
Surface area = 2( 4 × 2 ) + ( 3 × 4 )
+ 2( 4 × 4 ) + 3( 10 × 4 )
+ 3( 4 × 7 )
Surface area = 16 + 12 + 32 + 120 + 84
Surface area = 264 in^2
If 3(x - 1) – 5(x – 3) = 3, find the value of 7x-5.
Answer:
36.5
Step-by-step explanation:
First solve for x
Factor:
3x-3-5x+15 = 3
Combine Like Terms:
-2x+12=3
-2x = -9
x = 4.5
PLug it in:
7(4.5)-5
31.5-5
36.5
[tex]{\boxed{\mathcal{\red{Step-by-step\:explanation:-}}}}[/tex]
[tex]3(x - 1) - 5(x - 3) = 3 \\ ⇝3x - 3 - 5x + 15 = 3 \\ ⇝ - 2x + 12 = 3 \\ ⇝ - 2x = 3 - 12 \\ ⇝x = \frac{ - 9}{ - 2} \\ x = 4.5[/tex]
To verify:
[tex]3(4.5 - 1) - 5(4.5 - 3) = 3 \\ ✒ \: 13.5 - 3 - 22.5 + 15 = 3 \\ ✒ \: 28.5 - 25.5 = 3\\✒\: 3 = 3[/tex]
✒ L. H. S. = R. H. S.
[tex]\sf\pink{Hence\:verified.}[/tex] ✔
Now,
7 [tex]x[/tex] - 5 = 7 x 4.5 - 5
= 31.5 - 5
= 26.5
[tex]\sf\purple{Therefore,\:the\:value\:of\:''7\:x-\:5''\:is\:26.5.}[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Find the value of y in the equation. 3/y-2=8
Answer: 19/8 or 2 and 3/8
Step-by-step explanation:
Am I correct? K
Thanks for helping!
PLEASEEE CHECK ME WORK!
Answer:
yes you are correct on all of them good job
Can someone please help me?
Answer:
yes i can
Step-by-step explanation:
Answer:
(2,7)
Step-by-step explanation:
Order from least to greatest
1/8, 11/12, 9/8
Answer:
Step-by-step explanation:
First make the denominators the same.
Take the LCM of (8, 12 , 8) = 24
So,
[tex]\frac{1}{8}, \frac{11}{12}, \frac{9}{8} \ becomes \ \frac{3}{24}, \frac{22}{24}, \frac{27}{24}[/tex]
[tex]Order \ from \ least \ to \ greatest \ \\\\\frac{3}{24} < \frac{22}{24} < \frac{27}{24}[/tex]
That is,
[tex]\frac{1}{8}, \frac{11}{12}, \frac{9}{8}[/tex]
Extremely STUCK on this one help!