Answer:
Max Value: x = 400
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x)Calculus
AntiderivativesIntegral Property: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Integration Method: U-Substitution[Integration] Reverse Power Rule: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1} + C[/tex]Step-by-step explanation:
Step 1: Define
[tex]f(x) = \frac{1}{\sqrt{800-2x} }[/tex]
Step 2: Identify Variables
Using U-Substitution, we set variables in order to integrate.
[tex]u = 800-2x\\du = -2dx[/tex]
Step 3: Integrate
Define: [tex]\int {f(x)} \, dx[/tex]Substitute: [tex]\int {\frac{1}{\sqrt{800-2x} } } \, dx[/tex][Integral] Int Property: [tex]-\frac{1}{2} \int {\frac{-2}{\sqrt{800-2x} } } \, dx[/tex][Integral] U-Sub: [tex]-\frac{1}{2} \int {\frac{1}{\sqrt{u} } } \, du[/tex][Integral] Rewrite: [tex]-\frac{1}{2} \int {u^{-\frac{1}{2} }} \, du[/tex][Integral - Evaluate] Reverse Power Rule: [tex]-\frac{1}{2}(2\sqrt{u}) + C[/tex]Simplify: [tex]-\sqrt{u} + C[/tex]Back-Substitute: [tex]-\sqrt{800-2x} + C[/tex]Factor: [tex]-\sqrt{-2(x - 400)} + C[/tex]Step 4: Identify Domain
We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.
Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.
Find the length of the rectangle if the perimeter is 244 yards the length is 18 less than three times the width?
Answer:
The Length of rectangle is 87 yards.
Step-by-step explanation:
Let width = w
Length = 3w-18
Perimeter of rectangle = 244 yards
We need to find length of rectangle.
First we need to find value of w
The formula used will be: [tex]Perimeter=2(length+width)[/tex]
Putting values and finding w
[tex]Perimeter=2(length+width)\\244=2(3w-18+w)\\244=2(4w-18)\\244=8w-36\\244+36=8w\\8w=280\\w=\frac{280}{8}\\w=35[/tex]
So, w= 35
The width of rectangle w = 35 yards
The length of rectangle l = 3w-18 = 3(35)-18 = 105-18 = 87 yards.
So, the Length of rectangle is 87 yards.
CAN SOMEONE PLEASE HELP ME!!
Consider the polynomial function h(x) = -7x6 + 3x4 – 5x2.
What is the end behavior of the graph of h ?
Answer: As x -> ♾, h(x) -> -♾, and as x -> -♾,h(x) -> -♾
Step-by-step explanation:
The end behavior is x ----> ∞ then h(x) ----> -∞, and when x ----> -∞ then h(x) -----> -∞.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
h(x) = -7[tex]x^6[/tex] + 3 [tex]x^4[/tex]– 5x².
If we plot the Equation on the Graph we can see a parabolic Curve.
This Curve tells as x tends to ∞ the value of h(x) tends to -∞.
and, when x tends to -∞ the value of h(x) tends to -∞.
Hence, the end behavior is x ----> ∞ then h(x) ----> -∞.
and, when x ----> -∞ then h(x) -----> -∞.
Learn more about Function here:
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A car covers a distance of 600 m in 2 minutes whereas a train covers a distance of 75 km in 50 minutes. Find the ratio of their speed.
answer
1:5
Step-by-step explanation:
To find speed use the formula
speed=distance/time
The car's speed is 600m ÷2mins(120secs)
(600÷120)
5m/s
The trains speed will be
speed=distance/time
=75÷50mins(5/6hrs)
=90km/hr
Ratio of their speed should be
first change the speed of the car 5 m/s to km/hr. 5×18/5 = 18km/hr
the speed of the train is 90km/hr
18:90 simplified it will be 1:5
i really need help asap
Answer:
D (-3, 1)
Step-by-step explanation:
help asap!!! it’s due in 20 minutes .
Answer:
ab
Step-by-step explanation:
Mr. Stip bought a new pair of Jordans and 4 new polo shirts. The price of one pair of jordans were double the amount of one polo shirt. If Mr. Stip spent $510, determine the price he paid for the Jordans.
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Answer:
$170
Step-by-step explanation:
If the price of a pair of Jordans is the same as the price of two shirts, the total purchase has a value equivalent to that of 3 Jordans.
pair of Jordans = $510/3 = $170
Answer:
$170
Step-by-step explanation:
Spencer bought gas for his four-wheeler from Gas World on Saturday. On Sunday, he bought the same amount of gas from Fuel Stop for less money. Now, Spencer has $20 to spend on gas for his car. Fuel Stop is on his way home. If the gas prices haven't changed, will Spencer be able to get more or less gas at Fuel Stop than at Gas World?
Answer:
Step-by-step explanation:
spencer bought the same amount of gas from gas world and fuel stop. since the gas cost less money at fuel stop, the gas is cheaper at fuel stop at gas world.
spencer has $20 to spend on gas for his car at fuel stop.
since the gas is cheaper at fuel stop, spencer will get MORE gas from fuel stop with his money.
hope this helped
If the gas prices haven't changed, will Spencer be able to get more gas at Fuel Stop than at Gas World
What is Number system?A number system is defined as a system of writing to express numbers.
Given,
Spencer bought gas for his four-wheeler from Gas World on Saturday
He bought the same amount of gas from Fuel Stop for less money on Sunday
Now, Spencer has $20 to spend on gas for his car.
since the gas cost less money at fuel stop, the gas is cheaper at fuel stop at gas world. spencer has $20 to spend on gas for his car at fuel stop. since the gas is cheaper at fuel stop, spencer will get MORE gas from fuel stop with his money.
Hence if the gas prices haven't changed, will Spencer be able to get more gas at Fuel Stop than at Gas World
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What is the equation in slope intercept form of the line that passes through the point (2,2) and is perpendicular to the line represented by y=2/5x + 2
Answer:
y=
Step-by-step explanation:
Perpendicular means opposite reciprocal of the slope. This means that the slope would change from 2/5 to 5/2 and add a negative, so it is -5/2.
y=-5/2x+b
2=-5/2 (2) +b
7=b
y=-5/2x+7
Tom will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of and costs an additional per mile driven. The second plan has an initial fee of and costs an additional per mile driven. How many miles would Tom need to drive for the two plans to cost the same?
Complete question :
Tom will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $57.98 and costs an additional $0.14 per mile driven. The second plan has an initial fee of $53.98 and costs an additional $0.16 per mile driven. How many miles would Tom need to drive for the two plans to cost the same?
Answer:
200 miles
Step-by-step explanation:
Let miles driven = x
First option :
57.98 + 0.14x
Second option :
53.98 + 0.16x
First option = second option
57.98 + 0.14 = 53.98 + 0.16x
57.98 - 53.98 = 0.16x - 0.14x
4 = 0.02x
x = 200
200 miles
Determine the simple interest paid to the nearest cent for each loan, interest rate, and time. $2,650, 3.65%, 2 1/2 years
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Answer:
$241.81
Step-by-step explanation:
The interest is given by the formula ...
I = Prt
Filling in the values and doing the arithmetic, we have ...
I = $2650×0.0365×2.5
I = $241.81
The simple interest paid is $241.81.
MARKING PEOPLE AS BRAINLIST ARE THE TRRIANGLES CONGRUENT HOW DO YOU KNOW? Please help thank you :)
Show work too I’ll mark you brainlist hurry lol
Answer:
1
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
[tex]e(x)=\frac{1}{5}x\\\\e(5)= \frac{1}{5}*5\\\\\boxed{e(5)=1}[/tex]
Hope this helps.
ANSWER ASAP look at pic and answer #18
Answer:
Four
Step-by-step explanation:
why does math have to be so hard
Answer:
Math seems difficult because it takes time and energy. Many people don't experience sufficient time to "get" math lessons, and they fall behind as the teacher moves on. Many move on to study more complex concepts with a shaky foundation. We often end up with a weak structure that is doomed to collapse at some point.
Math is hard because it is a non-intuitive, non-natural activity. Math don't happen by chance only, it only happens with deliberate, focused work. For this you expend a lot of energy and cause a lot of mental strain, you put yourself on an uncomfortable condition for hours, days, sometimes weeks to solve a problem.
But some people love math, like me, because they study math more than others. If you study more and learn more about math, then you’ll start to feel more comfortable because you’ll be ahead of the class when your teacher teaches you something.
The most important thing is to keep trying and never give up.
Hope this helps! :)
An 8-ounce bottle of lotion costs $4.50. Find the Unit Rate. hint: What is the cost per ounce?
Answer:
approximately 56 cents
Step-by-step explanation:
4.5/8
I am doing a percent equation problem and I need help please here’s the question 20% of blank =10
Answer:
[tex]50[/tex]
Step-by-step explanation:
Let [tex]x =[/tex] blank (for convenience)
[tex]20\%x=10[/tex]
[tex]0.2x=10[/tex] (change [tex]20\%[/tex] into its decimal form)
[tex]x = 10\div 0.2[/tex] (divide [tex]0.2[/tex] on both sides)
[tex]x=50[/tex]
∴ Blank = 50
Hope this helps :)
Please help me!!!!!! I really neeeeeeed
Answer:
A-(x+4,y-5)
B- move 1 unit left and 7 units down
Step-by-step explanation:
A- 4 units right is x so
(x+4,y__)
5 units down is y so
(x+4,y-5)
B- move 1 unit left and 7 units down
because (x-1,y__) is going left because of the subtraction sign and its the x-coordinate, and (x-1,y-7) is down because its a Y-coordinate and sub so its going down.
TIP- Going left/down is always subtract/negative going right/up is positive/addition.find slope and y-intercept formed the graph if the linear equation
y=1/4x-8
Answer:
not sure exactly what its asking but if its asking the slope and y-intercept of this equation is here.
Step-by-step explanation:
the slope is 1/4 while the y-intercept is -8 or (0,-8)
Answer: slope: 1/4
y-intercept: (0,-8)
Hope this helps and good luck :)
Step-by-step explanation:
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of jocelyns estimate?
Answer:
12%
Step-by-step explanation:
So 5.5 to 5.62 is .12
Then calculate the difference of 5.5 *.12=0.66
Then do “0.66 is what percent of 5.5?”
The answer is 12%
Thank you for reading, and mark this brainliest
What’s the slope of the line that passes through (-9, -4) and (6, 15).
The circumefreence of a circle is 37.8. What is the area of the circle? Use 3.14 for pie
Answer:
b
Step-by-step explanation:
circumference= 2πr
37.8cm = 2πr
r= 6 cm
Area= πr^2
area = 113cm^2
What is the area of rectangle CDEF?
Area= ...square units
Step-by-step explanation:
I think it's 48 square units
2 1/3 + 3 2/4 =
Fractions
Step-by-step explanation:
2 1/3+3 2/4=7/3+14/4
=28/12+42/12 (common denominater)
=70/12
=5 10/12
for a relation to be a function what must never happen
Answer:
Step-by-step explanation:
A function is a relation in which each input has only one output
so a relation cannot have more than one output
Answer:
each input (x-value) only has one output (y-value)
Step-by-step explanation:
you can use the vertical line test; pretend to draw vertical lines and if there are two point on the graph where the vertical line touches, it cannot be considered function.
Can someone do this please
There are 12 circles and 15 triangles. What is the simplest ratio of circles to triangles
Answer:
4:5
Step-by-step explanation:
Sheila has 14 1/2 pounds of potato salad. She wants to divide the potato salad into containers, each of which holds 1 1/4 pounds. How many containers does she need? Complete the explanation.
Answer:
11 3/5 containers
Equivalent to 11.6 containers
Step-by-step explanation:
Total pounds of potato salad = 14 1/2 pounds
Pounds in each container = 1 1/4 pounds
How many containers does she need?
Number of containers needed = Total pounds of potato salad / Pounds in each container
= 14 1/2 ÷ 1 1/4
= 29/2 ÷ 5/4
= 29/2 × 4/5
= (29×4) / (2×5)
= 116/10
= 11 6/10
= 11 3/5 containers
Equivalent to 11.6 containers
Which system of inequalities describes the graph?
Answer:
It Would be C (the third one)
Step-by-step explanation:
Please mark me Brainlyest PLZ
i neeed thiss pleaseeeeeee!!!!!!
Please help me out!!
Answer: C or B
Step-by-step explanation:
Answer:
its the first answer
Step-by-step explanation: