Answer:
the equation is
Y-y = -33
-33y
SOMEONE HELP PLZ 20 POINTS
JUST NEED HELP IN THE LAST 4
Answer:
the last one is
four cubed plus 8 to the 4th power
4^3 + 8^4
4160
Step-by-step explanation:
Find a primitive Pythagorean triplet (a, b, c) where c=a+50.
Answer:
Pythagorean triple (PT) can be defined as a set of three positive whole numbers that perfectly satisfy the Pythagorean theorem: a2 + b2 = c2.
theorem: a2 + b2 = c2.
This set of numbers are usually the three side lengths of a right triangle. Pythagorean triples are represented as: (a, b, c), where, a = one leg; b = another leg; and c = hypotenuse.
There are two types of Pythagorean triples:
Primitive Pythagorean triples
Non-primitive Pythagorean triples
Primitive Pythagorean triples
A primitive Pythagorean triple is a reduced set of the positive values of a, b, and c with a common factor other than 1. This type of triple is always composed of one even number and two odd numbers.
For example, (3, 4, 5) and (5, 12, 13) are examples of primitive Pythagorean triples because each set has a common factor of 1 and also satisfies the
Step-by-step explanation:
Pythagorean theorem: a2 + b2 = c2.
(3, 4, 5) → GCF =1
a2 + b2 = c2
32 + 42 = 52
9 + 16 = 25
25 = 25
(5, 12, 13) → GCF = 1
a2 + b2 = c2
52 + 122 = 132
25 + 144 = 169
169 = 169.
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a student sketched some art on an 8 inch x 10 inch piece if paper he wants to resize it to fit an 4 inch x 6 inch frame. What percent of the original sketch was still able to be included?
The spread of a virus is modeled by V (t) = −t 3 + t 2 + 12t,
where V (t) is the number of people (in hundreds) with the virus and t is the number of weeks since the first case was observed.
(a) Sketch V (t).
(b) What is a reasonable domain of t for this problem?
(c) Find the average rate of infection from t = 0 to t = 2.
(d) Find the instantaneous rate of infection as a function of t using the limit definition of the derivative.
(e) Find V (2) and V ‘ (2). Write a sentence interpreting V (2) and V ‘ (2) in terms of the number of infected people. Make sure to include units.
(f) Sketch the tangent line to the graph you drew in a. at the point (2, V (2)). State the slope of the tangent line.
(g) Use V (2) and V ‘ (2) to estimate the value of V (2.1).
(h) Find the maximum number of people infected at the same time and when the maximum occurs. Determine the rate of infection at this time.
Functions can be used to model real life scenarios
The reasonable domain is [tex]\mathbf{[0,\infty)}[/tex].The average rate of change from t = 0 to 2 is 20 persons per weekThe instantaneous rate of change is [tex]\mathbf{V'(t) = -3t^2 + 2t + 12}[/tex].The slope of the tangent line at point (2,V(20) is 10 The rate of infection at the maximum point is 8.79 people per weekThe function is given as:
[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
(a) Sketch V(t)
See attachment for the graph of [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
(b) The reasonable domain
t represents the number of weeks.
This means that: t cannot be negative.
So, the reasonable domain is: [tex]\mathbf{[0,\infty)}[/tex]
(c) Average rate of change from t = 0 to 2
This is calculated as:
[tex]\mathbf{m = \frac{V(a) - V(b)}{a - b}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{V(2) - V(0)}{2}}[/tex]
Calculate V(2) and V(0)
[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]
[tex]\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}[/tex]
So, we have:
[tex]\mathbf{m = \frac{20 - 0}{2}}[/tex]
[tex]\mathbf{m = \frac{20}{2}}[/tex]
[tex]\mathbf{m = 10}[/tex]
Hence, the average rate of change from t = 0 to 2 is 20
(d) The instantaneous rate of change using limits
[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
The instantaneous rate of change is calculated as:
[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex]
So, we have:
[tex]\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}[/tex]
[tex]\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}[/tex]
Expand
[tex]\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex][tex]\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex]
Subtract V(t) from both sides
[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}[/tex]
Substitute [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]
[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}[/tex]
Cancel out common terms
[tex]\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}[/tex]
[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex] becomes
[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}[/tex]
[tex]\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}[/tex]
Limit h to 0
[tex]\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}[/tex]
[tex]\mathbf{V'(t) = -3t^2 + 2t + 12}[/tex]
(e) V(2) and V'(2)
Substitute 2 for t in V(t) and V'(t)
So, we have:
[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]
[tex]\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}[/tex]
Interpretation
V(2) means that, 20 people were infected after 2 weeks of the virus spread
V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week
(f) Sketch the tangent line at (2,V(2))
See attachment for the tangent line
The slope of this line is:
[tex]\mathbf{m = \frac{V(2)}{2}}[/tex]
[tex]\mathbf{m = \frac{20}{2}}[/tex]
[tex]\mathbf{m = 10}[/tex]
The slope of the tangent line is 10
(g) Estimate V(2.1)
The value of 2.1 is
[tex]\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}[/tex]
[tex]\mathbf{V(2.1) = 20.35}[/tex]
(h) The maximum number of people infected at the same time
Using the graph, the maximum point on the graph is:
[tex]\mathbf{(t,V(t) = (2.361,20.745)}[/tex]
This means that:
The maximum number of people infected at the same time is approximately 21.
The rate of infection at this point is:
[tex]\mathbf{m = \frac{V(t)}{t}}[/tex]
[tex]\mathbf{m = \frac{20.745}{2.361}}[/tex]
[tex]\mathbf{m = 8.79}[/tex]
The rate of infection is 8.79 people per week
Read more about graphs and functions at:
https://brainly.com/question/18806107
Express the number in terms of i
Answer:
[tex]\sqrt[]{9} i[/tex]
Step-by-step explanation:
[tex]\sqrt[]{ab}=\sqrt[]{a} *\sqrt[]{b} \\Therefore, \sqrt[]{-9} =\sqrt[]{9}*\sqrt[]{-1} \\\\\sqrt[]{-1}=i\\\\So, \sqrt[]{-9}= \sqrt[]{9}i[/tex]
Help me please!!!!!✨✨✨✨✨✨✨✨✨✨
A batting machine uses an automatic baseball feeder. During baseball
practice the feeder is a full. An attendant fills it with 15 baseballs so
that the feeder is now full. How many baseballs does the feeder
hold when full?
A. Write an equation to represent the problem.
The feeders in battling machine are represented in proportions and fractions.
The equation that represents the problem is: [tex]\mathbf{\frac 16x + 15 = \frac 23x}[/tex]The feeder can hold 30 baseballs, when fullThe given parameters are:
[tex]\mathbf{Initial = \frac 16x}[/tex] ------ 1/6 full
[tex]\mathbf{Additional = 15}[/tex] --- baseballs added
[tex]\mathbf{Final = \frac 23x}[/tex] ---- 2/3 full
So, the equation that represents the problem is:
[tex]\mathbf{Initial + Additional = Final}[/tex]
So, we have:
[tex]\mathbf{\frac 16x + 15 = \frac 23x}[/tex]
The number of baseballs it can hold is calculated as follows:
[tex]\mathbf{\frac 16x + 15 = \frac 23x}[/tex]
Multiply through by 6
[tex]\mathbf{x + 90 = 4x}[/tex]
Collect like terms
[tex]\mathbf{4x - x = 90 }[/tex]
[tex]\mathbf{3x = 90 }[/tex]
Divide through by 3
[tex]\mathbf{x = 30 }[/tex]
Hence, the feeder can hold 30 baseballs, when full
Read more about proportions and fractions at:
https://brainly.com/question/20337104
If p<0,q>0 and q=r what statement about is r true
Answer:
hell no
Step-by-step explanation:
bbbb
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answer:
All you have to do is divide 896 ÷ 32 which is 28 and multiply is by 3 since its 3 more nights and the answer is 84 centimeters.
Complete the multiplication problem to find the answer
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
Doug entered a canoe race. He rowed 3 1/2 miles in 1/2 hour what is his average speed in miles per hour
Answer: 7 miles per hour
Step-by-step explanation:
3 1/2 miles = 7/2 miles
1/2 hours= 30 minutes
So,
In 30 mins, travelled 7/2 miles
In 1 min, travelled 7/2 ÷ 30= 7/2× 1/30 = (7×1)/(2×30) = 7/60 miles
In 60 mins, travelled (7×60)/60 miles = 420/60 miles = 7 miles.
Hence, the speed is 7 miles per hour.
If 2.5 kg of potatoes cost $8.25 how much will u pay for 7 kg
Answer:
$23.10
Step-by-step explanation:
To get how much money you will have to pay for 7kg, you need to find out how much you have to pay for 1 kg. You will divided y divided by x = y.
8.25 (y) divided by 2.5 (x) = $3.30
You will pay $3.30 for 1 kg
So $3.30 x 7 = 23.10
You will pay $23.10 for 7 kg of potatoes.
** I hope this helps
Determine the midpoint of segment CD
Answer:
9
Step-by-step expation:
One gallon of water weighs approximately 8 1/3lbs. How much does 25 3/4 gallons of water weigh?
Please answer the following question:
Answer:
l
Step-by-step explanation:
The water level in a lake was monitored and was noted to have changed −1 1/5 inches in one year. The next year it was noted to have changed −1 3/10 inches.
What was the total change in the water level over the two years?
Enter your answer as a simplified mixed number by filling in the boxes.
$$
in.
Answer:
-2 1/2
Step-by-step explanation:
Prove the polynomial identity.
(4x^2−2)^2−(4x^2)^2=4(1−2x)(1+2x)
Drag and drop the lines of the proof in the correct order to complete the proof.
Answer:
(4x^2 - 2)^2 - (4x^2)^2 = 4(1 - 2x)(1 + 2x)
16x^4 - 16x^2 + 4 - 16x^4 = 4(1 - 2x)(1 + 2x)
4 - 16x^2 = 4(1 - 2x)(1 + 2x)
4(1 - 4x^2) = 4(1 - 2x)(1 + 2x)
4(1 - 2x^2)(1 + 2x) = 4(1 - 2x)(1 + 2x)
Find all exact solutions on the interval [0,2π) csc^2(x)-9= -5
Answer:
d
Step-by-step explanation:
Graph the ordered pair solutions of y = |x+2| when x = -5, -3, 0, 3, and 5
The perimeter of the rectangle below is 50cm.
find the value x
Answer: 13
Step-by-step explanation:
12 x 2 = 24 (because of the two sides)
50 - 24 = 26 (to find the remaining amount)
26 / 2 = 13 (to equally distribute the remaining amount.)
PLEASE HELP ME AND HURRY TOO NO LIBKS PLEASE I WILL GIVE BRAINLIEST
Which expressions are equivalent to?
Answer:
-6(b+2) +8
= -6b -12 +8
= -6b -4
Step-by-step explanation:
Is seven radical 2 rational?
If seven radical 2 means [tex]7\sqrt{2}[/tex], then the number is irrational.
It means that it goes on and on after the decimal place.
√2 is a surd, so it's irrational.
Mark deposit $ 200 into an account that pays an interest rate 3.5% compounded annually. He doesn't add or remove from his account for 4 years how much money will markbhave in 4 years
Answer:
30,012.5
Step-by-step explanation:
We power the number by itself for the past years so in this it will be 3.5 powered by itself four times equaling 150.0625 multiplied by the first deposit which is 200 so 200*150.0625= 30,012.5
Hope this helps
The sum of two consecutive odd numbers Is 364. Find the larger number.
Answer:
183
Step-by-step explanation:
If they are two consecutive odd numbers, than these two numbers will be close to half of the sum (364).
364/2=182
Now Find the two odd numbers in between 182, which are 181 and 183.
I had this type of question a few times recently, and this method worked every time :).
Bonus information:
For two consecutive odd/even numbers, find the half of the sum.
For three consecutive odd/even numbers, start off by finding the third of the sum. And so on...
Hope this helped! :D
A gardener will use up to 220 square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least twice the area used for flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of x and y that satisfy these requirements.
The scale of the drawing was 5 inches = 4 yards. What is the drawing's scale factor? Simplify your answer and write it as a fraction
Answer:
138889/144
Step-by-step explanation:
Solve: 1 × -23 = Question 9 options: -1 1 23 -23
Answer:
-23
Step-by-step explanation:
1 × -231. When multiply a positive number by a negative number, the answer will always be negative.
2. When we multiply any number by 1, that number will stay the same.
[tex]1 * -23[/tex] [tex]-23[/tex]Therefore, the answer is -23!
due at 5:30 help asap!! look at the photo
Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table
Answer:
First one is equivalent second one is not equivalent
Step-by-step explanation:
Which table can be represented by a line?
A)
А
B)
B
C С
D
D
Step-by-step explanation:
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