The instantaneous rate of change of power with respect to velocity is 1.6 W/mph.
What is the rate of change function?
The pace at which one quantity changes in relation to another is known as the rate of change function.
Given, P = 0.015[tex]V^{3}[/tex]
Differentiating P with respect to V:
P′=(0.015)(3)[tex]V^{2}[/tex]
At V = 5.9 mph, then
P′=(0.015)(3)[tex]5.9^{2}[/tex] = 1.6 W/mph
Hence, the instantaneous rate of change of power is 1.6 W/mph.
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A car travels 120 miles and one and a half hours what is the average speed for miles per hour
Answer:
80
Step-by-step explanation:
120 divided by 3 (for per half hr) is 40 and if you add 2 of the half hrs together (40+40) its 80
HELP THANKS SO MUCH!!!!!!
Answer:
.62 each
Step-by-step explanation:
A function's graph is shown below.
If you would like to enlarge the graph or make numbers and letters easier to read, you may click on it to open it in a new window. You may then enlarge that window with your mouse. To further enlarge the image, use your browser's zoom capabilities. On a PC this is usually ctrl shift + (and zooming out is ctrl -). On an Apple computer this is usually apple shift + (and zooming out is apple -).
Use interval notation to answer the following questions.
The domain of this function is ?
The range of this function is ?
The domain and the range of the function are given as follows:
Domain: (-2,3].Range: [-8, 2).How to obtain the domain and the range of the function?The domain of a function is composed by the set that contains all possible values assumed by the input of the function.
On a graph, the input of the function is given by the values of x, hence the domain of the graphed function is given by the following interval:
(-2,3].
The meaning of the circles on the intervals is of:
Open circle: open interval.Closed circle: closed interval.The range is composed by the set containing all the values assumed by the output of the function.
Hence, on the graph, the range is composed by the values of y of the function, which are given as follows:
[-8, 2).
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4) The trapezoid I'J'K'L' is a dilation of the trapezoid IJKL. What is the scale factor of the
dilation?
I
-10 -8 -6 -4
I'
~
104
8
6
4
2
2
-4
-6
-8
L'
L
J'
K'
4
6
J
K
10
10
4) Simplify your answer and write it as a proper fraction, an improper fraction, or a whole
number.
Answer:4
Step-by-step explanation:
16/4=4
The scale factor of the dilation is, 1/4.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The trapezoid I'J'K'L' is a dilation of the trapezoid IJKL.
Here, The length of IJ = 16
And, The length of I'J' = 4
Hence, The scale factor of the dilation is,
⇒ I'J' / IJ = 4 / 16
= 1/4
Thus, The scale factor of the dilation is, 1/4.
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Montraie has 1 1/2 cups of yogurt to make smoothies. Each smoothie uses cup of 3/4 yogurt. How many smoothies can Montraie make with the yogurt?
Montraie can make 2 cups of smoothies with the yogurt
How to determine the number of smoothies in the yogurtFrom the question, we have the following parameters that can be used in our computation:
Cups of yogurt = 1 1/2
Each smoothie = 3/4 yogurt
Assume there exist a proportional relationship between the cups and the yogurt
The number of smoothies in the yogurt can be calculated using the following equation
Smoothies = (1 1/2)/(3/4)
Evaluate the quotient
Smoothies = 2
Hence, the cups is 2 yogurt
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Determine the domain of the rational function ƒ(a) = 3/a+5
Answer:
domain { a ∈ R , a ≠ - 5 }
Step-by-step explanation:
the denominator of f(a) cannot equal zero as this would make f(a) undefined. Equating the denominator to zero and solving gives the value that a cannot be.
a + 5 = 0 ( subtract 5 from both sides )
a = - 5 ← excluded value
domain { a ∈ R, a ≠ - 5 }
Can anyone help me? Thank you
Answer:162
Step-by-step explanation:
1.5 ft = 18 inches
so
9 * 18 = 162
A population of lizards in a large region doubles every year. The number of lizards can be
modeled by the equation y = 500 * 2 ^ x where
× is the number of vears after a researcher
measures the population size . When x = - 3
-3what does the value of y represent ?
The value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the given equation of is, y = 500×2ˣ
We have to find the value of y when x = - 3.
y = 500×2ˣ
y=500×2⁻³
y=62.5
Thus, the value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.
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Please help I was sick and missed out on class.Thank you
Answer:
Step-by-step explanation:
Start with y intercept (Where the line crosses the y-axis)
You place the first dot on (0,2)
Negative slope goes down
For the second dot, you go down one and move two to the right
What is 4 1/4 x (-12.2)?
(x+1)+(x+4)+(x+7)+...+(x+40)=442
The value of the unknown variable x in the given sequence is; 14
What is the sum of the Arithmetic Sequence?
The formula for sum of an arithmetic sequence is;
Sₙ =ⁿ/₂(2a + (n − 1)d)
where;
a is first term
d is common difference
n is position of term
We are given the sequence as;
(x + 1) + (x + 4) + (x + 7) +...+ (x + 40) = 442
The common difference is;
x + 4 - (x + 1)
= 3
Now, to get the number of terms, we will say that the function follows the pattern;
aₙ = (x + 1) + 3n
Thus;
(x + 1) + 3n = x + 40
3n = 39
n = 13
Thus, there are n = 13 terms
Sₙ = ¹³/₂(2(x + 1) + (14 − 1)3) = 442
6.5(2x + 40) = 442
2x + 40 = 442/6.5
2x = 68 - 40
x = 28/2
x = 14
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HELP ME OUT THANKS SO MUCH
Answer:
R would equal 12
Step-by-step explanation:
Ashley's company makes solid spherical balls out of scrap metal for various industrial uses. A large order just came in to make aluminum balls with a radius of 4.5 in. If Ashley uses 74,325in^3 on average, of aluminum each day making these balls, how many balls does she make, on average, each day?
Using the formula of volume of a sphere, Ashely's company made 195 balls
Volume of SphereThe volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.
The formula of volume of a sphere is given as
v = 4/3πr³
r = radius = 4.5in
volume of each spherical ball = 4/3π(4.5)³
volume of sphere = 381.7in³
The number of balls she made from 74325 in³ can be found by dividing it by 381.7in³
Number of balls = 194.7≅195 balls
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what is the value of the expression 0.307+13.16+0.8
Answer:
The Answer of the 0.307+13.16+0.8 is 14.267
(01.06 MC)
Solomon invested money in his bank account. He had a principal, P,
of $100 in his account at the beginning of the period, which
increased at a rate, r, of 0.15 per year. At the end of the period, he
had interest, I, of $135 in his account. Use the simple interest
formula 1 = Prt, to solve for the time, t, in months that it took to
earn this amount. (1 point)
Answer:
700 months
Step-by-step explanation:
Express cos L as a fraction in simplest terms.
15
39
K
36
The representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.
What are trigonometric ratio?
The ratio of sides of a right angled triangle is known ars trigonometric ratios. There are six trigonometric ratios. Which are as follows:
sin = P/H, cos = B/H, tan = P/B
cosec = H/P, sec = H/B, cot = B/P
Here, P is perpendicular, H is hypotaneous, and B is base. These ratios simplify the calculation.
SInce the angle is not specified hence, consider the given angle is L. Now, L is given angle hence, the base will be 15 and hypotenous will be 39.
Now, consider the trigonometric ratio of cos.
[tex]cosL=\frac{Base}{Hypotenuse}\\[/tex]
Subsitute 15 for base and 39 for hypotenuse in the above expression.
[tex]cosL=\frac{15}{39}\\=\frac{5}{13}[/tex]
Hence, the representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.
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Which of the following is a requirement for employees who must wear PPE?
The option that's a requirement for employees who must wear PPE is C. Participate in PPE training.
What is a personal protective equipment?Personal protective equipment (PPE) is clothing that is comfortable to wear in order to reduce the risk of hazards at work that cause serious illnesses and injuries.
Personal protective equipment (PPE) will be divided into the following categories for this purpose: eye and face protection, hand protection, body protection, respiratory protection, and hearing protection.
Personal protective equipment (PPE) should be used when all other measures to control exposure are ineffective. It only protects the wearer while they are wearing it. PPE offers no protection if it fails.
All personal protective equipment should be designed and built safely, and it should be kept clean and reliable. It should be comfortable for workers to use. Personal protective equipment that does not fit properly can mean the difference between being safe and being dangerously exposed. Employers must provide personal protective equipment to their employees and ensure its proper use when engineering, work practices, and administrative controls are not feasible or provide adequate protection
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Complete question
Which of the following is a requirement for employees who must wear PPE?
a. Speak to the. project manager.
b. Get necessary clothes.
C. Participate in PPE training.
Given L(-6, -7) and M(3, 6), what is the length of LM to the nearest tenth?
LM
Answer:
LM ≈ 15.8
Step-by-step explanation:
calculate the length d using the distance formula
d = [tex]}\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = L (- 6, - 7 ) and (x₂, y₂ ) = M (3, 6 )
LM = [tex]\sqrt{(3-(-6))^2+(6-(-7))^2}[/tex]
= [tex]\sqrt{(3+6)^2+(6+7)^2}[/tex]
= [tex]\sqrt{9^2+13^2}[/tex]
= [tex]\sqrt{81+169}[/tex]
= [tex]\sqrt{250}[/tex]
≈ 15.8 ( to the nearest tenth )
When Terri makes fruit salad she uses 4 oranges and 3 cups of grapes for every 2 bananas. If Terry uses five bananas how many oranges and how many cups of grapes will she use? Write and solve a proportion
Answer:
7.5 cups of grapes
Step-by-step explanation:
4o:3g:2b
With 5b, there's an increase in 2.5 from 2b. (divide 5b/2b)
Since the increase in all the other fruits is proportional by the same amount of 2.5.
This leaves you with 10o:7.5g:5b
If the simple interest on $2000 for 4 years is $480, then what is the interest rate?
Answer: 6%
Step-by-step explanation:
R=100×480/2000×4
R=6%
Answer:
R
=
6
%
Step-by-step explanation:
The formula for Simple Interest is
S
I
=
P
R
T
100
Change the subject to be R.
R
=
100
×
S
I
P
T
Once that is done, we just need to substitute the values.
R
=
100
×
480
2000
×
4
R
=
6
%
Solve using order of operations
16÷2×6-3
The Order of Operations, also referred to as PEMDAS, is the rule that defines the sequence in which an expression with multiply operations can be solved.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this scenario, we are dividing, multiplying, adding, and subtracting numbers. This being laid out, lets begin.
1. Multiply and divide (left to right).
[tex]16[/tex] ÷ [tex]2 * 6 = 48[/tex]
[tex]=48-3[/tex]
2. Add and subtract (left to right).
[tex]48-3=45[/tex]
Hence, our final solution after using the order of operations would be [tex]45[/tex].
Hope this helps!
need help pelase i need it
Door:80( actual height) 44( height on set)
Table 28( actual height) 15.4 ( height on set)
Stool 18 ( actual height) 9.9 ( height on set)
Step-by-step explanation:
Times the actual height inches by 0.55 and you get your height on set.
A triangular banner for the basketball championship hangs in the gym. It has an area of 48 square feet. What is the length of the base and height (in ft), if the base is two-thirds of the height?
From the area of a triangle, the height of the triangle is 12ft
Area of TriangleThe area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, which is given by
A = 1/2 b * h
A = Area of triangleb = baseh = heightIn the given question, the base is two-thirds of the height.
b = 2/3h
Let's substitute the values into the formula
A = 1/2 * 2/3h * h
A = 2/6 * h²
A = 1/3h²
48 = 1/3h²
h² = 48 * 3
h = √144
h = 12ft
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kay walks upstairs yo make her legs stronger . Every day at work, she walks up 9 flights of stairs . If there are 13 steps in 1 flight of stairs in 1 flight of stairs , how many steps does kay climb in 5 days at work
In 5 days at work, kay climbs 585 steps
How to find how many steps kay climbsIf there are 13 steps in 1 flight of stairs then 9 flights of stairs will be
= 13 * 9
= 117 steps
Every day Kay climbs 117 steps in 9 flights in 5 days kay will climb
= 117 * 5
= 585 steps
Kay climbs 585 steps in a 5 days at work
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-4x+11y=-32
-9x+4y=11
elimination
Answer:
x = -3; y = -4
Step-by-step explanation:
We can start by eliminating x, which will give us y:
[tex]9(-4x +11y=-32)\\-4(-9x+4y=11)\\\\-36x+99y=-288\\36x-16y=-44\\\\83y=-332\\y=-4[/tex]
Now we can plug in -4 for y in the first equation to find x:
[tex]-4x+11(-4)=-32\\-4x-44=-32\\-4x=12\\x=-3[/tex]
Which equation is perpendicular to y = 2/3 x - 4?
a. y = -3/2 x + 4
b. y= 2/3 x - 4
c. y = -2/3 x + 4
d. y = 3/2 x - 4
Answer:
Your answer is A) [tex]y=-\frac{3}{2}x-4[/tex]
Step-by-step explanation:
This is because the slope of a perpendicular line is a negative reciprocal in relation to the original line. In this example, [tex]\frac{2}{3}[/tex] is flipped to [tex]-\frac{3}{2}[/tex]
Select all of the verbal phrases which can be represented by the expression 25.75x + 10
Answer:
B: 25.75 times a number x, plus 10 | D: the product of 25.75 and x, plus 10
Step-by-step explanation:
B: 25.75 times "x" = 25.75x + 10
D: The product of 25.75 and x = 25.75x + 10
In order to accumulate enough money for a down payment on a house, a couple deposits $406 per month into an account paying 3% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 6 years?
In 6 years, the couple will have $32,916.38 in the account.
À class counted how many banks were in all the nearby cities.
Richmond has________more banks than Dollarville
Answer:
4
Step-by-step explanation:
Richmond has 7 and Dollarville has 3. 7 - 3 = 4
4x^2 + 4x =3
help pls
Answer:
x = .5, - 1.5
Step-by-step explanation:
4x^2 + 4x =3
To solve for x, we can complete the square.
4 ( x^2 + x) = 3
x^2 + x = 3/4
Take the coefficient of x, divide by 2, and square.
(1/2)^2
Then add to each side.
x^2 + x + 1/4= 3/4 +1/4
(x+1/2) ^2 = 1
Take the square root of each side.
x+1/2 = ±1
x = ±1 -1/2
x = 1-1/2 or -1-1/2
x = 1/2, -3/2
x = .5, - 1.5
Answer:
x = 1/2 or -3/2
Step-by-step explanation:
Rewrite in Standard Form:
4x²+4x=3 ==> 4x²+4x-3=0
Identify: a=4 b=4 c= -3
Quadratic Formula:
[tex]x=\frac{-b+\sqrt{b^2-4ac}}{2a} or \frac{-b-\sqrt{b^2-4ac}}{2a}\\ \\=\frac{-4+\sqrt{4^2-4(4)(-3)}}{2(4)} or \frac{-4-\sqrt{4^2-4(4)(-3)}}{2(4)}\\\\=\frac{-4+\sqrt{16+48}}{8} or \frac{-4-\sqrt{16+48}}{8}\\\\=\frac{-4+\sqrt{64}}{8} or \frac{-4-\sqrt{64}}{8}\\\\=\frac{-4+8}{8} or \frac{-4-8}{8}\\\\=\frac{4}{8} or \frac{-12}{8}\\\\=\frac{1}{2} or -\frac{3}{2}[/tex]