Answer:
[tex]4h^2-48.6h-72.9[/tex]
Step-by-step explanation:
[tex](2h+2.7) (2h-27)\\4h^2-54h+5.4h-72.9\\4h^2-48.6h-72.9[/tex]
Calculate the volume of this triangular prism?
Answer:
960 sq cm
Step-by-step explanation:
(16*12*10)/2
Find y' if y= In (x2 +6)^3/2
y'=
Answer:
[tex]\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
ln Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = ln(x^2 + 6)^{\frac{3}{2}}[/tex]
Step 2: Differentiate
[Derivative] Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[ln(x^2 + 6)^{\frac{3}{2}}] \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{3}{2} - 1} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{d}{dx}[ln(x^2 + 6)] \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] ln Derivative: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot \frac{d}{dx}[x^2 + 6][/tex][Derivative] Basic Power Rule: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2 \cdot x^{2 - 1} + 0)[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3}{2}ln(x^2 + 6)^{\frac{1}{2}} \cdot \frac{1}{x^2 + 6} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2} \cdot \frac{1}{x^2 + 6} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)} \cdot (2x)[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{3(2x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Multiply: [tex]\displaystyle y' = \frac{6xln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Factor: [tex]\displaystyle y' = \frac{2(3x)ln(x^2 + 6)^{\frac{1}{2}}}{2(x^2 + 6)}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{3xln(x^2 + 6)^{\frac{1}{2}}}{x^2 + 6}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Anyone can help with this
Answer:
C
Step-by-step explanation:
Notice how C is the only function that is quadratic. If you expand (2x-1)^2, you get 4x^2-4x+1. Since x is raised to the power of two, it isn't linear, but quadratic.
Answer:
C
Step-by-step explanation:
i used photomath and C was not the linear one!
Can Someone please help me !!! ( you have to fill out the blanks )
Answer:
1. 5(a-6) = 5a-30
2. 2(3a-b) = 6a-2b
3. 5(-5x+3) = -25x+15
4. -(2c+3) = -2c-3
Both of their first step are correct (Show your calculations to explain)
x-9 = 5
x = 14
2x-18 = 10
2x = 28
x = 14
Step-by-step explanation:
All Above
Please help I don’t gat this
Answer:
30 yards
Step-by-step explanation:
the dotted line causes a rectangle and a triangle to be formed. the formula for area of a triangle is base times height divided by 2. you subtract 6 from 9 which is 3 and multiply it by 4 as it is the height of the triangle after, divide by 2 . since 4 and 3 is 12, dividing 12 by 2 is 6 which is the area of the triangle. the area of the rectangle is 6 times 4 which is 24. add 24 and 6 and u get 30
The hanger image below represents a balanced equation. Find the value of n that makes the equation true.
Answer:
6
Step-by-step explanation:
16=n +10
subtract 10 from both sides and your left with 6=n
Which graph best represents the equation -4x + 5y = 8? A. B. C. D.
Answer:
It will look like this
Step-by-step explanation:
The equation of line y = 4 / 5x + 8 / 5 can be represented on the basis of coordinates (0, 8/5), (1, 12/5), and (10, 48/5) in the graph attached below.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
-4x + 5y = 8
Write the line in slope intercept form as shown below,
5y = 4x + 8
y = 4 / 5x + 8 / 5
Put the random values of x and find y,
y = 4 / 5 × 0 + 8 / 5 (when x = 0)
y = 8 / 5
y = 4 / 5 × 1 + 8 / 5 (When x = 1)
y = 12 / 5
y = 4 / 5 × 10 + 8 / 5 (When x = 10)
y = 48 / 5
Plot the coordinates (0, 8/5), (1, 12/5), and (10, 48/5) in the graph and mark the points, joining all the points to get the line.
To know more about equation:
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A bag of 4 balls weighs 6 pounds. Each ball weighs the same amount. What is the weight of each ball?
Please help me with this :)
[tex]hope \: it \: helps[/tex]
PLEAS HELP THERE IS PIC drag the tiles to the correct boxes to complete the pairs. how many solutions does each equations have ?
Answer:
|2x+1|=0 has one solutions
2|x+1|=-2 has no solution
|x+21|=2 has two solution
Step-by-step explanation:
Solve for x if 26 = x/2
Answer:
x=52
Step-by-step explanation:
Help! Will give brainliest to first correct answer.
Answer:
a) 7n
b) n+7
c) n -7
d). [tex]\frac{n}{7}[/tex]
Step-by-step explanation:
All you have to do for this question is look at the key words. These will help you find the correct answers.
Product = multiplication (x)Sum = addition (+)Difference = subtraction (-)Quotient = DivisionFind two equivalent fractions
3/2
Answer:
4/6 8/12
Step-by-step explanation:
Item 5
Which measure of central tendency best describes the data?
47, 47, 48, 54, 102, 45, 100, 48, 83
either mean or median
median only
mean only
Answer:
the answer is either mean or median because you can find both of them given the data
please help!!!!!!!!!!!!!!!!!!!!
Answer:
I am not sure but think that the answer is 1/20
I believe you convert the whole number into a mixed fraction.
5 converted into quarters is 20/4. Then you divided 1/4 by 20/4.
1/4 divided by 20/4 is 1/20 or 0.05.
Please, don't refrain to tell me if this is incorrect. Thank you.
Which of the following is the correct way to state the similarity between these two figures?
A.) ABCDE ~ YXVZW
B.) ABCDE ~ VWXYZ
C.) ABCDE ~ VZWYX
D.) ABCDE ~ ZWYXV
Answer:
ABCDE is similar to the ZWYXV
Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $49. At another store she can borrow the tile saw for free if she buys tiles there for $1.29 per tile. How many tiles must she buy for the cost to be the same at both stores?
Margo must buy
tiles for the cost to be the same at both stores.
Answer:
Also need help
A brochure claims that the average maximum height a certain type of plant is 0.7 m. A gardener suspects that this estimate is not accurate locally due to soil conditions. A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m. Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m. Assume that the population standard deviation is 0.2 m.
Answer:
We accept the null hypothesis, that is, that the population mean is not different from 0.7.
Step-by-step explanation:
A brochure claims that the average maximum height a certain type of plant is 0.7 m.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 0.7[/tex]
A gardener suspects that this estimate is not accurate locally due to soil conditions.
Hypothesis test to determine whether the population mean is different from 0.7m, which means that the alternate hypothesis is:
[tex]H_{a}: \mu \neq 0.7[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that [tex]\mu = 0.7[/tex]
A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m.
This means, respectively, that [tex]n = 43, X = 0.65[/tex]
Assume that the population standard deviation is 0.2 m.
This means that [tex]\sigma = 0.2[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.65 - 0.7}{\frac{0.2}{\sqrt{43}}}[/tex]
[tex]z = -1.64[/tex]
Pvalue of the test:
Since we are testing that the mean is different of a value, and z is negative, the pvalue of the test is 2 multiplied by the pvalue of z = -1.64
z = -1.64 has a pvalue of 0.0505
2*0.0505 = 0.101
Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m.
0.101 > 0.01, which means that we accept the null hypothesis, that is, that the population mean is not different from 0.7.
A bucket has 16 tennis balls and 10 ping pong balls . What is the probability of selecting a ping pong ball , replacing it and then selecting a tennis ball
Answer:
40/169
Step-by-step explanation:
P(pp,tennis) = [tex]\frac{10}{26}[/tex] × [tex]\frac{16}{26}[/tex] = 40/169 in simplified form
The probability of selecting a ping pong ball, replacing it and then selecting a tennis ball is 40/169.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Tennis ball = 16
Ping pong balls = 10
So, probability of selecting a ping pong ball, replacing it and then selecting a tennis ball
= 10/ 26 x 16/26
= 40/169
Learn more about Probability here:
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A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.
Exercise (a)
How much work W is done in pulling the rope to the top of the building?
Exercise (b)
How much work W is done in pulling half the rope to the top of the building?
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]
The work done in pulling half the rope, W₂ = 562.5 lb·ft
2.75 round to the nearest hundreth
Answer:
Its already rounded. Rounded to tenths place would be 2.8
Step-by-step explanation:
5 or higher makes you round up. if its a 4 or lower it would stay the same.
Rotation 180° about the origin
Answer:
Step-by-step explanation:
to rotate about origin by 180 ° also means to change ( x, y) ⇔( -x,-y)
the double arrows just mean to change into.. or "transform" ( I think that there might have even been a movie about this, called "transformers" :D JK)
T=( -2, 1)
S = ( -4, 3)
R = ( -5, -2)
use the transform ( x, y) ⇔( -x,-y)
T' = (2,-1)
S' = ( 4, -3 )
R' = (5 , 2 )
if you draw this on a piece of graph paper, you'll see it's the triangle spun 180 ° around the origin :)
ASAP I WILL GIVE 100 POINTS AND BRAINIEST ASAP
Find the length of the model train.
Answer:
It would be 7.5 inches.
Hope this helped!!
find the slope
!!!!!please help QUICK!!!!
Answer:
3/4
Step-by-step explanation:
We can find the slope using two points
( 0,-5) and ( 4,-2)
The slope is given by
m = ( y2-y1)/(x2-x1)
= ( -2- -5)/( 4-0)
= (-2+5)/(4-0)
=3/4
Which fraction is marked by the point on the number line?
Answer:
where is the numer line?
Step-by-step explanation:
If the triangles below are similar, determine which of the statements below are TRUE. (There may be more than one correct answer.)
Similar Triangles
Question 5 options:
A.) BC¯¯¯¯¯≅YZ¯¯¯¯¯
B.) BC¯¯¯¯¯≅XY¯¯¯¯¯¯
C.) Side XY = 26
D.) Side BC = 48
E.) ∠A≅∠X
Answer:
Step-by-step explanation:
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
The answers are:
Side XY = 26
BC ≅ XY
Side BC = 48
may kapangyarihan bilang pinakamataas na hukuman sa kolonya
Answer:
which language is this .
abc~def what sequence of transformation will move ABC onto def
Answer:
c
Step-by-step explanation:
Answer:
is C guys
Step-by-step explanation:
Find the length of the third side. If necessary,
round
to
the nearest tenth.
4
7
Answer:
The answer would be 8.1
Step-by-step explanation:
Out of all of the topics covered so far in the course (whole numbers, fraction notation: multiplication, division, and mixed numerals), which did you enjoy the most? Which do you enjoy the least? Why?
Answer: I would say I've liked multiplication the most and division the least! I have always gotten multiplication because.. I don't really know. It's just easy for me. I can't really explain. For multiplication though.. I have never gotten it. It is the exact opposite. I've never understand how you have to skip a digit because you can't divide it to the other number.
Step-by-step explanation:
Hope this helps! This is my opinion.
I made this don't copy my answer