Step-by-step explanation:
Let's solve for the first one,
[tex]R.H.S. = Cos²A + cos²A.cot²A[/tex]
Step 1- Take Cos²A common,
[tex] = Cos²A( 1+ cot²A)[/tex]
[tex] \small \sf \: Now \: we \: know \: that \\ \small (1 + Cot^{2} \theta = Cosec^{2} \theta)[/tex]
Step 2 - Substituting above value in step 1,
[tex] = Cos^{2} A(Cosec^2A)[/tex]
[tex] \small \sf \: We \: know \: that \: Cosec \theta= \frac{1}{Sin \theta} [/tex]
Step 3 - Substitute Cosec²A with 1/Sin²A
[tex] = \frac{Cos^2A}{Sin^2A} [/tex]
[tex] \small \sf \: Now \: the \: basic \: trigonometric \: function \: is \\ \small \frac{Cos\theta}{Sin \theta} = Cot\theta[/tex]
Step 4 - Replacing the product of step 3 with above function,
[tex] = {Cot}^{2} A[/tex]
Hence proved,
[tex]R.H.S = L.H.S[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Now let's prove the second relation,
[tex](1-sin²A)(1+cot²A)=cot²A[/tex]
Let's solve for R.H.S.,
[tex]R.H.S.= (1-sin^{2} A)(1+cot^{2} A)[/tex]
As I told above,
[tex]\small(1+cot^{2} \theta) = cosec^{2} \theta[/tex]
Another important relation is,
[tex] \small sin^2\theta + cos^2\theta= 1 \: or \: \\ \small cos^2\theta = 1 - sin^2\theta[/tex]
Replacing both the above brackets with this relation we get,
[tex] = Cos^2A \cdot Cosec^2A [/tex]
Now follow the step 3 and step 4 of first question and you will get,
[tex]R.H.S. = L.H.S.[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Some important trigonometric relations that you must learn,
[tex]Sin^2\theta + Cos^2\theta = 1 \\ 1 + Cot^2\theta = Cosec^2\theta \\ 1+Tan^2\theta = Sec^2\theta[/tex]
[tex] \small\sf \: Thanks \: for \: joining \: brainly \: community! [/tex]
How many solutions does the system have?
Y= 4x8
4y = 4x - 8
The number of solutions to the system is 1
What is a linear equation?A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the number of solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y = 4x + 8
4y = 4x - 8
Substitute y = 4x + 8 in 4y = 4x - 8
4(4x + 8) = 4x - 8
Expand the equation
16x + 32 = 4x - 8
Evaluate the like terms
12x = - 40
Divide by 12
x = -10/3
The above means that the number of solutions to the system is 1
Read more about system of linear equations at
https://brainly.com/question/14323743
#SPJ1
A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 16 mm halfway across a horizontal distance of 80 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
Answer:
[tex]\textsf{A)} \quad (x-40)^2=-100(y-16)[/tex]
B) Focus = (40, -9)
Directrix: y = 41
Axis of symmetry: x = 40
Step-by-step explanation:
The x-intercepts of a parabola are the points at which the curve intercepts the x-axis (when y = 0).
The x-coordinate of the vertex of a parabola is halfway between the x-intercepts.
The y-coordinate of the vertex if the minimum or maximum height of the parabola.
Part AA jumping spider's movement is modeled by a parabola.
Define the variables:
x = horizontal distance of the spidery = height of the spiderFrom the information given:
x-intercepts = (0, 0) and (80, 0)vertex = (40, 16)Standard form of a parabola with a vertical axis of symmetry:
[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]
Vertex: (h, k)Focus: (h, k+p)Directrix: y = (k-p)Axis of symmetry: x = hIf p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.
Substitute the vertex (40, 16) and one of the x-intercept points (0, 0) into the formula and solve for p:
[tex]\implies (0-40)^2=4p(0-16)[/tex]
[tex]\implies 1600=-64p[/tex]
[tex]\implies p=-25[/tex]
Substitute the vertex and the found value of p into the formula:
[tex]\implies (x-40)^2=4(-25)(y-16)[/tex]
[tex]\implies (x-40)^2=-100(y-16)[/tex]
Part BGiven:
Vertex = (40, 16) ⇒ h = 40 and k = 16p = -25Substitute the given values into the formulas for focus, directrix and axis of symmetry:
Focus
⇒ (h, k+p)
⇒ (40, 16 + (-25)))
⇒ (40, -9)
Directrix
⇒ y = (k-p)
⇒ y = (16 - (-25))
⇒ y = 41
Axis of symmetry
⇒ x = h
⇒ x = 40
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
1.72 1.8 1.86 1.88 1.74 1.86
What is the mean height of the ocean's first high tide for the 6 days?
1.81 meters
1.83 meters
1.86 meters
1.87 meters
The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
Number of days = 1 2 3 4 5 6 Total = 6
1.72 1.8 1.86 1.88 1.74 1.86
The average of the values is the ratio of the total sum of values to the number of values.
Since the mean of the heights of the tides,
= sum of heights / number of heights observation
= (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters
Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
Learn more about average here:
brainly.com/question/24057012
#SPJ1
How many three-digit multiples of 5 have three different digits and at least one prime digit?
Using the Fundamental Counting Theorem, it is found that there are 124 three-digit multiples of 5 that have three different digits and at least one prime digit.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Multiples of 5 finish at 0 or 5, hence the parameters to find the number of three-digit multiples of 5, with different digits are:
[tex]n_1 = 9, n_2 = 8, n_3 = 2[/tex]
And the number is:
N = 9 x 8 x 2 = 144.
With no prime digits, 2, 3, 5 and 7 cannot be used, hence the parameters are:
[tex]n_1 = 5, n_2 = 4, n_3 = 1[/tex]
Hence 20 of the numbers have no prime digits, and 144 - 20 = 124 have at least one prime digit.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
#SPJ1
Find the total surface area.
answer choices
A. 731 cm²
B. 649 cm²
C. 900 cm²
D. 770 cm²
consider a two-factor factorial design with three levels for facts a, three levels for factor b, and four replicates in each of the nine cells
a. how many degrees of freedom are there in determining the A variation and the factor B variation
b. how many degrees of freedom are there in dreaming the interaction variation
c. how many degrees of freedom are there in determining the random variation
d. how many degrees of freedom are there in determining the total variation
In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.
What is a two-factorial design?A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.
Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.
From the data given:
a.
In calculating the factor A variation, there are two degrees of freedom.
In determining the variation of factor B, there are two degrees of freedom.
b.
Finding the degree of freedom using the interaction variation, there are four degrees of freedom.
c.
In finding the random variable, there are 9(4-1) = 27 degrees of freedom.
d.
In calculating the total variable, there are 9*4-1 =35 degrees of freedom.
Learn more about using a two-factor factorial design for determining the degree of freedom here:
https://brainly.com/question/14292694
#SPJ1
SOLVE THIS FOR ME PLEASE
How can you make a 95% confidence interval smaller without changing the confidence level?
Step-by-step explanation:
1. Lower the confidence level.
2. Use a one-sided confidence interval. ...
3. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...
4. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...
PLEASE MARK ME AS BRAINLIST
Answer:
Increase the sample size.
Usually, the more observations that you have, the narrower the interval around the sample statistic is.
Given 3x^2+x-4/x-1 what are the domain and range
Answer:
doman: x ≠ 1range: y ≠ 7Step-by-step explanation:
The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.
SimplifiedThe given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...
[tex]\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1[/tex]
DomainThe simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...
x ≠ 1
In interval notation, this is ...
(-∞, 1) ∪ (1, ∞)
Range
The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...
y ≠ 7
In interval notation, this is ...
(-∞, 7) ∪ (7, ∞)
2d(3*6)=48y when y=1/4
Answer: d = 1/3
Step-by-step explanation: 48y = 48/4 = 12. So, 2d(18) is equal to 12. 12/18 is 2/3 so 2d has to equal 2/3. That means d = 1/3.
The answer to this problem please and thank you
Answer:
C
Step-by-step explanation:
The red dotted line we see is the asymptote, which is a line that the functions will never cross.
The asymptotes we see currently is:
x = -3
and
x = 2
We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:
(x-2) (x+3)
If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.
Answer:
C
Step-by-step explanation:
there are 2 vertical asymptotes at x = - 3 and x = 2
then the factors on the denominator will be (x + 3) and (x - 2)
then
f(x) = [tex]\frac{1}{(x-2)(x+3)}[/tex]
HELP. Which statement best describes the domain of the function represented in the graph?
05 ≤x≤ 60, or x is from 5 to 60 05 ≤ x ≤ 30, or x is from 5 to 30 O 30 ≤ x ≤ 60, or x is from 30 to 60 00≤x≤ 30, or x is from 0 to 30
What are the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2?
The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)
How to determine the potential zeros of the function f(x)?The function is given as:
f(x)=6x^4+ 2x^3 - 4x^2 +2
For a function P(x) such that
P(x) = ax^n +...... + b
The rational roots of the function p(x) are
Rational roots = ± Possible factors of b/Possible factors of a
In the function f(x), we have:
a = 6
b = 2
The factors of 6 and 2 are
a = 1, 2, 3 and 6
b = 1 and 2
So, we have:
Rational roots = ±(1, 2)/(1, 2, 3, 6)
Split the expression
Rational roots = ±1/(1, 2, 3, 6)/ and ±2/(1, 2, 3, 6)
Evaluate the quotient
Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 1, 2/3, 1/3)
Remove the repetition
Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 2/3)
Hence, the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)
The complete parameters are:
The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)
Read more about rational roots at
brainly.com/question/17754398
#SPJ1
Five interlocked, colored rings make up the Olympic symbol. The rings are
blue, black, red, yellow, and green and represent Africa, the Americas, Asia,
Australia, and Europe. The symbol looks like this:
1. In how many ways could the five colors of the Olympic symbol have been
arranged among the rings?
Answer:
120
Step-by-step explanation:
5 rings 5 colors
for the first ring there are 5 colors to choose from
4 colors for the second
3 for the third
2 for the fourth
1 for the last one
so 5! = 120
Using a number line, find both the intersection and the union of the following
intervals:
(-∞, 6) and (-∞, 9)
The intersection of the two intervals in the number line will be = 4, 5, 6,.......+∞ = (-∞,6).
The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-∞),9)
How to illustrate the information?The given intervals are;
First interval = (-∞, 6)
Second interval = (-∞, 9)
Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞
The second interval includes, 4, 5,.....,+∞
Which gives the intersection as 4, 5, 6,7, 8,9......+∞
The union is the interval that combines the two sets of intervals which is given as follows;
The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞
Learn more about number line on:
https://brainly.com/question/24644930
#SPJ1
Let f(x)=x^2 and g(x)=(x+3)^2. Describe the transformation from f(x) to g(x).
Select one:
Shift right 3
Shift up 3
Shift down 3
Shift left 3
Answer:
shift left 3
Step-by-step explanation:
(x+3)²
x = -3
therefore translation by (-3,0)
The negative number shows it move to the left
You can work 40 hours per pay period while attending school earning $12.50 an hour. There are two pay periods per month. NOW Assume you have deductions for health care of $25 per pay period and 401K deduction of $50 per pay period. These deductions are pretax.
Gross Pay per pay period: $
Taxable Income per pay period:
You pay 11% in federal taxes. Federal tax withholding per pay period: $
Use the state tax rates below and calculate State tax withholding per pay period: $
(round to two decimals)
-- from image...
Calculate FICA withholding per pay period: $
Calculate Medicare withholding per pay period: $
(round to two decimals)
What is your Net pay per pay period: $
(round to two decimals)
Answer:
Step-by-step explanation:
yes
The gross pay, taxable income, withholding taxes, and net pay can be computed as follows:
a) The gross pay per pay period = $500
b) Taxable income per pay period = $425
c) Federal tax withholding per pay period = $46.75
d) FICA withholding per pay period = $26.35
e) Medicare withholding per pay period = $6.16
f) State tax wtihholding per pay period = $10
g) Net pay per pay period = $335.74
How the gross earnings, net pay, taxable income, and withholdings are computed:The number of hours per pay period = 40 hours
The number of pay periods in a month = 2
The total number of hours worked per month = 80 hours (40 x 2)
Earnings per hour = $12.50
a) The gross pay per pay period = $500 (40 x $12.50)
Deductions per pay period:
Health care = $25
401k = $50
The gross pay per pay period = $500
Total deductions per pay period = $75
b) Taxable income per pay period = $425 ($500 - $75)
c) Federal tax withholding per pay period = $46.75 ($425 x 11%)
d) FICA withholding per pay period = $26.35 ($425 x 6.2%)
e) Medicare withholding per pay period = $6.16 ($425 x 1.45%)
f) State tax wtihholding per pay period = $10 ($500 x 2%)
Total withholding taxes = $89.26
g) Net pay per pay period = $335.74 ($425 - $89.26)
Learn more about the gross and net pay and taxable income at https://brainly.com/question/4356180.
#SPJ2
MR MARK MARKS HIS CLASS ON A NORMAL CURVE. THOSE WITH z-SCORES ABOVE 1.8 WILL RECEIVE AN A, THOSE
BETWEEN 1.8 AND 1.1 WILL RECEIVE A B, THOSE BETWEEN 1.1 AND -1.2 WILL
RECEIVE A C, THOSE BETWEEN -1.2 AND -1.9 WILL RECEIVE A D, AND THOSE
UNDER -1.9 WILL RECEIVE AN F.
FIND THE PERCENT OF GRADES THAT WILL BE
A, B, C, D, AND F.
Using the normal distribution, it is found that the percentages are given as follows:
3.59% of the grades will be A.9.98% of the grades will be B.74.92% of the grades will be C.8.64% of the grades will be D.2.87% of the grades will be F.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The prorportion of students who receive an A is one subtracted by the p-value of Z = 1.8.
Looking at the z-table, Z = 1.8 has a p-value of 0.9641.
1 - 0.9641 = 0.0359.
3.59% of the grades will be A.
For B, it is the p-value of Z = 1.8 subtracted by the p-value of Z = 1.1, hence:
0.9641 - 0.8643 = 0.0998.
9.98% of the grades will be B.
For C, it is the p-value of Z = 1.1 subtracted by the p-value of Z = -1.2, hence:
0.8643 - 0.1151 = 0.7492.
74.92% of the grades will be C.
For D, it is the p-value of Z = -1.2 subtracted by the p-value of Z = -1.9, hence:
0.1151 - 0.0287 = 0.0864.
8.64% of the grades will be D.
For F, it is the p-value of Z = -1.9, hence 2.87% of the grades will be F.
More can be learned about the normal distribution at https://brainly.com/question/15181104
#SPJ1
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0) B(6, 0) C(6, 7) D(2, 7)
What is the area of rectangle ABCD?
Check the picture below.
Answer: 28 [tex]units^{2}[/tex]
Step-by-step explanation:
X is 30% of Y and Y is 45% of 600. What is the value of X?
Answer:
X = 81
Step-by-step explanation:
600 × 0.45 = 270
270 × 0.3 = 81
X = 81
Which geometric sequence has a common ratio of -9? (only one is correct)
a) {-1, -9, 81, 729, …}
b) {-9; -81; -729; -6,561; …}
c) {1, -9, 81, -729, …}
d) {81; 729; 6,561; 59,049; …}
C
1, -9 , 81 , -729 .....
ratio :-
R1 = -9/1 = -9
R2 = 81/-9 = -9
R3 = -729 / 81 =-9
so ,. R1= R2= R3
A candle on pauline’s dresser is 10 inches tall and burns at a rate of 0.75 inches per hour. how many hours will it take for the candle to burn down to a height of .25 inches?
Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:
h(t) = 10 - 0.75t
The height will be of 0.25 inches when h(t) = 0.25, hence:
0.25 = 10 - 0.75t
0.75t = 9.75
t = 9.75/0.75
t = 13 hours.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
A client named Tommy wants us to prepare a 3300-word Marketing Report + Poster. If a task is quantifiable by word count, we charge $110 per 1000 words. If a task is not quantifiable by word count, we estimate how many hours are required to complete the task and we charge based on $5 per hour. How much should we charge Tommy? Work out the total price.
The amount we should charge Tommy is $363.
What does the amount charged mean?When you charge someone money, you are requesting payment from them in exchange for something you have either sold to them or performed for them.The total sum that the Owner is obligated to pay under the charge obligations as outlined in the payment schedule is referred to as the "Total Charge Amount."How much should we charge Tommy:
The amount charged for 1000 words = $110
The amount charged per word = $110/1000
Amount to be charged for 3300 words = $(110/1000) × 3300
= $(0.11) × 3300
= $363
The amount we should charge Tommy is $363.
To learn more about the amount charged, refer to:
https://brainly.com/question/25922783
#SPJ9
Maytag Company earns $2.60 per share. Today the stock is trading at $46. The company pays an annual dividend of $1.60 a. Calculate the price-earnings ratio (Round your answer to the nearest whole number.) Price-earings natio b. Calculate the stock yield. (Round your answer to the nearest tenth percent.) Stock yield
a. The price-earnings ratio of Maytag Company's stock is 17.
b. The stock yield of Maytag Company's stock is 3.48%.
What are the price-earnings ratio and stock yield?The price-earnings ratio is a financial measurement of the worth of Maytag Company.
The price-earnings (P/E) ratio is computed as the current stock price divided by the company's earnings per share.
The P/E ratio shows the potential investor how much to pay per share for each $1 of earnings.
The stock yield is a financial measurement that shows the dividends paid relative to the market value per share.
Data and Calculations:Earnings per share = $2.60
Current share price = $46
Annual dividend = $1.60
a. Price-earnings ratio = Price per share/earnings per share
= 17 ($46/$2.60).
b. Stock yield = Annual dividend per share/Current stock price x 100
= 3.48% ($1.60/$46 x 100)
Thus, while the price-earnings ratio is 17, the stock yield is 3.48%.
Learn more about the price-earnings ratio and stock yield at https://brainly.com/question/17162588
#SPJ1
Identify the lateral area and the surface area of a cube with edge length 15 in.
The Lateral area of the cube = 900 in.²
The Surface area of the cube = 1,350 in.².
What is the Lateral Area of a Cube?A cube's lateral area is the area covered by the lateral surfaces of the cube shape. The formula for the lateral area of a cube is given as: LA = 4a², where:
a = edge length of cube.
What is the Surface Area of a Cube?The surface area of a cube is the total area of all its 6 surfaces. The formula for finding the surface area of a cube is: 6a², where:
a = edge length of cube.
Edge length of cube (a) = 15 in.
Lateral area = 4a² = 4(15²)
Lateral area = 4(225)
Lateral area of the cube = 900 in.²
Surface area = 6a² = 6(15²)
Surface area = 6(225)
Surface area of the cube = 1,350 in.².
Learn more about the surface area and lateral of a cube on:
https://brainly.com/question/15726306
#SPJ1
For the following geometric sequence find the explicit formula.
(12, -6, 3, ...]
Answer: [tex]a_n=12(-\frac{1}{2})^{n-1}[/tex]
Step-by-step explanation:
Let's first find the common ratio this sequence. To get to the next term, we divide by 2 and we alternate signs. Hence, the common ratio is [tex]-\frac{1}{2}[/tex].
We can now use the formula [tex]a_n=a_1(r)^{n-1}[/tex] to get the formula, where [tex]a_1[/tex] is the first term and r is the common ratio.
[tex]a_n=a_1(r)^{n-1}\\a_n=12(-\frac{1}{2})^{n-1}[/tex]
Prove usin's Mathematical induction 2^n ≤(n+1)!, for n≥0
Answer:
Step-by-step explanation:
2^0 is less than or equal to 1!, because 1<= 1
if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since
(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0
Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60
centimeters, as shown.
63 cm
60 cm
Answer:
the height would be around 19.2 cm
Step-by-step explanation:
hyp length = 63
base = 60
length = sqrt(63^2 - 60^2) = sqrt(369)
A 30g bullet travelling horizontally at 50 m/s penetrates 10 cm into a wooden block. The average force exerted by the block is:
The average force exerted by the block exists at -375 N.
How to find the average force exerted by the block?Given:
Initial Velocity, u = 50m/s
Displacement, s = 10cm = 0.10m
Mass, m = 0.03Kg
Using the relation,
[tex]$v^{2}-u^{2}=2 a s[/tex]
Substitute the values in the above equation, we get:
[tex]$&0^{2}-50^{2}=2 \mathrm{a}(0.10) \\[/tex]
[tex]$ \mathrm{a}= -12500 \mathrm{~ms}^{-2}[/tex]
We know that, f = ma
Putting the values, we get:
f = (0.03)(-12500)
f = -375 N
The average force exerted by the block exists at -375 N.
To learn more about average force refer to:
https://brainly.com/question/18652903
#SPJ9
Determine the real life solutions of 9x^2+6x+1=0
Answer:
1 (double root)
Step-by-step explanation:
Given quadratic equation:
[tex]9x^2+6x+1=0[/tex]
To find the solutions to the given quadratic equation, factor the equation.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=9 \cdot 1=9[/tex]
[tex]\implies b=6[/tex]
Therefore, the two numbers are: 3 and 3.
Rewrite the middle term as the sum of these two numbers:
[tex]\implies 9x^2+3x+3x+1=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 3x(3x+1)+1(3x+1)=0[/tex]
Factor out the common term (3x + 1):
[tex]\implies (3x+1)(3x+1)=0[/tex]
Therefore:
[tex]\implies(3x+1)^2=0[/tex]
This means that the curve has one root with multiplicity 2. So the curve touches the x-axis and bounces off the axis at one point. (See attached graph).
Apply the zero-product property:
[tex]\implies 3x+1=0 \implies x=-\dfrac{1}{3}[/tex]
Therefore there is one real solution of the given quadratic equation.
Learn more about factoring quadratic equations here:
https://brainly.com/question/27956741
https://brainly.com/question/27947331