Answer:
1) has bigger answer
Step-by-step explanation:
1)
solving parenthesis first we get
5 × 10
so, the answer = 50
2)
solving 3 × 5 first as we have to see multiplication first then addition
2 + 15 + 5
22
comparing both
50 > 22
so problem 1 has a bigger answer
Finding the Coordinates of the Image On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C is dilated to create triangle A prime A C prime. The points of A B C are (negative 3, 3), (negative 1, 1), and (negative 3, 1). The points of A prime A C prime are (negative 9, 9), (negative 3, 3), and (negative 9, 3). The dilation DO,3 (x, y) → (3x, 3y) is performed on the pre-image △ABC to make a similar triangle. Which statements are true? Check all that apply. ∠A corresponds to ∠A'. ∠A'AC' corresponds to ∠B. CB corresponds to C'A. Segment A'A is parallel to segment C'C. △ABC ~ △A'AC'.
Answer:
- A corresponds to A’
- A’AC’ corresponds to B
- CB corresponds to C’A
- ABC ~ A’AC’
Step-by-step explanation:
WILL MARK BRAINLIEST PLEASE HELP
Answer:
Step-by-step explanation:
Find the limit of f as or show that the limit does not exist. Consider converting the function to polar coordinates to make finding the limit easier. f(x,y)
Answer:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Required
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Multiply by 1
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]
Express 1 as
[tex]\frac{y^2}{y^2} = 1[/tex]
So, the expression becomes:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]
Rewrite as:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]
In limits:
[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]
Convert to polar coordinates; such that:
[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]
Expand
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]
Factor out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]
Cancel out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]
So:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]
In trigonometry:
[tex]\cos^2\theta + \sin^2\theta = 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
Evaluate the limits by substituting 0 for r
[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0}{1+\sin^2\theta}[/tex]
Since the denominator is non-zero; Then, the expression becomes 0 i.e.
[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]
So,
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
) A patient drank 12 ounces of orange juice. How many milliliters did the patient drink?
Answer:
[tex]Drink = 354.882\ mL[/tex]
Step-by-step explanation:
Given
[tex]Drink = 12oz[/tex]
Required
Equivalent in mL
We have:
[tex]1\ oz = 29.5735\ mL[/tex]
So:
[tex]Drink = 12 * 29.5735mL[/tex]
[tex]Drink = 354.882\ mL[/tex]
Which of the following is equivalent to the product below?
Square root 3 square root 21
I NEED HELP ILL GIVE BRAINLIEST
The equivalent of the products given = 3√7
Simplifying square rootsA perfect square root is said to be a number that gives rise to an integer when it's square root is carried out. Examples are √16, √9 which is 4 and 3 respectively.
√3 × √21
But √a ×√b = √ a×b
Find the prime factors which when multiplied would give 21 = 3 and 7.
Therefore,
[tex] \sqrt{3 \times 3 \times 7} [/tex]
[tex] \sqrt{9 \times 7} [/tex]
[tex] 3 \sqrt{7} [/tex]
Therefore, the equivalent of the products of √3 × √21 =
3√7
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Use cylindrical shells to find the volume of the solid generated when the region
R under y = x2 over the interval (0,2) revolved about the line y = -1
Answer:
[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsExpandingFunctionsFunction NotationGraphingExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method:
[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] x is the radius[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is the volumeStep-by-step explanation:
Step 1: Define
Identify
Graph of region
y = x²
x = 2
y = 4
Axis of Revolution: y = -1
Step 2: Sort
We are revolving around a horizontal line.
[Function] Rewrite in terms of y: x = √y[Graph] Identify bounds of integration: [0, 4]Step 3: Find Volume Pt. 1
[Shell Method] Find distance of radius x: [tex]x = y + 1[/tex][Shell Method] Find circumference variable f(x) [Area]: [tex]\displaystyle f(x) = 2 - \sqrt{y}[/tex][Shell Method] Substitute in variables: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - \sqrt{y})} \, dy[/tex][Integral] Rewrite integrand [Exponential Rule - Root Rewrite]: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - y^\bigg{\frac{1}{2}})} \, dy[/tex][Integral] Expand integrand: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(-y^\bigg{\frac{3}{2}} + 2y - y^\bigg{\frac{1}{2}} + 2)} \, dy[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{-2y^\bigg{\frac{5}{2}}}{5} + y^2 - \frac{2y^\bigg{\frac{3}{2}}}{3} + 2y \bigg) \bigg| \limits^4_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = 2\pi (\frac{88}{15})[/tex]Multiply: [tex]\displaystyle V = \frac{176 \pi}{15}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20
Answer:
(4, 2 )
Step-by-step explanation:
Given the 2 equations
3x + y = 14 → (1)
7x - 4y = 20 → (2)
Rearrange (1) making y the subject by subtracting 3x from both sides
y = 14 - 3x → (3)
Substitute y = 14 - 3x into (2)
7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side
7x - 56 + 12x = 20
19x - 56 = 20 ( add 56 to both sides )
19x = 76 ( divide both sides by 19 )
x = 4
Substitute x = 4 into (3) for corresponding value of y
y = 14 - 3(4) = 14 - 12 = 2
solution is (4, 2 )
Answer:
[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]
Suppose you buy a home and finance $275,000 at $2,223.17 per month for 30 years. What is the amount of interest paid? (Round your answer to the nearest cent.)
Explanation:
30 years = 30*12 = 360 months
If the monthly payment is $2,223.17 for 360 months, then you'll pay back a total of 2223.17*360 = 800,341.20 dollars overall.
Subtract off the amount financed, or amount loaned, to get the total interest.
800,341.20 - 275,000 = 525,341.20 is the amount of interest paid (in dollars).
This works because effectively, the total amount paid back consists of principal + interest. The principal is the amount the bank loans you.
So we could rephrase that last equation into saying
principal + interest = 275,000 + 525,341.20 = 800,341.20 = total amount paid back.
Find three consecutive odd integers whose sum is -213.
Answer:
-73, -71, -69
Step-by-step explanation:
Suppose the middle of the 3 integers is x.
(x-2)+(x)+(x+2)=-213
x-2+x+x+2=-213
3x=-213
x=-71
The integers are -69, -71, and -73
Answer:
-73,-71,-69
Step-by-step explanation:
Let x represent an odd interger
Odd intergers are serpated by the value of 2 so let the three consective intergers be represented by
[tex](x )+ (x + 2) +( x + 4)[/tex]
Set that equation equal to 213.
[tex]x + x + 2 + x + 4 = - 213[/tex]
[tex]3x + 6 = - 213[/tex]
[tex]3x = - 219[/tex]
[tex]x = - 73[/tex]
Plug -73 in the consective intergers expression.
[tex] - 73 + ( - 73 + 2) + ( - 73 + 4)[/tex]
So our three intergers are
[tex] - 73[/tex]
[tex] - 71[/tex]
[tex] - 69[/tex]
It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon. A recent survey was conducted from 1000 of these individuals. For the sampling distribution of the sample proportion to be reasonably Normal, the sample must have been obtained in the right way (ideally, a simple random sample) and the sample size must be large (so that at least 10 or more successes and failures). Are these conditions met
Answer:
Random sample, [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], so yes, both conditions were satisfied.
Step-by-step explanation:
60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.
This means that [tex]p = 0.6[/tex]
A recent survey was conducted from 1000 of these individuals.
This means that [tex]n = 1000[/tex]
Also, a random sample, so the first condition was satisfied.
The sample size must be large (so that at least 10 or more successes and failures).
[tex]np = 1000*0.6 = 600 \geq 10[/tex]
[tex]n(1-p) = 1000*0.4 = 400 \geq 10[/tex]
So yes, both conditions were met.
if 8km=5miles.how many miles are in 56m?
Answer:
89.6 miles
Step-by-step explanation:
[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{56}[/tex]
5x = 448
x=89.6
Step-by-step explanation:
if 8km=5
x =56km
5x=8×56
5x=448
x=89.6 miles
A family eats out at a restaurant and the total for their meals is $73.89. They also pay sales tax of 5.8% and leave a tip for their server. If the family leaves a total of $93, which of the following might be a description of the service they received?
a.
They left a 10% tip, so the service was probably below average.
b.
They left a 15% tip, so the service was probably average.
c.
They left a 20% tip, so the service was probably above average.
d.
They left a 25% tip, so the service was probably outstanding.
The answer is They left a 20% tip, so the service was probably above average.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
First step is to the amount of the sales tax.
If 100% is $73.89,
5.8% will be x (tax):
100% : $73.89 = 5.8% : x.
x = $73.89 * 5.8% : 100%.
x = $4.28.
Now, we have the price for meals, sales tax, and the total amount of money left, so we can calculate how much the tip is:
$93.00 - $73.89 - $4.28 = $14.83.
So, the tip is $14.83.
Let represent it as percent.
If $73.89 is 100%, $14.83 will be x.
$73.89 : 100% = $14.83 : x.
x = $14.83 * 100% : $73.89.
x = 20%.
So, they left a 20% tip, so the service was probably above average.
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Jack and Diane are jogging back and forth along a one-mile path. They started out at 9:00 A.M. from opposite ends of the path. They passed each other in 10 minutes when Diane has gone 1/3 mile. What time will they first meet at one end of the path? You have to assume they keep jogging at the same speeds.
Explain :
Answer:
30 minutes
Step-by-step explanation:
that problem description is imprecise.
I think what is meant here : they each keep jogging at their own same speed.
Diane's speed is 1/3 miles / 10 min.
Jack's speed is 2/3 miles / 10 min.
now, to bring this to regular miles/hour format, we need to find the factor between 10 minutes and an hour (60 minutes) and multiply numerator and denominator (top and bottom of the ratio) by it.
60/10 = 6.
so, we need to multiply both speeds up there by 6/6 to get the miles/hour speeds.
Diane : (1/3 × 6) / hour = 2 miles / hour
Jack : (2/3 × 6) / hour = 4 miles / hour
since Jack is running twice as fast as Diane, she will finish one length in the same time he finishes a round trip (back and forth).
Diane running 1 mile going 2 miles/hour takes her 30 minutes.
Jack running 2 miles (back and forth) going 4 miles/hour will take him also 30 minutes.
so, they will meet at his starting point after 30 minutes.
help me pleaseeeeeeeeeeeeeeeeee………….
Answer:
C
Step-by-step explanation:
200 x 5 = 1,000
100 x 10 = 1,000
C - 5 to 10 days
Answer:
C. 5 to 10 days
Step-by-step explanation:
If she drove 100 miles per day, then
1000/100 = 10
it took her 10 days.
If she drove 200 miles per day, then
1000/200 = 5
it took her 5 days.
Since she drove between 100 miles and 200 miles per days,
it took her from 5 to 10 days.
Answer: C. 5 to 10 days
Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease. a. Increase the differences between the sample means. b. Increase the sample variances.
Answer:
(a) Increase the differences between the sample means this will increase the Numerator.
(b) Increase the sample variances will increase the denominator.
Step-by-step explanation:
F Ratio = Variance between treatments/ Variance within treatments.
Here,
(a) Increase the differences between the sample means:
- Will increase the Numerator and
- Size of the F-ratio would increase
(b) Increase the sample variances:
- Will increase the denominator and
- Size of the F Ratio would decrease.
Which rectangle has an area of 18 square units? On a coordinate plane, a rectangle is 2 units high and 7 units wide. On a coordinate plane, a rectangle is 2 units high and 6 units wide. On a coordinate plane, a rectangle is 3 units high and 5 units wide. On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
On a coordinate plane, a rectangle is 3 units high and 6 units wide.
Answer:
option "B"
You Welcome
Step-by-step explanation:
ABCD-EFGH what does y=?
Answer:
y = 3
Step-by-step explanation:
Given that the shapes are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{EF}[/tex] = [tex]\frac{CD}{GH}[/tex] , substitute values
[tex]\frac{3}{2}[/tex] = [tex]\frac{4.5}{y}[/tex] ( cross- multiply )
3y = 9 ( divide both sides by 3 )
y = 3
Need help
Identify the domain of the function shown in the graph
Answer:
B
Step-by-step explanation:
You are making a committee from the class and need to have 6 students on it. There are 32 students in the class.
answer in permutations
Answer:
32P6
Step-by-step explanation:
nPr
n=32
r=6
The owners of a baseball team are building a new baseball field for their team and must determine the number of seats to include. The average game is attended by 6,500 fans, with a standard deviation of 450 people. Suppose a random sample of 35 games is selected to help the owners decide the number of seats to include. Identify each of the following and be sure to round to the nearest whole number:
Provide your answer below:
μ =------------
μx=-----------
σx=-----------
σ=------------
n=------------
Answer:
μ = 6500
μx= 6500
σx= 76
σ= 450
n= 35
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average game is attended by 6,500 fans, with a standard deviation of 450 people.
This means that [tex]\mu = 6500, \sigma = 450[/tex]
35 games:
This means that [tex]n = 35[/tex]
Distribution of the sample mean:
By the Central Limit Theorem, we have [tex]\mu_x = \mu = 6500[/tex] and the standard deviation is:
[tex]\sigma_x = \frac{450}{\sqrt{35}} = 76[/tex]
Find the volume of the figure. Express answers in terms of t, then round to the nearest whole number
Please help :)
Answer:
729π ft³
Step-by-step explanation:
Applying,
Volume of a cone
V = πr²h/3.............. Equation 1
Where r = radius of the base, h = height, π = pie
From the question,
Given: r = 9 ft, h = 27 ft
Substitite these values into equation 1
V = π(9²)(27)/3
V = 729π ft³
Hence the volume of the figure in terms of π is 729π ft³
A teacher teaches two classes with 8 students each. Each student has a 95% chance of passing their class independent of the other students. Find the probability that, in exactly one of the two classes, all 8 students pass.
Answer:
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Probability that all students pass in a class:
Class of 8 students, which means that [tex]n = 8[/tex]
Each student has a 95% chance of passing their class independent of the other students, which means that [tex]p = 0.95[/tex]
This probability is P(X = 8). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634[/tex]
Find the probability that, in exactly one of the two classes, all 8 students pass.
Two classes means that [tex]n = 2[/tex]
0.6634 probability all students pass in a class, which means that [tex]p = 0.6634[/tex].
This probability is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466[/tex]
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.
URGENT!!! Picture included
What is the solution set of the equation x2+3*-4=6
Answer:
x=9
Step-by-step explanation:
What is the value of y?
Answer:
y=0
Step-by-step explanation:
1. Make variable y as subject for the first equation, which is y= -2x +10
2. substitute the first eq to the second one
3. x - (-2x+10) -5=0
4. solve x, which x = 5
5. substitute in eq 1 which is y= -2x +10
6. solve the eq, the possible solution is y=0
Evaluate 12 sin 85° correct to two decimal places.
Answer:
12 x sin(85)
12x 0.99619
155.40
Solution:
12 x sin (85) = 11.95 (Since sin85 is 0.996194)
So, the answer is 11.95.
If the domain of a function that is reflected over the x-axis is (1, 5), (2, 1), (-1, -7), what is the range?
A. (1, -5), (2, -1), (-1, 7)
B. (5, 1), (1, 2), (-7, -1)
C. (-5, -1), (-1, -2), (7, 1)
D. (-1, 5), (-2, 1), (1, -7)
Answer:
A. (1, -5), (2, -1), (-1, 7)
Step-by-step explanation:
Reflecting a function over the x-axis:
When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:
[tex](x,y) \rightarrow (x,-y)[/tex]
To find the range:
We apply the transformation to the points in the domain. Thus:
[tex](1,5) \rightarrow (1,-5)[/tex]
[tex](2,1) \rightarrow (2,-1)[/tex]
[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]
Thus the correct answer is given by option a.
Answer:
It is letter A and please give me brainliest
Step-by-step explanation:
Yuki bought a drop–leaf kitchen table. The rectangular part of the table is a 2–by–3–foot rectangle with a semicircle at each end, as shown.
Answer:
[tex](a)\ Area = 13.0695[/tex]
[tex](b)\ Area = 26.139[/tex]
Step-by-step explanation:
Given
The attached image
Solving (a): The area (one side up)
This is calculated as:
Area= Area of semicircle + Area of rectangle
So, we have:
[tex]Area = \pi r^2 + l *w[/tex]
Where:
[tex]l,w =2,3[/tex] --- the rectangle dimension
[tex]d = 3[/tex] --- the diameter of the semicircle
So, we have:
[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]
[tex]Area = \pi * 2.25 + 6[/tex]
[tex]Area = 2.25\pi + 6[/tex]
[tex]Area = 2.25*3.142 + 6[/tex]
[tex]Area = 13.0695[/tex]
Solving (b): Area when both leaves are up.
Simply multiply the area in (a) by 2
[tex]Area = 2 * 13.0695[/tex]
[tex]Area = 26.139[/tex]
The slope of diagonal OA IS__,
and its equation is__
Answer:
[tex](a)\ m = \frac{4}{3}[/tex] --- slope of OA
[tex](b)\ y = \frac{4}{3}x[/tex] --- the equation
Step-by-step explanation:
Given
The attached graph
Solving (a): Slope of OA
First, we identify two points on OA
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (3,4)[/tex]
So, the slope (m) is:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{4-0}{3-0}[/tex]
[tex]m = \frac{4}{3}[/tex]
Solving (b): The equation
This is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Recall that:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]m = \frac{4}{3}[/tex]
So, we have:
[tex]y = \frac{4}{3}(x - 0) + 0[/tex]
[tex]y = \frac{4}{3}(x)[/tex]
[tex]y = \frac{4}{3}x[/tex]
divide 64.050÷0.12. need whole process
Answer:
533.75
Step-by-step explanation:
Given the expression;
64.050÷0.12
Express first as a fraction
64.050 = 64050/1000
0.12 = 12/100
Divide both fractions
= 64050/1000÷12/100
= 64050/1000 *100/12
= 64050/10 * 1/12
= 64050/120
= 533.75
Hence the required answer is 533.75