A rain gutter is made of sheets of metal 9 inches wide. The gutters have a 3 inch base and two 3 inch sides, folded up at an angle of . What angle will maximize the cross sectional area of the rain gutter?
Answers
The value of angle that maximizes the cross sectional area is 60°
What is the cross sectional area of a solid?The cross sectional area of a solid is the two dimensional surface formed when the solid is sectioned by a plane.
The shape of the cross sectional area of the gutter is a trapezoid
Area of a trapezoid = ((Sum of the lengths of the parallel sides)/2) × Height
Let a and b represent the parallel sides of the trapezoid, and let a represent the base of the trapezoid we get;
A = ((a + b)/2) × h
a = 3 inches
b = The longer parallel side
h = The height of the trapezoid
The angle formed by the sides of a trapezium and the horizontal = θ
Therefore;
h = 3 × sin(θ)
b = 3 + 2 × 3·cos(θ)
A(θ) = ((3 + 3 + 2 × 3·cos(θ)) × 3 × sin(θ))/2 = 9·sin(θ)·cos(θ) + 9·sin(θ)
At the extremum value of θ, we get;
A'(θ) = 18·cos²(θ) + 9·cos(θ) - 9 = 0
Solving, we get;
cos(θ) = 0.5 or cos(θ) = -1
Therefore;
θ = arccos(0.5) = 60° and θ = arccos(0.5) = 180°
When θ = 60°, we get;
A(max) = 9·sin(60)·cos(60) + 9·sin(60) ≈ 11.69
The cross sectional area when θ is 60° is about 11.69 square inches which is larger than the 9 square inched when θ = 90°
The angle that maximizes the cross sectional area is θ = 60°
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Related Questions
Jim and Sally mow lawns in their neighborhood. Sally mows 5 less than twice the number of lawns Jim mows. Together they mow 25 lawns.
Which system of equations models this situation if j represents the number of lawns Jim mows and s represents the number of lawns sally mows?
Answers
Answer:
D
Step-by-step explanation:
Sallys= 2(Jims) -5
Sally's + Jim's = 25
Answer:
s = 2j -5s +j = 25Step-by-step explanation:
You want the system of equations that models, "Sally mows 5 less than twice the number of lawns Jim mows, and together they mow 25 lawns."
TranslationThe letters 's' and 'j' represent the number of lawns that Sally and Jim mow, respectively.
Then "twice the number of lawns Jim mows" is represented be 2j. And 5 less than that is represented by 2j-5. Since this is the number of lawns Sally mows, the equation is ...
s = 2j -5 . . . . . . . matches only one answer choice (D)
The equation for "together they mow 25 lawns" is ...
s +j = 25
Chau had 4/5 of a spool of yarn. He used 3/5 of his yarn for a project. What fraction of the spool was used for the project?
Answers
Answer: 3/5
Step-by-step explanation:
Chau had 4/5 of a spool of yarn, and he used 3/5 of it for a project.
The fraction of the spool used for the project is:
3/5
So, 3/5 of the spool was used for the project.
if A is 20% more than B, by what percent is B less than A?
Answers
Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:
A = B + 0.2B
Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:
A = 1.2B
Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:
(B lebih kecil dari A) / A x 100%
Substitusikan nilai A = 1.2B dan kita dapatkan:
(B lebih kecil dari 1.2B) / 1.2B x 100%
Maka:
0.2B / 1.2B x 100%
= 0.1667 x 100%
= 16.67%
Jadi, B adalah 16.67% lebih kecil dari A.
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Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Answers
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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using the following statements to compare how the aas congruence therom and the asa congruence therom are similar and how they are different.
Answers
In summary, both theorems require two pairs of congruent angles, but the AAS Congruence Theorem requires an included side to be congruent while the ASA Congruence Theorem requires a non-included side to be congruent.
What is similarity theorem?A similarity theorem is a statement in geometry that describes a relationship between similar geometric figures. Similar figures are figures that have the same shape but may have different sizes. A similarity theorem states that certain corresponding angles of similar figures are congruent and that the ratio of corresponding sides is constant. This constant ratio is called the scale factor, and it is used to find missing side lengths or to enlarge or reduce the size of a figure. The most commonly used similarity theorem is the AA (angle-angle) theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Here,
The AAS Congruence Theorem and the ASA Congruence Theorem are both used to prove that two triangles are congruent. However, they differ in the conditions required for the triangles to be congruent.
The AAS Congruence Theorem requires that two pairs of corresponding angles and one pair of corresponding included sides be congruent. This means that if two triangles have two pairs of congruent angles and a side included between them is congruent, then the triangles are congruent.
On the other hand, the ASA Congruence Theorem requires that two pairs of corresponding angles and one pair of corresponding non-included sides be congruent. This means that if two triangles have two pairs of congruent angles and a side not included between them is congruent, then the triangles are congruent.
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2. Urn A contains 4 black, 3 red, and 3 white balls, whereas urn B contains 3 white, I red, and 3 black balls. A ball is drawn at random from urn A and placed in urn B. A ball is then drawn from urn B. It happens to be red. What is the probability that the ball transferred was red?
Answers
The probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
What is probability ?
Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to happen.
To calculate probability, we usually take the number of favorable outcomes and divide it by the total number of possible outcomes. For example, if we flip a coin, the probability of getting heads is 1/2 because there is only one favorable outcome (heads) out of two possible outcomes (heads or tails).
According to the question:
Let's use Bayes' theorem to find the probability that the ball transferred was red:
Let R be the event that a red ball is drawn from urn B, and T be the event that the transferred ball was red.
Then we want to find P(T = red | R = red).
By Bayes' theorem, we have:
P(T = red | R = red) = P(R = red | T = red) * P(T = red) / P(R = red)
We can calculate each of these probabilities as follows:
P(R = red | T = red): The probability of drawing a red ball from urn B, given that a red ball was transferred from urn A to urn B, is 1/4, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we added one more red ball to it.
P(T = red): The probability that a red ball was transferred from urn A to urn B is 3/10, since urn A originally contained 3 red balls out of 10 total balls and we transferred one ball at random.
P(R = red): The overall probability of drawing a red ball from urn B is:
P(R = red) = P(R = red | T = black) * P(T = black) + P(R = red | T = red) * P(T = red)
where T = black means that a black ball was transferred from urn A to urn B. We can calculate each of these conditional probabilities as follows:
P(R = red | T = black): The probability of drawing a red ball from urn B, given that a black ball was transferred from urn A to urn B, is 1/7, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we did not add any more red balls to it.
P(T = black): The probability that a black ball was transferred from urn A to urn B is 4/10, since urn A originally contained 4 black balls out of 10 total balls and we transferred one ball at random.
Therefore, we have:
P(R = red) = 1/7 * 4/10 + 1/4 * 3/10 = 1/35 + 3/40 = 11/140
Putting it all together:
P(T = red | R = red) = (1/4) * (3/10) / (11/140) = 21/55
So the probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
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The happy widget company has a fixed cost of $1277 each day to run their factory and a variable cost of $1.93 for each widget they produce. How many widgets can they produce for $2127?
Answers
PLEASEE HELP! DUE TONIGHT
Find the perimeter of the figure below, in feet.
Answers
Answer:
79.2ft
Step-by-step explanation:
(9+9+10.3+10.3+10+10+10.3+10.3)ft
79.2ft
valuate the triple integral. $\int\!\!\int\!\!\int e {\color{red}} y \,dv$, where e is bounded by the planes $ x
Answers
The final answer is $\frac{1}{12}$.
We need to evaluate the triple integral $\iiint e y , dv$ over the region $e$ bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$, and $x + y = 2$.
To evaluate this triple integral, we can use the limits of integration obtained by considering the intersection of the planes. From the plane equations $x+y+z=1$ and $x+y=2$, we can solve for $z$ and $x$ in terms of $y$ to obtain the limits:
0≤z≤1−x−yand0≤x≤2−y.
Since $e$ is bounded by the planes $x=0$ and $y=0$, we have $0 \leq x \leq 2-y$ and $0 \leq y \leq 2$. Thus, we can set up the triple integral as follows:
Next, integrating with respect to $x$, we obtain∫
02[22−22]
02−∫ 02 [eyx− 2eyx 2 − 2ey 2 x ] 02−ydy.Simplifying this expression, we get
∫02(2−522+32)
.∫ 02 (2ey− 25 ey 2 + 2ey 3 )dy.
Evaluating the integral, we get the final answer of $\frac{1}{12}$.
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question:-Evaluate the triple integral $\int!!\int!!\int e y ,dv$, where $e$ is bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$ and $x + y = 2$.
Given: ABCD is a parallelogram.
Prove: AB CD and BC DA
Answers
Answer:
Step-by-step explanation:
Since ABCD is a parallelogram, we know that its opposite sides are parallel. That is, AB is parallel to CD and BC is parallel to DA.
To prove that AB = CD, we can use the fact that opposite sides of a parallelogram are congruent. That is, AB is congruent to DC. So, we can write:
AB = DC
Similarly, to prove that BC = DA, we can use the same fact. That is, BC is congruent to AD. So, we can write:
BC = AD
Therefore, we have proven that AB = CD and BC = DA, which shows that the opposite sides of the parallelogram ABCD are congruent.
C Select the correct answer. Which equation is equivalent to the given eq -4(x - 5) + 8x = 9x - 3
Answers
Answer:
-4(x - 5) + 8x = 9x - 3
Simplifying the left side:
-4x + 20 + 8x = 9x - 3
4x + 20 = 9x - 3
Subtracting 4x from both sides:
20 = 5x - 3
Adding 3 to both sides:
23 = 5x
Dividing both sides by 5:
x = 23/5
Therefore, the equation equivalent to the given equation is:
5x - 23 = 0
Help I don’t just this
Answers
The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.
Describe conditional relative frequency ?Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.
To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.
From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.
So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:
0.16 / 0.96 ≈ 0.17
Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.
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An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows:F(x) =0 x < 10.31 1 ≤ x < 30.42 3 ≤ x < 40.46 4 ≤ x < 60.82 6 ≤ x < 121 12 ≤ xa) What is the pmf of X?x 1 3 4 6 12p(x) _____
Answers
For the given CDF of X, the pmf of X at 1,3,4,6 and 12 is written as :
P(X = k) = 0.30 for k = 1 , P(X = k) = 0.10 for k = 3,
P(X = k) = 0.05 for k = 4 , P(X = k) = 0.15 for k = 6,
P(X = k) = 0.40 for k = 12.
In order to find the probability mass function (PMF) of X, we need to calculate the probability that X takes on each possible value.
Since X can take on any positive integer value, we can start by calculating the probability that X equals each positive integer.
⇒ P(X = 1) = 0.30,
⇒ P(X = 3) = F(3) - F(1) = 0.40 - 0.30 = 0.10
⇒ P(X = 4) = F(4) - F(3) = 0.45 - 0.40 = 0.05
⇒ P(X = 6) = F(6) - F(4) = 0.60 - 0.45 = 0.15
⇒ P(X = 12) = F(12) - F(6) = 1 - 0.60 = 0.40
Therefore, the required PMF of X is: P(X = 1) = 0.30 , P(X = 3) = 0.10 , P(X = 4) = 0.05 , P(X = 6) = 0.15 and P(X = 12) = 0.40 .
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The given question is incomplete, the complete question is
An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments.
The CDF of X is as follows:
F(x) = {0 x < 1
{0.30 1 ≤ x < 3
{0.40 3 ≤ x < 4
{0.45 4 ≤ x < 6
{0.60 6 ≤ x < 12
{1 12 ≤ x
What is the pmf of X at 1,3,4,6 and 12?
12. What is the height of the trapezoid in yards? (Hint: Use the formula
A = 1/2h (b 1, + b2,) (Lesson 2)
Answers
Answer:
height = 7 yards
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the 2 parallel bases
here b₁ = 12 , b₂ = 9 and A = 73.5 , then
[tex]\frac{1}{2}[/tex] h(12 + 9) = 73.5 ( multiply both sides by 2 to clear the fraction )
h(21) = 147
21h = 147 ( divide both sides by 21 )
h = 7 yards
can you find the slope of the given graph?
slope of graph=?
Answers
The slope of the graph f(x) = 3x² + 7 at (-2, 19) is -12
What is the slope of a graph?The slope of a graph is the derivative of the graph at that point.
Since we have tha graph f(x) = 3x² + 7 and we want to find its slope at the point (-2, 19).
To find the slope of the graph, we differentiate with respect to x, since the derivative is the value of the slope at the point.
So, f(x) = 3x² + 7
Differentiating with respect to x,we have
df(x)/dx = d(3x² + 7)/dx
= d3x²/dx + d7/dx
= 6x + 0
= 6x
dy/dx = f'(x) = 6x
At (-2, 19), we have x = -2.
So, the slope f'(x) = 6x
f'(-2) = 6(-2)
= -12
So, the slope is -12.
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Please help me anyone please ?!!!?!!
Answers
Answer:
7. 23
8. (3 - 8) x 5
Step-by-step explanation:
I think the second one is right but I know the first one is.
(Evaluating Reports MC)
The dot plot below shows the number of hours of sleep preferred by 25 patients chosen randomly in a particular medical office.
Calculate the mean, median, and mode of the data. Based on the results, which list shows a comparison of the measures of central tendency, from least to greatest?
A) Median, mode, mean
B) Median, mean, mode
C) Mode, median, mean
D) Mean, median, mode
Answers
Answer:
D
Step-by-step explanation:
Mean- 6.78
Median- 7
Mode- 8
Find the standard normal area for each of the following(round your answers to 4 decimal places)
Answers
The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.
What is the standard normal area?To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:
[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]
[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]
[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]
The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.
Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.
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I need help with this
Answers
Answer:
(x -14)² +(y -7)² = 1²
Step-by-step explanation:
You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.
Equation of a circleThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...
(x -14)² +(y -7)² = 1²
two cards are drawn at random from an ordinary deck of 52 cards what is the probability that thee are no sixes
Answers
there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
The probability of drawing a card from an ordinary deck without replacement can be determined using the concept of conditional probability. Conditional probability is the probability of an event occurring, assuming that another event has already occurred.
In order to calculate the probability that the two cards drawn are not sixes, we can use the formula:
P(A and B) = P(A) x P(B|A)
Where A and B represent two independent events, P(A) is the probability of event A occurring, and P(B|A) is the conditional probability of event B occurring given that event A has already occurred.
The probability of drawing the first card that is not a six is:
P(A) = 48/52 = 0.9231
The probability of drawing the second card that is not a six, given that the first card drawn was not a six, is:
P(B|A) = 47/51 = 0.9216
Therefore, the probability of drawing two cards at random from an ordinary deck of 52 cards and having neither of them be a six is:
P(A and B) = P(A) x P(B|A) = 0.9231 x 0.9216 = 0.8503 or approximately 85%.
This means that there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.
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Consider the function represented by the table.
Answers
Answer:c) 6
Step-by-step explanation:i.e. corresponding to different values of x we are given the values of f(x)
we have to find the value of f(0)
i.e. we have to find the value of f(x) when x=0
As we can see from the table the value of f(x) at x=0 is 6
b.) make a conjecture about the relation between det(a), and det(ka) where k is a number (scalar). type your answer after %.
Answers
Based on the properties of determinants, my conjecture is that the determinant of ka is equal to k raised to the power of the dimension of the matrix multiplied by the determinant of the original matrix a.
My conjecture is that the determinant of a matrix multiplied by a scalar k is equal to the determinant of the original matrix a multiplied by k raised to the power of the number of rows or columns in the matrix.
In other words, if a is an n-by-n matrix and k is a scalar, then:
det(ka) = k^n * det(a)
This conjecture is based on the fact that multiplying a matrix by a scalar k multiplies every entry in the matrix by k. Therefore, the determinant, which is a sum of products of matrix entries, is also multiplied by k^n, where n is the number of rows or columns in the matrix.
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What if the equation of the line that passes through (-4,5) and is parallel to the line 4x+2y=10
Answers
Answer: y = -2x -3
Step by step explanation
First, we find the gradient of the line 4x + 2y = 10 by making y the subject of the formula.
4x + 2y = 10
2y = 10 - 4x which is the same as 2y = -4x + 10
Divide each term by 2
2y/2 = -4x/2 + 10/2
y = -2x + 5
From the equation, the gradient (coefficient of x) is -2
Since the line is parallel to 4x+2y=10, therefore the gradient of the lines are the same
The equation of the line can be gotten from y - y1 = m(x -x1)
where y1 = 5, x1 = -4 and m = -2
Therefore subtitiuiting into y - y1 = m(x -x1)
y - 5 = -2(x-(-4))
y - 5 = -2(x + 4)
y - 5 = -2x - 8
y = -2x -8 + 5
y = -2x -3
you can see that the gradients are the same (coefficent of x = -2)
Which of the ten basic functions in
our toolkit have all real numbers for
their range?
Answers
The functions that have all real numbers for their range are the ones in the option B.
Which set of ten basic functions has all real numbers for their range?Remember that for a function y = f(x), we define the range as the set of possible outputs of the function, that is, possible values of y.
Here we can see a lot of functions, first, the option with the absolute value function can be discarded because we know that:
|x| ≥ 0
So it never takes negative values.
We also can discardthe option with the sine and cosine, because the range of these two functions is [-1, 1].
The only remaining option is B, and the range of these 3 functions is (-∞, ∞), so that is the correct option in this case.
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Cells ire approximately round with a diameters ranging from 1 to >100 micrometers. The graph below shows the cross section of half a cell with a diameter of 2μm. The curvature of the cell surface determines if and how vesicles can form. Find the curvature of the cell surface y at the red point x=0.25 from the equation for a circle: y= (2−x)x
Answers
The curvature of the cell surface that has a shape of circle y at the red point x=0.25 is 1.75.
What is diameter?Diameter is a line segment that passes through the center of a circle or sphere and has its endpoints on the circumference of the circle or sphere. The diameter of a circle is twice the length of its radius, so if the radius is given, the diameter can be calculated by multiplying the radius by two.
The equation is given as y = (2 - x)2, where x is the distance from the centre of the circle and y is the curvature of the circle at that distance. To calculate the curvature of the cell surface at any given point, the distance from the centre needs to be known. In this example, the distance from the centre is 0.25, and the curvature of the cell surface at this point is 1.75.
A low curvature, such as 1.75, will allow for more vesicles to form on the surface of the cell. A low curvature will allow for more vesicles to form, and a high curvature will prevent the formation of vesicles.
The equation for a circle with a diameter of 2μm is given as y = (2 - x)2. Substituting x = 0.25 into the equation yields y = (2 - 0.25)2 = 1.75.
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The circle-shaped cell surface's (or circumference's) curvature at the red spot x=0.25 is 0.66.
What is diameter?A circle or sphere's diameter is defined as a line segment with its endpoints on the circumference and that travels through the middle of the object. If the radius is known, the diameter can be determined by multiplying the radius by two since the diameter of a circle is twice the length of its radius.
It is possible to compute the cell surface's curvature at x = 0.25 as follows:
Let's look at the circle's calculation.
y = √(2 - x)x
Now, when x = 0.25,
y = √(2 - 0.25)×0.25
y = √1.75×0.25
y = 0.66
As a result, the cell surface's slope at x = 0.25 is 0.66.
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A local service club has monthly luncheon meetings. Each person chooses from a preset menu with three beverage choices, an appetizer of soup or salad, and four sandwiches to choose from. How many different lunches consisting of a beverage, appetizer, and sandwich are possible?
Answers
Answer:
24 different lunches
Step-by-step explanation:
There are three choices for the beverage, two choices for the appetizer (soup or salad), and four choices for the sandwich. Therefore, using the multiplication principle of counting, the number of different lunches possible is:
3 choices for beverage x 2 choices for appetizer x 4 choices for sandwich = 24 different lunches.
Answer the question below:
A rocket is launched from atop a 76-foot cliff with an initial velocity of 113 ft/s. The height of the rocket
above the ground at time is given by h = -161 +1131+ 76. When will the rocket hit the ground after it is
launched? Round to the nearest tenth of a second.
0.6 seconds
7.7 seconds
3.5 seconds
7.1 seconds
Answers
Answer:
t=7.7 s
Step-by-step explanation:
h=ut+1/2gt²
-76=113t+1/2(-32)t²
-76=113t-16t²
16t²-113t-76=0
[tex]t=\frac{113\pm\sqrt{(-113)^2-4 \times 16 \times(-76)} }{2 \times 16} \\t=\frac{113 \pm\sqrt{12769+4864} }{32} \\t=\frac{113 \pm\sqrt{17633} }{32} \\t=\frac{113+\sqrt{17633} }{32} \approx 7.68~s \approx7.7 s\\or\\t=\frac{113-\sqrt{17633} }{32} \approx~-0.62 ~s \approx-0.6~s[/tex]
negative~sign~rejected.
I need help with this
Answers
Answer:
D.
Step-by-step explanation:
Solve the polynomial equation by factoring and then using the zero-product principle.
2
8x-4=2x-x
Rewrite the equation in factored form.
(Blank)= 0
What is the solution pair?
Answers
the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.
Why it is and what is Zero-Product formula?
First, we can simplify the equation by combining like terms:
28x - 4 = 2x - x
Simplifying further:
26x - 4 = 0
Now, we can factor out 2 from the left side of the equation:
2(13x - 2) = 0
Using the zero-product principle, we can set each factor equal to zero:
2 = 0 or 13x - 2 = 0
The first equation is impossible since 2 is not equal to zero. Solving the second equation, we get:
13x - 2 = 0
Adding 2 to both sides:
13x = 2
Dividing both sides by 13:
x = 2/13
Therefore, the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.
The zero-product property or formula states that if the product of two factors is zero, then at least one of the factors must be zero. In other words, if a and b are real numbers such that ab = 0, then either a = 0, b = 0, or both a and b are zero. This property is often used to solve polynomial equations by factoring the expression and then setting each factor equal to zero.
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Zinnia wrote the following proof to show that the diagonals of rectangle ABCD are congruent:
Zinnia's proof:
Statement 1: Rectangle ABCD is given
Statement 2: segment AD ≅ segment BC because opposite sides of a rectangle are congruent
Statement 3: segment DC ≅ segment DC by the reflexive property of congruence
Statement 4: Angles ADC and BCD are both right angles by definition of a rectangle
Statement 5: Angles ADC and BCD are congruent because all right angles are congruent
Statement 6:
Statement 7: segment AC ≅ segment BD by CPCTC
Which statement below completes Zinnia's proof? (1 point)
Triangles ADC and BCD are congruent (by ASA postulate)
Triangles ADC and BCD are congruent (by SAS postulate)
Triangles ADC and CBA are congruent (by ASA postulate)
Triangles ADC and CBA are congruent (by SAS postulate)
Answers
ADC & BCD are congruent triangles (by SAS postulate). Since triangle ADC & BCD are congruent according to the SAS postulate, we may utilize CPCTC to determine that section AC is equal to segment BD.
All are triangles 3/4 of a five?In arithmetic progression, the triangles 3: 4: 5 are the only ones with edges. Pythagorean triple-based triangles are Herodian, which means they have integer areas and sides.
Are the numbers 3 4 5 a right triangle?The easiest approach I've found to know for sure if an aspect is 90 degrees is to use the 3:4:5 triangle. According to this rule, a triangle is said to be a right triangle if one of its sides is 3 and the other is 4.
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