Answer: 5/9 of a mile
Step-by-step explanation:
2/6 + 2/9
3/9 + 2/9
5/9
What is the error due to using linear interpolation to estimate the value of sinxsinx at x = \pi/3? your answer should have at least three significant figures, accurate to within 0.1%. (e.g., 1.23 and 3.33e-8 both have three significant figures.)?
The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.
If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...
... x -sin(x) @ x=π/3
... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812
You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.
___
If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...
... (x+1-π/4)/√2 -sin(x) @ x=π/3
... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620
Therefore, the error due to linear interpolation to estimate the value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] is approximately [tex]\( 29.59 \% \).[/tex]
To estimate the error due to linear interpolation for [tex]\( \sin(x) \)[/tex] at [tex]\( x = \frac{\pi}{3} \)[/tex], we need to compare the actual value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] with the value obtained through linear interpolation.
The actual value of [tex]\( \sin\left(\frac{\pi}{3}\right) \)[/tex] is [tex]\( \frac{\sqrt{3}}{2} \)[/tex], which is approximately [tex]\( 0.8660 \)[/tex] .
For linear interpolation, we typically use two nearby points to estimate the value of a function at an intermediate point. Let's consider the points [tex]\( (\frac{\pi}{4}, \sin(\frac{\pi}{4})) \) and \( (\frac{\pi}{2}, \sin(\frac{\pi}{2})) \)[/tex], which are [tex]\( \left(\frac{\pi}{4}, \frac{\sqrt{2}}{2}\right) \) and \( \left(\frac{\pi}{2}, 1\right) \)[/tex], respectively.
Now, we'll use linear interpolation to estimate [tex]\( \sin\left(\frac{\pi}{3}\right) \):[/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \sin\left(\frac{\pi}{4}\right) + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{\sin\left(\frac{\pi}{2}\right) - \sin\left(\frac{\pi}{4}\right)}{\frac{\pi}{2} - \frac{\pi}{4}} \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{2} - \frac{\pi}{4}} \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx \frac{\sqrt{2}}{2} + \left(\frac{\pi}{3} - \frac{\pi}{4}\right) \cdot \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\pi}{4}} \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + \left(\frac{\pi}{3} - 0.7854\right) \cdot \frac{1 - 0.7071}{0.7854} \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + (0.5236 - 0.7854) \cdot \frac{0.2929}{0.7854} \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 + (-0.2618) \cdot 0.3732 \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.7071 - 0.0977 \][/tex]
[tex]\[ \sin\left(\frac{\pi}{3}\right) \approx 0.6094 \][/tex]
Now, we can find the error:
[tex]\[ \text{Error} = \left| \frac{\text{Actual value} - \text{Interpolated value}}{\text{Actual value}} \right| \times 100 \% \][/tex]
[tex]\[ \text{Error} = \left| \frac{0.8660 - 0.6094}{0.8660} \right| \times 100 \% \][/tex]
[tex]\[ \text{Error} = \left| \frac{0.2566}{0.8660} \right| \times 100 \% \][/tex]
[tex]\[ \text{Error} = 0.2959 \times 100 \% \][/tex]
[tex]\[ \text{Error} = 29.59 \% \][/tex]
Are these steps correct let me know
The first step is correct, because you changed the order of two terms in an addition, and the property [tex] a+b=b+a [/tex] is indeed called commutative property of addition.
In the second step, you do the same, but with multiplication: you use [tex] (6x)\cdot y = y \cdot (6x) [/tex]. This means that you're using the commutative property again, except for multiplication. So, the answer should be "commutative property of multiplication.
Finally, the third step is correct, because you're distributing the multiplication by 3 to both terms in the parenthesis, and this is called distributive property: it states that
[tex] a(b+c)=ab+ac [/tex]
The mayor of a city records the population each year since 1980. He models the data as P(t)=16.8(0.94)^t. Where P represents the city’s population, in thousands of people and t represents the number of years since 1980
Select each true statement based on the population model.
A. The population has been increased since 1980
B. The population has changed by 94% each year since 1980
C. The population has changed by 6% each year since 1980
D. The population was 16,800 people in 1980
E. The population was 9,400 people in 1980
F. The population has been decreased since 1980
Answer:
C, D, F are correct.
Step-by-step explanation:
If we look at the equation:
[tex]P(t)=16.8(0.94)^t[/tex]
Is molded after this equation:
[tex]Population_{final}=Population_{initial}(1+r)^t[/tex]
Where 1 represents 100%, r is the rate in decimals and t is time.
So this means that the initial population is 16.8 thousand or in other words 16,800 people. The rate is 1-r, so the rate that the population is decreasing is 0.06 i.e. 6% (because 1-0.06=0.94).
The expression once The left side of an equation is shown below. 3(x+1)+9 if the equation has no solution which expression can be written in the box on the other side of the equation
A. 3(x+4)
B. 2(x+6)+x
C. 4(x-3)-x
D. 3(x+1)+9
C. 4(x-3)-x
Step-by-step explanation:All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...
... 3(x +1) +9 = 4(x -3) -x
... 3x +12 = 3x -12
... 12 = -12 . . . . . false
There is no value of x that will make this true, hence NO SOLUTION.
_____
Comment on the other choices
3x+12 = 3x+12 has an infinite number of solutions, as any value of x will make this true.
c
BECAUSE I SAID SO HUH YOU GOTTA PROBLEMO??
What is the coefficient of abc when the product (a + 2b)(b + 2c)(c + 2a) is expanded and
like terms are combined? Please help
Answer:
The coefficient is 9
Step-by-step explanation:
(a)(b)(c)+(a)(2c)(2a)+(2b)(b)(c)+(2b)(2c)(2a)
abc+4ca^2+2cb^2+8abc
9abc+4ca^2+2cb^2
are theese rational
-3/8 +3/5
Answer:
The sum is rational.
Step-by-step explanation:
-3/8 is a rational number (the ratio of 2 integers)
3/5 is a rational number (the ratio of 2 integers)
When you add 2 rational numbers, you get a rational number.
What is the Value of this X? i feel like it's 90 just double checking
Answer:
x=56
Step-by-step explanation:
There are 3 angles in the triangle
x, 60 and the unknown angle we will call y
y and 2x+4 make a straight line, so that adds to 180
y + 2x+4 = 180
Solve for y
y = 180 - (2x+4)
y = 180 -2x-4
y = 176 -2x
The three angles in a triangle add to 180
x + 60 + y = 180
Substitute in for y
x + 60 + 176 -2x = 180
Combine like terms
-x +236 = 180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply by -1
x = 56
Find the constant of proportionality for the graph and write in the form y = kx. A) y = 1 7 x B) y = 5x C) y = 7x D) y = 35x
Find the x and y for each dot:
5,35
10,70
15,105
etc.
Divide the Y by the X:
35 / 5 = 7
70 / 10 = 7
etc.
The answer would be C) y = 7x
Answer:
Option C is correct
[tex]y = 7x[/tex]
Step-by-step explanation:
Direct variation states that:
[tex]y \propto x[/tex] ......[1]
then, the equation is in the form of:
[tex]y=kx[/tex], where k is the constant of variation
From the given graph we have points in the form of (x, y) i.e,
(0, 0), (5, 35), (10, 70), (15, 105), (20, 140), (25, 175) and (30, 210)
Substitute any points i.e (5, 35) in [1] we have;
[tex]35 = 5k[/tex]
Divide both sides by 5 we have;
7 = k
or
k = 7
then;
[tex]y = 7x[/tex]
Therefore, the constant of proportionality for the graph is, 7 and its form is, [tex]y = 7x[/tex]
In right triangle QRS,the measure of an angle R is 90. Which ratio represents tan Q
tan(Q) = RS/RQ
Step-by-step explanation:The mnemonic SOH CAH TOA reminds you that ...
... Tan = Opposite/Adjacent
The side opposite angle Q is RS. The side adjacent is RQ. (QS is the hypotenuse, which does not come into play in the tangent function.)
Then ...
... tan(Q) = Opposite/Adjacent = RS/RQ
In right triangle QRS, with angle R being 90 degrees, tan Q is represented by the length of the side opposite to angle Q divided by the length of the side adjacent to Q which tan Q = SR/ QR.
In right triangle QRS, with angle R being 90 degrees, the ratio that represents tan Q is the length of the opposite side to angle Q divided by the length of the adjacent side.
In trigonometry, the tangent (tan) of an angle in a right triangle is a ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.
Therefore, if we label the sides opposite and adjacent to angle Q as opposite and adjacent respectively, the formula for tan Q would be:
tan Q = opposite/adjacent
= SR/QR
For example, if a right triangle has sides of lengths 3, 4, and 5, with the side lengths of 3 and 4 being adjacent to and opposite angle Q respectively, the tan Q would be calculated as 4/3.
If the alternative hypothesis of an experiment is "The true mean height of children is less than 60 inches," what is the null hypothesis?
if correct will give brainliest!!
Answer:
Null Hypothesis : The true mean height of children is more than 60 inches.
Step-by-step explanation: Null Hypothesis is defined as a hypothesis that there is no significant difference between the observed and sampled mean.
So, if alternative hypothesis is " the true mean height of children is less than 60 inches" which denotes there is significant difference between sampled and observed mean heights so null hypothesis is taken as " true mean height of children is more than 60 inches"
At the zoo the polar bears are fed 7/9 bucket of fish a day. The penguins are fed 4/7 that amount. What fraction are the penguins fed?
Answer: They are fed 4/9 of what the polar bears are fed.
Step-by-step explanation:
7/9*4/7=
1/9*4/1=4/9
The 7's get cancelled out.
The penguins at the zoo are fed 4/9 bucket of fish a day. This fraction has been calculated by multiplying the amount of food the polar bears get (7/9 bucket) by 4/7 as specified in the problem.
Explanation:To find out how much the penguins are fed, we first understand the given units involving the polar bears and penguins. The polar bears are fed 7/9 bucket of fish a day, and the penguins are fed 4/7 that amount. Therefore, to calculate the amount the penguins are fed, we multiply the amount the polar bears are fed by 4/7.
We get this by performing the calculation (7/9) * (4/7). The sevens cancel out, leaving us 4/9, which is the fraction of the bucket of fish that the penguins are fed each day.
Learn more about Fraction calculations here:https://brainly.com/question/29633725
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A polynomial function P(x) with rational coefficients has the given roots. Find two additional roots of P(x)=0.
i and 7 + 8i
a) -1,1
b) -i, 7-8i
c)-1, 56i
d) no additional roots are possible
Also if anyone has the answers to the practice and the quick check i'm super behind and I need help ASAP!!
Answer:
B
Step-by-step explanation:
Answer:
Step-by-step explanation:
If a polynomial function P(x) with rational coefficients has a root z. the so is the complex conjugate of z is a root. (In order to see that, take the complex conjugates of the equation P(x)=0, and note that complex conjugates of rational numbers equal to itself.)
Therefore the complex conjugates of the given roots i and 7+8i , are -i and 7-8i is the required answer.
Given: ABD = CDB which of the following must be true if the triangle are congruent?
PLZZZZ
C. AB ║ DC
Step-by-step explanation:The congruence of the two triangles means ∠ABD≅∠CDB. These, then, are alternate interior angles on either side of transversal BD between lines AB and DC. If alternate interior angles are congruent, the lines are parallel:
... AB ║ DC
_____
Congruence of the triangles does not require ∠B to be bisected or that it be 90°.
All the three sides of the given triangles are equal to the sides of another triangle then, [tex]\rm \overline{AB}=\overline{DC}[/tex]. Therefore the correct option is C).
Given :
Triangle ABD is congruent to the triangle CBD.
A triangle has three sides and the sum of all the interior angles are equal to [tex]180^\circ[/tex].
If the triangle ABD is congruent to the triangle CBD then:
AB = DC
AD = BC
BD = BD
If all the three sides of the given triangles are equal to the sides of another triangle then, [tex]\rm \overline{AB}=\overline{DC}[/tex]. Therefore the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/19325053
Let D={6,9,11}, E={6,8,9,10} and F={5,7,8,9,11}
List the elements in the set D U E.
Answer:
D U E = { 6,8,9,10,11}
Step-by-step explanation:
U stands for union, which is join the sets together
D U E = { 6,8,9,10,11}
At a county fair, 9 people out of 1,000 earned a perfect score in a carnival game. What decimal represents the number of people who earned a perfect score?
Answer:
0.009
Step-by-step explanation:
So 9/1000 can be written as 0.009
Answer:
The answer is 0.009.
Step-by-step explanation:
The total number of people from which only 9 earned a perfect score = 1,000.
The number of people who earned a perfect score = 9
The decimal that represents the number of people who earned a perfect score = The number of people who earned a perfect score ÷ The total number of people concerned = 9 ÷ 1,000 = 0.009.
Point A is located at (4, 8) and point B is located at (14, 10) . What point partitions the directed line segment AB¯¯¯¯¯ into a 1:3 ratio?
(6 1/2, 8 1/2)
(11 1/2, 9 1/2)
(6, 6)
(9, 9)
Answer:
A is the answer or (6 1/2, 8 1/2) or (13/2, 17/2) or (6.5,8.5)
Step-by-step explanation:
Given : A line segment AB with
[tex]A= (x_1,y_1)=(4,8)[/tex] and [tex]B= (x_2,y_2)=(14,10)[/tex]
let C partitioned the line AB by 1:3 let m:n = 1:3
shown in the figure attached
Formula used:
[tex]C= (\frac{n x_1 + m x_2 }{m+n},\frac{n y_1+ m y_2 }{m+n})[/tex]
putting value in formula we get,
[tex]C= (\frac{(4) (3)+ (14)(1) }{1+3},\frac{(8)(3)+ (10)(1)}{1+3})[/tex]
[tex]C= (\frac{(13 }{2},\frac{17}{2})[/tex]
[tex]C= (6.5 ,8.5)[/tex]
[tex]C= ( 6 1/2,8 1/2)[/tex]
therefore, A is the answer
Please help with homework!!!!‼️‼️‼️‼️‼️‼️
Answer:
3.04 m18Step-by-step explanation:
The midsegment of a triangle is half the length of the side it is parallel to.
1. For a distance of 6.08 m between wall plates, the colar tie will be half that, or 3.04 m.
2. The perimeter of ΔXYZ is ...
... 10 + 12 + 14 = 36
The sides of ΔABC are half the length of the sides of ΔXYZ, so the perimeter of ΔABC is half the perimeter of ΔXYZ.
... perimeter of ΔABC = 36/2 = 18
HELP HELP fast please
102°
Step-by-step explanation:Opposite angles of an inscribed quadrilateral are supplementary.
∠Q = 180° -∠A = 180° -78°
∠Q = 102°
WILL MARK BRAINLIEST
Evaluate each expression for g = -7 and h = 3 and match it to its value
Values:
a. -2
b.:4
c. 46
d: 10
e: -10
f: -21
Expressions:
a: g + h
b: g - h
c: h - g
d: gh
e: g + h ^2
f: g^2 - h
Answer:
g + h = -4
g - h = -10
h -g = 10
gh = -21
g+ h^2 = 2
g^2 -h = 46
Step-by-step explanation:
We know g = -7 and h = 3
g + h = -7 +3 = -4
g - h = -7 - 3 = -10
h -g = 3 --7 = 3+7 = 10
gh = (-7) * 3 = -21
g+ h^2 = -7 + (3)^2 = -7+9 = 2
g^2 -h = (-7)^2 -3 = 49 -3 = 46
There are 17 students participating in a spelling bee. how many ways can the students who go first and second be chosen?
To determine the number of ways to choose two students to go first and second in a group of 17 students, we use permutations, resulting in a total of 17 * 16 = 272 ways.
The question inquires about the number of ways two students can be chosen from a group of 17 to go first and second in a spelling bee, which can be solved using combinatorics.
To choose the first student, we have 17 options. After choosing the first student, we have 16 remaining students to choose from for the second student. Therefore, the total number of ways to choose students for these two positions is the product of these two numbers. This scenario calls for a permutation calculation since the order in which we select the students matters.
The formula is n!/(n-r)!, where n is the total number of items to pick from, and r is the number we are picking. For our case, n = 17 and r = 2.
Total number of ways (permutations) = 17 * 16 = 272 ways.
Which ratio forms a proportion with 18/27 ?
Answer:
2/3
Step-by-step explanation:
2 • 9 = 18
3 • 9 = 27
2/3 is equal to 18/27. All you have to do is multiply 9 to the numerator and the denominator for proof.
Hope this helps :)
Using graph paper, solve the following inequality. Then click on the graph until the correct one is displayed. y ≥ |x - 1|
Answer:
see attached plot for y ≥ |x - 1|
Step-by-step explanation:
Answer:
Graph below. x=1.
Step-by-step explanation:
1) Check the graph below. Take a closer look at the green area. This great Triangle intercepts the y-axis at the point (0,1) since it's an absolute value.
2) Algebraically, turning this function into an equation, since modulus
|x|=0, x=0.
[tex]y\geq |x-1|\\ |x-1|\geq 0\\ x-1\geq 0\\ x-1+1\geq 0+1\\ x\geq 1[/tex]
Triangles △ABC and △DFG are similar. The lengths of the two corresponding sides are 1.4m , and 56 cm. What is the ratio of the perimeters of these triangles ?
5/2
Step-by-step explanation:The ratio of perimeters is the same as the ratio of corresponding sides:
... (140 cm)/(56 cm) = 5/2
Answer:
5:2
Step-by-step explanation:
We have been given that triangles △ABC and △DFG are similar. The lengths of the two corresponding sides are 1.4 m and 56 cm.
Since both triangles are similar, therefore all corresponding sides will have same proportion.
Let us find proportion of corresponding sides of both triangles.
1 meter = 100 centimeter
1.4 meter = 1.4* 100 centimeters = 140 centimeters.
[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{140}{56}[/tex]
[tex]\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=\frac{5}{2}[/tex]
The ratio of sides of △ABC to sides of△DFG is 5:2.
Since perimeter of a triangle is sum of lengths of three sides of the triangle and all sides of both triangle have the ratio 5:2, therefore, their perimeters will be in same ratio, that is 5:2.
Figure RHOM is a rhombus. and are the diagonals of the rhombus, as well as angle bisectors of the vertex angles, and they create four isosceles triangles: HOM, MHR, RHO, and OMR. What is true about MSR? It must be acute. It must be a right angle. It must be equal to MRH. It must be equal to RMS.
Answer:
∠MSR is right angle
Step-by-step explanation:
It is given that RHOM is a Rhombus
Also ΔHOM, ΔMHR, ΔRHO and ΔOMR are isosceles triangles
Let us take ΔMSR and ΔRSH
∠MRS =∠HRS ( since it is given that the diagonal RO bisects ∠R)
∠RMS =∠RHS ( since Δ MRH is isosceles triangle )
RS = RS ( common side )
By AAS congruency rule ΔMSR ≅ ΔHSR
so we have
∠MSR=∠RSH ( corresponding parts of congruent triangles are congruent)
also we have
∠MSR +∠RSH =180° ( supplementary angles)
∠MSR +∠MSR=180° ( since ∠MSR=∠RSH)
2∠MSR= 180°
∠MSR =90°
Hence ∠MSR is right angle
Answer:
It must be a right angle.
Step-by-step explanation:
The figure attached shows the rhombus RHOM with RO and HM as diagonals and are the angle bisectors of the vertex angles.
Let S be the point where the diagonals RO and HM intersects each other.
ΔHOM, ΔMHR, ΔRHO, ΔOMR are four isosceles triangles in the given rhombus.
Since, Diagonals of a rhombus bisect each other at right angle.
Therefore, we have ∠MSR= 90°
That is, ∠MSR is a right angle.
Can someone help me figure out the answer?
Answer:
8763
Step-by-step explanation:
Let x represent the number of students the college had last year. Then this year's enrollment is ...
... x - 3%·x = 8500
... x(1 - 0.03) = 8500 . . . . . collect terms
... x = 8500/0.97 ≈ 8762.89 . . . . divide by the coefficient of x
Enrollment last year was about 8763.
_____
Of course, you know 3% = 3/100 = 0.03.
Linda is on her way home in her car. She has driven 36 miles so far, which is three-fourths of the way home. What is the total length of her drive?
Answer:
The Answer is 48 miles.
Step-by-step explanation:
Linda has driven 36 miles home and that is 3/4 of the way home. If you divide 36 by 3 equals 12 miles per 1/4 drive. Multiply 12x4 and the answer is 48.
Hope that helps!
The total cost for Sophia to build b birdhouses is represented by the function f(b)=3.5b+24.
What does the value 3.5 represent in this situation?
The total cost to build b birdhouses is $3.50.
The initial cost is $3.50.
For each birdhouse built, the total cost increases by $3.50.
For each birdhouse built, the total cost decreases by $3.50.
For each birdhouse built, the total cost increases by $3.50.
Step-by-step explanation:The number 3.5 multiplies b, so when b increases by 1, f(b) increases by 3.5. Making 1 more birdhouse increases the total cost by $3.50.
Answer: For each birdhouse built, the total cost increases by $3.50.
Step-by-step explanation:
Given: The total cost for Sophia to build b birdhouses is represented by the function [tex]f(b)=3.5b+24[/tex]
We can see in the function 3.5 is multiplied to b, so when b increases , f(b) increases by 3.5.
[tex]f(1)=3.5(1)+24=3.5+24=27.5[/tex]
[tex]f(2)=3.5(2)+24=7+24=31[/tex]
[tex]f(3)=3.5(3)+24=10.5+24=34.5[/tex]
and [tex]f(2)-f(1)=f(3)-f(2)=3.5[/tex]
Therefore, the value of 3.5 represents that for each birdhouse built, the total cost increases by $3.50.
There are 90 sixth graders at Wilson Middle School. Only 50% of the sixth graders will attend the morning assembly. How many sixth graders will be at the morning assembly?
Answer: 45
Step-by-step explanation:
Divide 90 by 2 and you will the the answer of 45.
Rhombus ADEF is inscribed in △ABC such that the vertices D, E, and F lie on the sides AB , BC , and AC respectively. Find the side of the rhombus if AB=7 cm, BC=5 cm, and AC=8 cm.
3 11/15 cm
Step-by-step explanation:AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:
... BE:CE = BA:CA = 7:8
Then ...
... BE:BC = 7 : (7+8) = 7:15
ΔDBE ~ ΔABC, so DE = 7/15 × AC
... DE = 7/15 × 8 cm = (56/15) cm
... DE = 3 11/15 cm
To find the side of the inscribed rhombus, we can use the Pythagorean theorem and the properties of inscribed rhombuses.
Explanation:To find the side of the rhombus, we need to understand the properties of inscribed rhombuses. In an inscribed rhombus, the diagonals are perpendicular bisectors of each other.
Let's label the side of the rhombus as 's'.
Using the given information, we can see that AB and AC are the diagonals of the rhombus.
Since AB = 7 cm and AC = 8 cm, we know that the diagonals bisect each other and form right angles.
Therefore, we can use the Pythagorean theorem to find the side of the rhombus:
s^2 = (AB/2)^2 + (AC/2)^2
s^2 = (7/2)^2 + (8/2)^2
s^2 = (49/4) + (64/4)
s^2 = (113/4)
s = sqrt(113/4)
Find the length of AC. Round answer to the nearest tenth.
Answer:
16.0
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
... Tan = Opposite/Adjacent
... tan(32°) = 10/AC
Multiplying by AC and dividing by the tangent gives you ...
... 10/tan(32°) = AC = 16.0
Answer: The required length of AC is 16.1 units.
Step-by-step explanation: We are given to find the length of side AC of triangle ABC.
From the figure, we note that
the triangle ABC is a right-angled triangle, where
m∠C = 90°, m∠A = 32° and BC = 10 units.
For the acute angle A, side AC is the base and side BC is the perpendicular.
So, from trigonometric ratios, we have
[tex]\tan m\angle A=\dfrac{perpendicular}{base}\\\\\\\Rightarrow \tan32^\circ=\dfrac{BC}{AC}\\\\\\\Rightarrow \tan32^\circ=\dfrac{10}{AC}\\\\\\\Rightarrow 0.62=\dfrac{10}{AC}\\\\\\\Rightarrow AC=\dfrac{10}{0.62}\\\\\Rightarrow AC=16.13.[/tex]
Rounding to nearest tenth, we get
AC = 16.1 units.
Thus, the required length of AC is 16.1 units.