Answers
Answer:
[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]
Step-by-step explanation:
We want to find a formula for s in terms of a, b, and cos(x).
Let the point where s intersects AB be D.
Notice that s bisects ∠C. Then by the Angle Bisector Theorem:
[tex]\displaystyle \frac{a}{BD} = \frac{b}{AD}[/tex]
We can find BD using the Law of Cosines:
[tex]\displaystyle BD^2 = a^2 + s^2 - 2as \cos x[/tex]
Likewise:
[tex]\displaystyle AD^2 = b^2+ s^2 - 2bs \cos x[/tex]
From the first equation, cross-multiply:
[tex]bBD = a AD[/tex]
And square both sides:
[tex]b^2 BD^2 =a^2 AD^2[/tex]
Substitute:
[tex]\displaystyle b^2 \left(a^2 + s^2 - 2as \cos x\right) = a^2 \left(b^2 + s^2 - 2bs \cos x\right)[/tex]
Distribute:
[tex]a^2b^2 + b^2s^2 - 2ab^2 s\cos x = a^2b^2 + a^2s^2 - 2a^2 bs\cos x[/tex]
Simplify:
[tex]b^2 s^2 - 2ab^2 s \cos x = a^2 s^2 - 2a^2 b s \cos x[/tex]
Divide both sides by s (s ≠ 0):
[tex]b^2 s -2ab^2 \cos x = a^2 s - 2a^2 b \cos x[/tex]
Isolate s:
[tex]b^2 s - a^2s = -2a^2 b \cos x + 2ab^2 \cos x[/tex]
Factor:
[tex]\displaystyle s (b^2 - a^2) = 2ab^2 \cos x - 2a^2 b \cos x[/tex]
Therefore:
[tex]\displaystyle s = \frac{2ab^2 \cos x - 2a^2 b \cos x}{b^2- a^2}[/tex]
Factor:
[tex]\displaystyle s = \frac{2ab\cos x(b - a)}{(b-a)(b+a)}[/tex]
Simplify. Therefore:
[tex]\displaystyle s = \frac{2ab\cos x}{a+b}[/tex]
Related Questions
Please help its urgent:
11. A fish tank has dimensions 3 feet by
2 feet by 1.5 feet. Two feet is the
height of the aquarium. If the tank is
not filled all the way and there are
two inches of empty space at the top,
how many cubic inches of water are
in the tank? (7 points) im not sure how to show my work
Answers
a car gets 27 miles per gallon in the city and 35 miles per gallon on the highway. what range of miles can the car travel on 3 gallons of gas
Answers
Explanation: Since the car gets 27 mpg in the city and gets 35 mpg on the highway, you can set it up in the inequality 27 < < 35 and this represents the range a car can drive for 1 gallon, so to find the range for 3 gallons, you multiply this inequality by 3.
27(3)<<35(3)
27(3)=81
35(3)=105
Then you can insert the numbers into the inequality to get 81<<105.
Re write the statement 19 +7 / 2 x 6 + 1 by including two pairs of brackets to make the total value equal to 2
Answers
PREMISES
y=the expression 19+7/2×6+1 rewritten by including two sets of brackets or parentheses to get a result of 2
CALCULATIONS
To clearly express the mathematical phrase 19+7/2×6+1 to get a result of 2 requires specific parenthetical treatment.
y=19+7/2×6+1 becomes
y=(19+7)/(2×6+1)
y=26/(12+1)
y=26/13
y=
2
PROOF
If y=2, then the inverse of the phrase (19+7)/(2×6+1) returns
y(2×6+1)=19+7
2(2×6+1)=19+7
2(12+1)=19+7
2(13)=26 and
26=26 proves the solution y=2 to the phrase (19+7)/(2×6+1)
eexpres -25/60 as a rational number whose denominator is -12
Answers
Explanation
Divide both the denominator and the numerator by -5 to obtain the denominator of -12 and the numerator of 5.
5/-12
Hope this helps :)
SCREAMING HELP ALERT !!
Answers
Answer: 1/3
Step-by-step explanation:
On side of the smaller quadrilateral is 8, the same side on the larger one is 24. 8 times 3 is 24. So the scale factor from the smaller to the larger is 1/3.
Answer:
1/3
Step-by-step explanation:
similar means all sides are proportinal, in this case one side is 3x bigger in the 2nd figure, so the same must be true of the other fig.
1.Find x,y and z in the figure. 2. find the x and y in the figure
Answers
[tex]\\ \sf\longmapsto x+2x+90=180[/tex]
[tex]\\ \sf\longmapsto 3x+90=180[/tex]
[tex]\\ \sf\longmapsto 3x=180-90[/tex]
[tex]\\ \sf\longmapsto 3x=90[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{90}{3}[/tex]
[tex]\\ \sf\longmapsto x=30[/tex]
Now
[tex]\\ \sf\longmapsto x=2y[/tex](Opposite interior angles)
[tex]\\ \sf\longmapsto 2y=30[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{30}{2}[/tex]
[tex]\\ \sf\longmapsto y=15[/tex]
And
[tex]\\ \sf\longmapsto x+z=180[/tex]
[tex]\\ \sf\longmapsto z+30=180[/tex]
[tex]\\ \sf\longmapsto z=180-30[/tex]
[tex]\\ \sf\longmapsto z=150[/tex]
Answer:
Figure 1Straight angle is 180°:
2x + 90° + x = 180° ⇒ 3x = 90° ⇒ x = 30°Alternate interior angles are congruent:
2y = x ⇒ 2y = 30° ⇒ y = 15°Consecutive interior angles are supplementary:
x + z = 180° ⇒ z = 180° - 30° ⇒ z = 150°Figure 2Alternate interior angles:
3x = 5x - 20° ⇒ 2x = 20° ⇒ x = 10°Sum of interior angles of a triangle:
2y + 4y + 5x - 20 = 180° ⇒ 6y + 5*10° = 200° ⇒ 6y = 150° ⇒ y = 25°Expand.
Your answer should be a polynomial in standard form.
Answers
Answer:
-p^4 + 4p^3 - 5p^2 + 8p - 6
Step-by-step explanation:
Distribute the -p^2 to the p^2 and the 2. Then distribute the 4p to the p^2 and the 2. Then distribute the -3 to the p^2 and the 2.
When we expand:
-p^4 - 2p^2
+ 4p^3 + 8p
-3p^2 - 6
Group, ordering from highest to lowest "degree" (exponent).
-p^4 + 4p^3 - 2p^2 - 3p^2 + 8p - 6
Combine like terms.
-p^4 + 4p^3 - 5p^2 + 8p - 6
(Ight ima need some help!! ) solve the following equation (2x + 3) (3x + 2) − (3x + 2) (2x− 3) = 0. solve for x and show work
(2x + 3) (3x + 2) − (3x + 2) (2x− 3) = 0
Answers
Answer:
x = [tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
I used the FOIL method
[(2x + 3) (3x + 2)] − [(3x + 2) (2x− 3)] = 0
[tex](6x^{2} +4x+9x+6) - (6x^{2} -9x+4x-6)=0[/tex]
[tex](6x^{2} +13x+6) - (6x^{2} -5x-6)=0[/tex]
[tex](6x^{2} +13x+6) - 6x^{2} +5x+6=0[/tex]
combine like terms
[tex]6x^{2} -6x^{2} = 0[/tex]
[tex]13x+5x=18x[/tex]
[tex]6+6=12[/tex]
so, [tex]18x +12 = 0[/tex]
subtract 12 on both sides
[tex]18x=-12[/tex]
divide by 18 to isolate x
[tex]x=-\frac{12}{18}[/tex]
and simplifies to
[tex]x=-\frac{2}{3}[/tex]
Go Which operation would be completed second in the following expression? 7² -3+9+8 dividend by two
Choices:
Subtract
Multiply
divide
Simplify the exponet
Answers
second step: 49 -3
but the thing is when it’s both addition and subtraction u just go from left to right
hope it helps
Answer:
Divide
Step-by-step explanation:
Using PEMDAS, the first would be parenthesis, but there are none, so we do not use P. Next is E which is exponents, which would be the first thing completed. Then is M and D which is multiplication and division. The division is used which is "dividend by two" as it's the second thing completed.
Hope this helped.
ans of this
fast to get 10 pts
Answers
Answer:
2.equivalent sets is answer.|Large{\frac {x}{x + 3} = \frac {5}{2}}
Answers
Answer:
x=-5
Step-by-step explanation:
[tex]\frac{x}{x+3} =\frac{5}{2} \\5x+15=2x\\5x-2x=-15\\3x=-15\\x=-15/3=-5[/tex]
Evaluate Equation Below
Please help!
Answers
Answer:
2nd answer
Step-by-step explanation:
4x^3+2
4*(-1)^3+2
4*(-1)+2
-4+2
-2
Answer: -2
Step-by-step explanation:
Replacing x for -1 would make the equation [tex]4(-1^3)+2[/tex]. Knowing PEMDAS, we know that the parentheses goes first. [tex]-1^3[/tex] means that we need to multiply -1 by itself 3 times ([tex]-1*-1*-1[/tex], * equals "times"). [tex]-1*-1=1[/tex] so [tex]1*-1=-1[/tex]. Now our equation is [tex]4(-1)+2[/tex]. [tex]4*-1=-1[/tex] and -4 + 2 = -2. Hope this explanation helps :)
which expression is equivalent to \root(3)(x^(5)y)
Answers
Answer:
[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{x^{5}y}[/tex]
Required
The equivalent expression
We have:
[tex]\sqrt[3]{x^{5}y}[/tex]
Rewrite as an exponent
[tex]\sqrt[3]{x^{5}y} = (x^{5}y)^\frac{1}{3}[/tex]
Open bracket
[tex]\sqrt[3]{x^{5}y} = x^{5*\frac{1}{3}}y^\frac{1}{3}[/tex]
[tex]\sqrt[3]{x^{5}y} = x^{\frac{5}{3}}y^\frac{1}{3}[/tex]
[tex]( - 12) \times ( - 4) + ( - 8) + ( + 3)[/tex]
could you help..
Answers
[tex] \sf \: ( - 12 )\times( - 4) + (- 8 )+ (+ 3) \\ \sf \: = (- 12 \times - 4 )+ (- 8 + 3) \\ \sf \: = 48 - 5 \\ = 43[/tex]
Hope it helps.
RainbowSalt2222
Find the sum of the first 40 terms of an arithmetic series whose first term is 7 and 40th term is 115. Type answer as an integer (no decimals)
arithmetic sum formula:
Sn = (a1 +
+ an)
geometric sum formula:
az (1 - p)
S =
1-r
Answer:
Answers
Answer:
2440
Step-by-step explanation:
an=115
a=7
Sn=n/2(a+an) [Where n is no. of terms]
= 40/2(7+115)
= 20(122)
= 2440
Factor Z squared minus 3Z -18
Answers
Answer:
z^2-3z-18
=(z^2+3z)+(-6z-18)
=z(z+3)-6(z+3)
=(z+3)(z-6)
PLEASE HELP ASAP PLEASE!!!!!!!
Find the measure of GE.
A. 20
B. 14
C. 15
D. 16
Answers
The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 30%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 65 have PC's at home. What assumptions are necessary for this test to be satisfied
Answers
Solution :
Given data :
x = 65, n = 300
[tex]$\hat p = \frac{x}{n}[/tex]
[tex]$=\frac{65}{300}$[/tex]
= 0.2167
The hypothesis are :
[tex]$H_0: p \leq 0.3$[/tex]
[tex]$H_0: p> 0.3$[/tex]
The [tex]\text{level of significance}[/tex], α = 0.05
The test is right tailed.
The standard deviation is :
[tex]$\sigma = \sqrt{\frac{0.3(1-0.3)}{300}}$[/tex]
σ = 0.0265
The test statistics is :
[tex]$z=\frac{\hat p - p}{\sigma}$[/tex]
[tex]$z=\frac{0.2167 - 0.3}{0.0265}$[/tex]
= -3.14
The critical value is 1.645
The rejection region is : If z > 1.645, then we reject [tex]H_0[/tex]
Decision :
Since the test statistics does not lie in the rejection, so we fail to . [tex]\text{reject the null hypothesis}[/tex].
P-value : [tex]$P(z > - 3.14)$[/tex] = 0.9992
Therefore, the p-value is not less than the level of significance so we fail to [tex]\text{reject the null hypothesis}[/tex].
I don’t really understand this…
Steps:
Calculate MU/P
Compare MUx with MUy
Choose highest MU
Continue until you spend all of your money
Answers
Answer:
In the real world, a consumer may purchase more then one commodity. Let us assume that a consumer purchases two goods X and Y. How does a consumer spend his fixed money income in purchasing two goods so as to maximize his total utility? The law of equi-marginal utility tells us the way how a consumer maximizes his total utilit
-6>t-(-13)
slove for the inequality
Answers
Answer:
-19>t
Step-by-step explanation:
-6>t-(-13)
-6>t +(13)
Subtract 13 from each side
-6-13 > t+13-13
-19>t
Which of the eee-values satisfy the following inequality?
Answers
Answer:
Enterprises usually adopt some quality practices to control the product quality during the manufacturing process in order to assure the delivery of qualitative good products to customers. The quality practices or quality management systems adopted by industries will further evolve due to the changes of quality concepts as time goes by. This chapter discusses the change of quality concepts and the related revolution of quality management systems in the past century. The quality concepts were gradually changed from the achievement of quality standards, satisfaction of customer needs, and expectations to customer delight. Since merely satisfying customers is not enough to ensure customer loyalty, the enterprises gradually focus on customers’ emotional responses and their delight in order to pursue their loyalty. The emotion of “delight” is composed of “joy” and “surprise,” which can be achieved as the customers’ latent requirements are satisfied. Thus, the concept of “customer delight” and the means to provide the innovative quality so as to meet the unsatisfied customers’ latent needs are elaborated on. Finally, a framework of innovation creation is developed that is based on the mining of customer's latent requirements. This outline will manifest the essential elements of the related operation steps.
Tha length of a side of equilateral traingle is give below. find the perimeter of traingles
i. l=4cm
ii. 5.5 cm
Answers
Answer:
i. 12cm
ii. 16.5cm
Step-by-step explanation:
The side lengths on an equilateral triangle are all equal to each other. So if one side is given we can find the perimeter of the triangle by multiplying one of the sides by 3.
4*3=12
5.5*3=16.5
Please help hurry!
Find the lateral surface area of the instant oatmeal container. Round your answer to the nearest hundredth.
SA = in2
Answers
Answer:
≈ 145.23 in²Step-by-step explanation:
The lateral surface area is:
SA = 2πrh = 2*3.14*2.5*9.25 ≈ 145.23 in²[tex]\\ \tt\longmapsto SA=2\pi rh[[/te]
[tex]\\ \tt\longmapsto SA=2\times 22}{7}\times (2.5)(9.25)[/tex]
[tex]\\ \tt\longmapsto SA=145.23in^2[/tex]
(2 + 6i)(8 – 9i)
Divide and simp
Answers
Answer:
70+30i
Step-by-step explanation:
Solve the problem below where X=4 3X+7=
Answers
X = 4×3 X + 7
Resultado
X = 12 X + 7
Forma alternativa
-11 X - 7 = 0
X = -7/11
Explanation: 3 x 4 + 7 = 19
Dilbert invests a total of $26,000 in two accounts paying 14% and 2% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $2,560.00
Answers
Answer:
$17,000 at 14% and $9,000 at 2%
Step-by-step explanation:
Let x = amount invested at 14%.
Let y = amount invested at 2%.
x + y = 26000
0.14x + 0.02y = 2560
-0.02x - 0.02y = -520
(+) 0.14x + 0.02y = 2560
-------------------------------------
0.12x = 2040
x = 17,000
x + y = 26000
17000 + y = 26000
y = 9000
Answer: $17,000 at 14% and $9,000 at 2%
What is the value of a?
Answers
Answer:
90
Step-by-step explanation:
Use angle-arc relation,
For a and 45, Inscribed angle's relation can be utilized
Inscribed angle=Half the arc
45=1/2a
Therefore, a=90
What is the simplest shape in Mathematics?
Answers
the equation of the line that goes through the points (5,5) and is parallel to the line going through the points (-5,5) and (6,1) can be written in the form y=mx+b where m is and b is
Answers
Answer:
y = -4/11x + 75/11
Step-by-step explanation:
y2 - y1 / x2 - x1 1 - 5 / 6 - (-5) -4/11
y = -4/11x + b
5 = -4/11(5) + b
5 = -20/11 + b
75/11 = b
TO BE ANSERED ASAP
If n = 4, then 9ˆ8 ÷ 9 n is equal to__________________.
Answers
Answer:
1,195,742.25 (final answer since instructions did not include rounding up or anything)
Step-by-step explanation:
n = 4
The given expression is:
9^8 ÷ 9n
USE PEMDAS order of operations and solve:
9^8 ÷ 9n
= 43046721 ÷ 9n
Substitue n with 4 and solve:
43046721 ÷ 9(4)
= 43046721 ÷ 36
= 1,195,742.25
Answer:
9^4
Step-by-step explanation:
We know that a^b ÷ a^c = a^ (b-c)
9^8 ÷ 9^4
9^(8-4)
9^4
