Se tiene un lote baldío de forma triangular bardeado. La barda de enfrente tiene una medida de 4 m,las otras dos bardas no es posible medirlas directamente pues hay mucha basura. Sin embargo,se sabe que el ángulo que está frente a la barda frontal mide 34° y otro de sus ángulos mide 64°. Se quiere calcular la medida de la barda que está enfrente del ángulo de 64°. Explica por qué no es posible resolver el problema aplicando sólo las razones trigonométricas o el teorema de Pitágoras
Answer:
a) La medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m. b) El triángulo en cuestión no es un triángulo rectángulo, es decir, ninguno de sus ángulos internos es recto (90 grados sexagesimales). En estos casos, no se puede aplicar el Teorema de Pitágoras o la simple utilización de las razones trigonométricas; se aplican, en cambio, leyes para la resolución de triángulos oblicuángulos (o triángulos no rectángulos).
Step-by-step explanation:
Este problema no se puede resolver "aplicando sólo las razones trigonométricas o el teorema de Pitágoras" porque es sólo aplicable a triángulos rectos, es decir, uno de los ángulos del triángulo es recto o igual a 90 grados sexagesimales. Los dos restantes triángulos suman 90 grados sexagesimales, o se dice, son complementarios.
La resolución de triángulos que no son rectos (conocida en algunos textos como solución de problemas de triángulos oblicuángulos) pueden resolverse usando, la ley de los senos (o teorema del seno), ley de los cosenos y la ley de las tangentes. El caso propuesto en la pregunta se ajusta a la ley de los senos:
[tex] \\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)} = \frac{c}{\sin(\gamma)}[/tex]
Es decir, la razón entre el lado de un triángulo y el seno del ángulo que tiene frente a él es igual para todos los lados y ángulos del triángulo.
El triángulo de la pregunta no tiene un ángulo recto
La suma de los ángulos internos de un triángulo es de 180 grados sexagesimales:
[tex] \\ \alpha + \beta + \gamma = 180^{\circ}[/tex]
En la pregunta tenemos que la suma de los dos ángulos propuestos es:
[tex] \\ 34^{\circ} + 64^{\circ} + \gamma = 180^{\circ}[/tex]
[tex] \\ 98^{\circ} + \gamma = 180^{\circ}[/tex]
Restando 98 grados sexagesimales a cada lado de la igualdad:
[tex] \\ 98^{\circ} - 98^{\circ} + \gamma = 180^{\circ} - 98^{\circ}[/tex]
[tex] \\ 0 + \gamma = 180^{\circ} - 98^{\circ}[/tex]
[tex] \\ \gamma = 82^{\circ}[/tex]
Con lo que se deduce que no hay ningún ángulo recto en el triángulo propuesto y no se podría usar el Teorema de Pitágoras o simples razones trigonométricas para resolverlo.
Resolución del lado del triángulo
De la pregunta tenemos:
La barda de enfrente tiene una medida de 4m. El ángulo que está enfrente de esta barda (barda frontal) es de 34°. No se sabe el valor del lado que está enfrente del ángulo de 64°, pero se puede calcular usando la Ley de los senos.Digamos que:
[tex] \\ a = 4m, \alpha = 34^{\circ}[/tex]
[tex] \\ b = x, \beta = 64^{\circ}[/tex]
Entonces, aplicando la Ley de los senos:
[tex] \\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)}[/tex]
Multiplicando a cada lado de la igualdad por [tex] \\ \sin(\beta)[/tex]
[tex] \\ \frac{a}{\sin(\alpha)}*\sin(\beta) = \frac{b}{\sin(\beta)}*\sin(\beta)[/tex]
[tex] \\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*\frac{\sin(\beta)}{\sin(\beta)}[/tex]
[tex] \\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*1[/tex]
[tex] \\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b[/tex]
Sustituyendo cada valor en la expresión anterior:
[tex] \\ b = \frac{a}{\sin(\alpha)}*\sin(\beta)[/tex]
[tex] \\ b = \frac{4m}{\sin(34^{\circ})}*\sin(64^{\circ})[/tex]
[tex] \\ b = 4m*\frac{0.8988}{0.5592}[/tex]
[tex] \\ b = 6.4292m[/tex]
En palabras, la medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m.
El lado c puede obtenerse de manera similar considerando que [tex] \\ \gamma = 82^{\circ}[/tex].
A metal shop is cutting a rectangular piece of sheet metal with a width of 60 inches and a length of 144 inches. The shaded parts of the diagram represent two rectangular sections, A and B, that will be cut and removed.
Part A :What are the dimensions of section B?
Part B:What will be the area, in square inches, of the piece of sheet metal after both sections are cut and removed?
Answer:
Dimensions of section B = 36 inches, 48 inches
Area of the piece of sheet metal after both sections are cut and removed = 6336 square inches
Step-by-step explanation:
Given: Width and length of a rectangular piece of sheet metal are 60 inches and 44 inches.
To find: dimensions of section B, the area of the piece of sheet metal after both sections are cut and removed
Solution:
Length of rectangle B = TR = SR - ST = PQ - ST (As SR = PQ being opposite sides of rectangle)
Length of rectangle B = PQ - ST = 60 - 24 = 36 inches
Breadth of rectangle B = UR = QR - QV - VT - TU
Here, QR = PS = 144 inches (opposite sides of rectangle PQRS are equal )
QV = 36 inches
VT = WX = 24 inches ( opposite sides of rectangle WVTX are equal)
TU = 36 inches
So,
Breadth of rectangle B = 144 - 36 - 24 - 36 = 48 inches
Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches
Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches
Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches
Area of the piece of sheet metal after both sections are cut and removed =8640 - ( 1728 + 576 ) = 8640 - 2304 = 6336 square inches
Flora made 4 withdrawals of $80 each from her bank account. What was the overall change
in her account?
The total change in her account is $
Answer:
320$
Step-by-step explanation:
Answer:
Step-by-step explanation:
80 divided by 4 should be 20? sorry if i am wrong
what is the square root of 144?
Answer:
12
Step-by-step explanation:
12 times 12 is 144
Hope this helps
If you multiply any number by zero, your answer will be
that same number.
impossible.
zero.
negative.
Answer:
zero
Step-by-step explanation:
for example,
2 x 0 = 0
124 x 0 = 0
its some number zero times so when you multiply by zero, its zero
How do you find compound probability
Answer:
Compound probability is equal to the probability of the first event multiplied by the probability of the second event.
Step-by-step explanation:
Please help me in this question.I need it right now!!!
Answer:
X=102 y=288 =390
Step-by-step explanation:
X=50+32=82=180-82=102
Y= 50+32=82=360-82=288
Total answer is =390
What’s the answer to this
Answer:
C is the correct answer. F(x) = -[tex]x^{3}[/tex]
Which expression is equivalent to 6 (a-3)?
Answer:
6a-18
Step-by-step explanation:
multiply by 6
6a-(6×3)
6a-18
=6a-18
Aiden is grocery shopping and wants to know which packages are cheapest. He is
looking at four different bottles of liquid laundry detergent: Bottle A is 175 fluid
ounces for $19.25; Bottle B is 138 fluid ounces for $8.97; Bottle C is 100 fluid ounces
for $8.00; and Bottle D is 72 ounces for $7.56. Assuming the detergent is of equal
quality, which bottle is the best deal?
Answer:Bottle B
Step-by-step explanation:
Given
Bottle A has 175 fluid ounce and cost [tex]\$19.25[/tex]
So it cost [tex]\frac{175}{19.25}=9.09\ \text{ounce per}\ \$[/tex]
Bottle B has 138 fluid ounce and cost [tex]\$8.97[/tex]
So it cost [tex]\frac{138}{8.97}=15.38\ \text{ounce per}\ \$[/tex]
Bottle C has 100 fluid ounce and cost [tex]\$8.0[/tex]
So it cost [tex]\frac{100}{8}=12.5\ \text{ounce per}\ \$[/tex]
Bottle D has 72 fluid ounce and cost [tex]\$7.56[/tex]
So it cost [tex]\frac{72}{7.56}=9.52\ \text{ounce per}\ \$[/tex]
So, Bottle B delivers more ounces at same price
The first term of a geometric sequence is 1 and its common ratio is 6. What is the sixth term?
a. 31
b. 3176
c. 7776
d. 46,656
Answer:
c. 7776
Step-by-step explanation:
1, 6, 36, 216, 1296, 7776
Therefore, c. 7776
I hope this helped and have a good rest of your day!
HELP PLEASE thank you!!
Answer:
x = 180 -117
x = 63°
y = 90 - 63
y = 27°
Step-by-step explanation:
Which of the following represents the factorization of the trinomial below?
-2x3-14x2 - 12x
A. -2(x2 + 1)(x+6)
B. -202 + 1)(x-6)
C. -2x(x + 1)(x+6)
a
D. -2x(x + 1)(x-6)
Answer:
-2(x + 1)(x + 6)
Step-by-step explanation:
Please use " ^ " to denote exponentiation: -2x^3-14x^2 - 12x
Note that all three terms are evenly divisible by -2x, leaving the quotient x^2 + 7x + 6.
This quotient is also easily factored:
-2x^3-14x^2 - 12x = -2(x^2 + 7x + 6) = -2(x + 1)(x + 6)
a right triangle has the coordinates a(6,0), b(0,0) and c(0,8). what is the perimeter of the triangle
Answer:
28
Step-by-step explanation:
sry if I'm wrong although I used calculator
You have an ice cream scoop with a 2-inch diameter. You have an ice cream cone with a 2-inch diameter and a height of 5 inches. If you place one scoop of ice cream on the cone and let the ice cream melt, will it spill over the cone?
Answer:
No, because the volume of the cone is greater than the volume of the ice cream scoop.
Step-by-step explanation:
To solve this problem we just need to compare the volume of the ice scream scoop with the volume of the ice cream cone.
The ice scream scoop is a sphere with a diameter of 2 inches (so a radius of 1 inch), then the volume is:
V = (4/3) * pi * r^3
V = (4/3) * pi * 1^3
V = 4.1888 in3
Now, to find the volume of the ice cream cone, we just need to use the formula of the cone volume (with radius = 1 inch):
V = (1/3) * pi * r^2 * h
V = (1/3) * pi * 1^2 * 5
V = 5.236 in3
As the volume of the cone is greater than the volume of the ice cream scoop, the ice cream will not spill over the cone after melting.
5c+4 = 2 (c – 5)
What is the solution?
Answer:
0
Step-by-step explanation:
if I'm correct it's 0 because when you do all of the math that's what it came out to
2. Evaluate f(3) for f(x) = 2x - 9
Answer:
-3
Step-by-step explanation:
[tex]f(x) = 2x - 9[/tex]
[tex]f(3) = 2(3) - 9\\f(3) = 6 - 9\\f(3) = -3[/tex]
Task 5—Polynomial Division and the Remainder Theorem
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function
Answer:
See Explanation
Step-by-step explanation:
Let our quadratic polynomial function [tex]f(x)=x^2-7x+6[/tex]
Let our linear binomial in the form (x − a)=x-1
Part 1: We use long division to divide the polynomial by the binomial.
[tex]\left|\begin{array}{c|c}&x-6\\-----&-----\\x-1&x^2-7x+6\\Subtract&-(x^2-x)\\&------\\&-6x+6\\Subtract&-6x+6\\&------\\&0\end{array}\right|[/tex]
Therefore:[tex]\dfrac{x^2-7x+6}{x-1}=x-6[/tex]
Part 2: In our chosen linear monomial x-1, a=1
[tex]f(a)=f(1)\\f(1)=1^2-7(1)+6=1-7+6=0\\f(a)=0[/tex]
Part 3:
To determine whether a linear binomial is a factor of a polynomial function using the remainder theorem
Given a linear binomial x-aSubstitute a into the polynomial function f(x)If the value of f(a)=0, the linear binomial is a factor. However, if f(a) is not equal to zero, then by the remainder theorem, x-a is not a factor of f(x)I need help with this answer can you plz help
Please help with this
Answer: She sold 5 shirts
Step-by-step explanation: 100 + 12x6 + 5t + 7x4 + 5x5 - 8x5
you get 100 + 72 + 28 + 25 - 45 + 5t
You add all that and subtract but not the 5t and you get 180 then you can do 205-180 and get 25 then you you find what times 5 equals 25 and then you get 5 t shirts sold
i need to find the value of x
Answer:
x = 24
Step-by-step explanation:
Since all the angles share a common vertex 'U' lying on a straight line QT.
Therefore, sum of all angles formed at U will be equal to 180°.
m∠RUQ + m∠RUS + m∠SUT = 180°
(2x - 4) + (3x + 5) + (2x + 11) = 180°
(2x + 3x + 2x) + (5 - 4 + 11) = 180
7x + 12 = 180
7x = 180 - 12
x = [tex]\frac{168}{7}[/tex]
x = 24
Therefore, value of x = 24
A net of a triangular prism is shown below. 42 8 ft 3 ft 5 f 5 ft What is the surface area, in square feet, of the triangular prism? A 44 B 96 C 108 D 120
Answer:
(C)108 square feet
Step-by-step explanation:
A net of triangular prism consists of two triangular and three rectangular faces.
The net attached is that of a right triangular prism.
Area of One Triangular Face =0.5 X 3 X 4=6 square feet
The rectangular faces are of dimension 4 ft by 8 ft, 5ft by 8ft and 3ft by 8 ft respectively.
Therefore:
Surface Area of the net =2(6)+(4X8)+(5X8)+(3X8)
=12+32+40+24
=108 square feet
The correct answer is C.
Answer:
108
this is correct, trust me
Which of the following statements is equivalent to P(z < −2.1)? P(z > –2.1) 1–P(z < 2.1) P(z < 2.1) 1–P(z > 2.1)
Answer:
It's b
Step-by-step explanation:
Just answered it
The given statement P(z < −2.1) is equivalent to the expression 1 – P(z < 2.1). Option B is correct.
What is the Z -a score?A Z-score is stated as the fractional model of data point to the mean using standard deviations.
here, z = x - μ / σ
where, μ = mean and σ = standard deviation
Here,
P(z < −2.1)
By the property of the Z score,
P(z < −2.1) = 1 – P(z < 2.1)
Thus, the given statement P(z < −2.1) is equivalent to the expression 1 – P(z < 2.1).
Learn more about the z-score here:
brainly.com/question/13793746
#SPJ2
HELPPP ASAP
which point represents the ordered pair
Answer:
point S
Step-by-step explanation:
mooo! hope this helps
Quando colocamos roupas molhadas no varal em dias quentes percebemos que as roupas depois de um tempo ficam secas. Qual o estado físico que se encontra nas roupas molhadas? e nas roupas secas?
Answer:
Liquid water to vapor waterStep-by-step explanation:
This problem is about our wet clothe, when we put it under the Sun to dry.
Notice that the clothe is wet at the beginning, but after a certain time, it gets dry. This phenomenon is beacuse the change of the state of the water inside the clothe.
You see, at the beginning, the water is in liquid state making the wet effect, then that water transforms into vapor, makign the dry effect.
Therefore, the answer is "liquid water to vapor water", that's the change.
Please help! I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking an even number and then picking an even number?
Simplify your answer and write it as a fraction or whole number.
1/6 and you got the comment why
Answer:
1/6
Step-by-step explanation:
Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!
The value of 1 tenth is less the value of 3 tenth
Answer:
True, 3 tenths is closer to one whole
Step-by-step explanation:
↓ ↓
A.366
B.318
C.342
D.294
Answer:
318 mm2
Step-by-step explanation:
Please see the step-by-step solution in the picture attached below.
Hope this answer can help you. Have a nice day!
Answer:
[tex]318mm^{2}[/tex]
You can break the shape into pieces you can work with, and then add up the areas individually.
Solve the following system by graphing:
Answer:
Option B (-3,-8)
Step-by-step explanation:
Use a graphing tool to graph the lines [tex]-4x+3y=-12[/tex] and [tex]-2x+3y=-18[/tex].
When graphed, the lines pass at the point (-3, -8).
Graph B matches this, so Option B is the answer.
Sarah picks two hats at random from 5 bill caps and 3 beanies. What is the probability she picks a BILL cap, DOES NOT REPLACE IT, then chooses ANOTHER BILL cap?
Answer:
The probability is 5/14
Step-by-step explanation:
Here, we are to calculate/estimate a probability
Firstly , we need to know the total number of caps
we have 5 bill caps and 3 beanies.
Total number of caps = 5 + 3 = 8 caps
The probability of picking the first bill cap is 5/8
Now after removing this and not replacing, we have 4 bill caps left and 3 beanies
Total cap remaining is 7 caps while the probability of picking a bill cap now is 4/7
The combined probability is thus 5/8 * 4/7 = 5/14