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2 years ago

If triangle abc, a=3, b=5 and c=7. Find the measure of angle b

Mathematics

2 answers:

Ray Of Light [21]2 years ago

7 0

Answer:

b = 38.22

Step-by-step explanation:

In the given triangle ABC, a = 3, b = 5 and c = 7 is given.

We have to find the measure of angle b.

To get the measure of any angle we will apply cosine rule in the triangle.

b² = a² + c² - 2ac(cosb)

5² = 3² + 7² - 2×3×7×cosb

25 = 9 + 49 - 42×cosb

25 = 58 - 42cosb

-42cosb = 25 - 58 = -33

cosb = $\frac{33}{42}$

cosb = 0.7856

$b= cos^{-1}(0.7856)$

b = 38.22

b = 38.22 is the correct answer.

krek1111 [17]2 years ago

4 0

Answer:

β = arccos((a^2 + c^2 - b^2)/(2·a·c))

β = arccos((3^2 + 7^2 - 5^2)/(2·3·7)) = 38.21°

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Find the domain and range of f(x). Please explain your answer.<br> f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

4 0

2 years ago

|-5| – 45 ÷ 3 <br> Explain how to solve

Alinara [238K]

Order of operations.
Parentheses: there are none
Exponents: also none
Multiplication: also none
Division: yep. 45 / 3 = 15
Addition: none
Subtraction: Yes

The absolute value of -5 is 5. (Absolute values are always positive or 0)
5-15= -10

8 0

3 years ago

Someone please help me answer this!!

steposvetlana [31]

Answer:

10 units is the answer.

Step-by-step explanation:

points are (-3,2) and (-9,-6)

Pythagorean theorem can be written as,

$d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(-9-(-3))^2 + (-6-2)^2}\\\\d=\sqrt{(-6)^2+(-8)^2} \\\\d=\sqrt{36+64} \\\\d=\sqrt{100} \\\\d=10$

∴ distance between the points = 10 units

4 0

3 years ago

A scale model of the Vancouver Olympic cauldron is to be built in memory of the 2010 Olympics. If the scale to be used is 1:27,

timurjin [86]

Answer:

23/54 meters

Step-by-step explanation:

Assuming that the scale model is smaller, then the scale model should be 1/27th of the actual thing. Therefore:

11.5/27

= 23/54 meters tall

4 0

3 years ago

Divide x^3+x^2-x+2 divides by x+4

Furkat [3]

Answer:

Step-by-step explanation:

x^3 + x^2 - x + 2 \ x + 4 = x^2 -3x + 11 - 42/(x+4)

5 0

3 years ago