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maxonik [38]
3 years ago
9

Given cos A = 0.25 find angle A in degrees. Round your answer to the nearest hundredth.

Mathematics
1 answer:
Fantom [35]3 years ago
8 0
We have that
cos A=0.25
so
A=arc cos (0.25)-------> using a calculator----> A=75.5225°
Round to the nearest hundredth-----> A=75.52²

the answer is
the option <span>75.52°</span>
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If f(x)=x^3-x+2, then (f^-1)'(2)
yawa3891 [41]

Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,

f\left(f^{-1}(x)\right) = x

\implies f^{-1}(x)^3 - f^{-1}(x) + 2 = x

which is a cubic polynomial in f^{-1}(x) with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).

Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.

f'(x) = 3x² - 1 = 0   ⇒   x = ±1/√3

So, we have three subsets over which f(x) can be considered invertible.

• (-∞, -1/√3)

• (-1/√3, 1/√3)

• (1/√3, ∞)

By the inverse function theorem,

\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}

where f(a) = b.

Solve f(x) = 2 for x :

x³ - x + 2 = 2

x³ - x = 0

x (x² - 1) = 0

x (x - 1) (x + 1) = 0

x = 0   or   x = 1   or   x = -1

Then \left(f^{-1}\right)'(2) can be one of

• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);

• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or

• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)

6 0
2 years ago
Write in point-slope form an equation of the line that passes through the
QveST [7]

Answer:

y+6 = - 5(x-4)

Step-by-step explanation:

With the given information, use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line. Substitute values for the m, x_1, and y_1 to find the answer.

m represents the slope, so substitute -5 in its place. The x_1 and y_1 represent the x and y values of one point the line intersects, so substitute 4 for x_1 and -6 for y_1. This gives the following equation:

y+6 = - 5(x-4)

3 0
3 years ago
From a distance of 42 feet from the base of a building, the angle of elevation to the top of the building is 67 degrees. Estimat
Nataliya [291]
A diagram would surely help here.  But imagine that you stand at spot A and someone finds that your distance from the base of the building is 42 feet.  Call this point B.
 
Imagine a vertical line from that spot, straight up.  Label the top of this line C.

The acute angle at A is 67 degrees.  You want to find the height of the building, which would be the length of the "opposite side of triangle ABC."
The length of the "adjacent side of triangle ABC" would be 42 feet.

We don't know the length of the hypotenuse, altho' we could easilyl calculate it using the Pyth. Them.

We choose the tangent function to solve for the height of the building (which is the length of the opposite side. 

                                                                         height
By definition, tangent (67 degrees) = -------------------------------------
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Find tan 67.  Multiply your result by 42 feet.  This product is the height of the building.
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3 years ago
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Since you have an equation equal to both x and y, you can either substitute the equation equal to x for x or the equation equal to y for y.
x=y-1
y=4-2x
I would substitute the y in using 4-2x
x=(4-2x)-1
x=3-2x
3x=3
x=1
Then plug in x and solve for y
1=y-1
2=y
5 0
3 years ago
PLEASE HELP QUICK!! (25 Points) Name the postulate or theorem you can use to prove the triangles congruent.
Akimi4 [234]
Hello!

You know that two sides and one of the angles are congruent

The only choice that has two sides and 1 angle is ASA postulate

The answer is ASA postulate

Hope this helps!
7 0
3 years ago
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