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Cloud
15 days ago
9

Value of sec Square 26 degrees - cot square 64 degrees is

Mathematics
1 answer:
Leona [4.1K]15 days ago
4 0

Answer:

The value equals 1

Step-by-step explanation:

Consider the expression

sec^{2}(26\°)-cot^2(64\°)

Recall that

cot^2(64\°)=\frac{cos^2(64\°)}{sin^2(64\°)}

sec^{2}(26\°)=\frac{1}{cos^2(26\°)}

For two complementary angles A and B (where A+B=90°),

the identity is

cos(A) = sin(B)

Here, 26° and 64° are complementary angles, so

\frac{1}{cos^2(26\°)}=\frac{1}{sin^2(64\°)}

Substituting values,

\frac{1}{sin^2(64\°)}-\frac{cos^2(64\°)}{sin^2(64\°)}

\frac{1-cos^2(64\°)}{sin^2(64\°)}

From this, we find

1-cos^2(64\°)=sin^2(64\°)

By substitution,

\frac{sin^2(64\°)}{sin^2(64\°)}=1

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Joaquin is constructing the perpendicular bisector of AB. He opens his
Zina [3914]

Answer:

A

Step-by-step explanation:

To construct the perpendicular bisector, follow these steps:

Step 1:

Set the compass to a distance greater than half the length of segment AB, place it on point A, and draw an arc across AB.

Step 2:

Keeping the same width, place the compass on point B and create another arc across AB.

Step 3:

With the ruler, connect the two intersection points of the arcs by drawing a line.

Step 4:

This line will be the perpendicular bisector of the segment AB.

Thus, option A is the correct choice.

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3 days ago
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The quotient of 9 3/4 and 5/8​
AnnZ [3877]

Answer:

15.6

Step-by-step explanation:

  1. 9\frac{3}{4} = \frac{39}{4}
  2. Insert 39/4: 39/4 ÷ 5/8
  3. 39/4 ÷ 5/8 = 39/4 × 8/5
  4. 39/4 × 8/5 = 312/20
  5. \frac{312}{20} = 15.6

I hope this information is helpful!

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3 days ago
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Assess the extent to which bad road use has a direct impact on the physical,emotional,social,and economic aspects to the family
PIT_PIT [3919]
The condition of poor roads can indeed have significant repercussions on numerous aspects such as physical health, emotional well-being, and economic stability for families, communities, and the nation. Dangerous roads can lead to accidents, affecting individuals physically. The stress of navigating damaged roads can cause mental strain. Economically, poor road conditions can lead to increased prices for goods, as it takes more time to transport them by road. Additionally, transport costs can rise significantly.



3 0
12 days ago
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Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard
Inessa [3907]

Answer:

V(x)=(4x^{3}-40x^{2}+100x)\ cm^3

The variable x lies within the interval of all positive real numbers less than 5 cm.

Detailed solution:

Problem statement:

Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.

Refer to the provided diagram for clarity.

Define:

x → length in centimeters of each square cutout side

The volume of the box with open top can be written as:

V=LWH

Given this, we have:

L=(10-2x)\ cm

W=(10-2x)\ cm

H=x)\ cm

By substitution:

V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3

Determine the domain of x:

Because:

(10-2x) > 0\\10> 2x\\ 5 > x\\x < 5\ cm

Therefore:

Domain is the interval (0,5)

That means all real numbers strictly greater than zero and less than 5 cm are valid for x.

Hence, the volume V as a function of x is:

V(x)=(4x^{3}-40x^{2}+100x)\ cm^3

5 0
15 days ago
Triangle MRN is created when an equilateral triangle is folded in half. Triangle N R M is shown. Angle N R M is a right angle. A
Inessa [3907]

Answer:

El valor de x es 4.

Explicación paso a paso:

Se indica que el triángulo MRN surge al doblar un triángulo equilátero por la mitad.

Esto sugiere que el triángulo equilátero original es MNO y que NR actúa como bisectriz perpendicular (una línea que divide un segmento en dos partes iguales formando un ángulo recto).

La longitud del lado del triángulo es

NO = NS + SM = 6 + 2 = 8

Dado que un triángulo equilátero tiene todos sus lados iguales y NR es la bisectriz perpendicular, se tiene que

RM = MO/2 = 8/2 = 4

El valor de x es 4.

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5 days ago
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