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2 years ago

Evaluate: sec(5 pie/4)

Mathematics

1 answer:

zysi [14]2 years ago

7 0

Answer:

$sec(\frac{5\pi}{4})=-\sqrt{2}$

Step-by-step explanation:

$sec(\frac{5\pi}{4})\\\\=\frac{1}{cos(\frac{5\pi}{4})}\\ \\=\frac{1}{-\frac{\sqrt{2}}{2}}\\ \\=-\frac{2}{\sqrt{2}}\\ \\=-\frac{2\sqrt{2}}{2}\\ \\=-\sqrt{2}$

It really helps to use the unit circle for solving these kinds of problems. I've attached one for your convenience. Note that a point on the unit circle, given the angle in radians, is defined as $(cos\theta,sin\theta)$ .

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Nichior compared the slope of the function graphed to the slope of the linear function that has an x-intercept of 2/3 and a y-in

marusya05 [52]

Answer:

The slope of f(x) is 1.5

Step-by-step explanation:

step 1

Find the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1

we have the points

(2/3,0) and (0,-1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-1-0}{0-2/3}$

$m=\frac{-1}{-2/3}$

$m=\frac{3}{2}=1.5$

step 2

Find the slope of the function graphed

take the points

(0,-1) and (3,6) approximately

substitute in the formula

$m=\frac{6+1}{3-0}$

$m=\frac{7}{3}=2.33$

step 3

we know that

f(x) represents the function with the smaller slope

The smaller slope is 1.5

therefore

The slope of f(x) is 1.5

4 0

3 years ago

Write the equation of the line that passes thriugh the points (3,-2) and (5,-9)?

Tanya [424]

Answer:

y = -7/2x + 17/2

Step-by-step explanation:

Slope = (-9 - - 2)/(5 - 3)

= -7/2

y-intercept: -2 - (-7/2)(3)

= -2 + 21/2 (-2*2+21)/2

= 17/2

4 0

2 years ago

An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is <u>0.5 s and 7 s.</u>

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$

Therefore, the debris will reach a height of 56 ft twice.

When time $t=0.5\ s$ during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at $t=7\ s$ , the height is 56 ft.

5 0

3 years ago

The product of the roots of the equation x2 + x=2 is:<br> 0-2<br> 01

gregori [183]

Answer:

-2

Step-by-step explanation:

x^2 + x=2

Subtract 2 from each side

x^2 + x-2=2-2

x^2 + x-2=0

Factor

What 2 numbers multiply to -2 and add to 1

2*-1 = -2

2+-1 =1

(x-1)(x+2)=0

Using the zero product property

x-1 = 0 x+2 = 0

x=1 x = -2

Product of the roots

1*-2 = -2

5 0

2 years ago

a class with 30 students had an average score of 80 on a test. A class with 20 students had an average score of 90 on the same t

snow_tiger [21]

The average score of all the students in both classes is 84.

<h3>How to calculate the average?</h3>

The class with 30 students had an average score of 80 on a test. The total score will be:

= 30 × 80

= 2400

A class with 20 students had an average score of 90 on the same test. The total score will be:

= 20 × 90

= 1800

Total scores = 2400 + 1800 = 4200

Number of students = 20 + 30 = 50

The average score will be:

= Total score / Total students

= 4200 / 50

= 84

Learn more about average on:

brainly.com/question/24313700

#SPJ1

8 0

1 year ago

Evaluate: sec(5 pie/4)￼

Evaluate: sec(5 pie/4)