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2 years ago

Which of the following is equivalent to sec2θ−1sec2θ for all values of θ for which sec2θ−1sec2θ is defined?

Mathematics

1 answer:

galina1969 [7]2 years ago

5 0

Answer:

$2 sin^2 \theta$

Step-by-step explanation:

According to the scenario, the following information is given:

$= \frac{sec^2 \theta - 1 }{sec^2 \theta}$

$= (\frac{1}{\frac{cos^2\theta}{\frac{1}{cos^2\theta} }} - 1)$

$= 1 - cos^2\theta\\\\= 1 - (1 - 2 sin^2 \theta)\\\\= 2 sin^2 \theta$

Therefore for the given equation, the answer is $2 sin^2 \theta$

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A factory robot recently examined some bulbs, of which 2 were flawed and 18 were not. If 30 more bulbs are examined, predict how

Oksanka [162]

Answer:

3 bulbs should be flawed

Step-by-step explanation:

2+ 18 = 20

20 bulbs were examined

2/20 = 1/10 were flawed

looking at the next 30 bulbs

30 * 1/10 = 3

3 of the next 30 bulbs should be flawed

5 0

3 years ago

William and Stephanie are playing a rather dangerous game of catch on the rooftops of skyscrapers in downtown Chicago. William i

olasank [31]

The question involves the concept & equations associated with projectile motion.

Given:
y₁ = 1130 ft
v₁ = +46 ft/s (note positive sign indicates upwards direction)
t = 6.0 s
g = acceleration due to gravity (assumed constant for simplicity) = -32.2 ft/s²

Of the possible equations of motion, the one we'll find useful is:

y₂ = y₁ + v₁t + 1/2gt²

We can just plug and chug to define the equation of motion:

y = (1130 ft) + (46 ft/s)t + 1/2(-32.2 ft/s²)t²

(note: if you were to calculate y using t = 6.0 s, you'd find that y = 826.4 ft, instead of 830 ft exactly because of some rounding of g and/or the initial velocity)

7 0

3 years ago

Which shows the expression below in simplified form? (2.2 × 1012) + (1.7 × 109)

AleksAgata [21]

(2.2 × 1012) + (1.7 × 109) = 2411.7

7 0

3 years ago

Read 2 more answers

How many significant figures does .00000004 have

siniylev [52]

It contains one significant digit and the rule for this one is that leading zeros in fractions less than one are not significant.

4 0

3 years ago

Read 2 more answers

9.01 prove that the two circles are similar

il63 [147K]

Answer:

see the procedure

Step-by-step explanation:

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.

In this problem to prove circle C and circle A are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that

Circle C is centered at (0,-1) and has a radius of 2 units

Circle A is centered at (3,4) and has a radius of 5 units

step 1

Move the center of the circle C onto the center of the circle A

the transformation has the following rule

(x,y)--------> (x+3,y+5)

(0,-1)------> (0+3,-1+5)-----> (3,4)

center circle C is now equal to center circle A

The circles are now concentric (they have the same center)

step 2

A dilation is needed to increase the size of circle C to coincide with circle A

scale factor=radius circle A/radius circle C-----> 5/2=2.5

radius circle C will be=2*scale factor-----> 2*2.5=5 units

radius circle C is now equal to radius circle A

therefore

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

4 0

3 years ago