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3 years ago

Solve sec2theta + tantheta - 3 =0 for 0

Mathematics

1 answer:

Serhud [2]3 years ago

7 0

Answer:

Ф = $\frac{\pi }{4} ,\frac{5\pi}{4}$

Step-by-step explanation:

It is a bit difficult to input the work here, so I uploaded an image

First we can use the trig identities to change sec²(Ф) to tan²(Ф) + 1
Then we can combine like terms
Then we can factor this as a polynomial function
Then we can set each term equal to zero and solve for Ф
The first term tan(Ф) - 2 = 0 has no solution because tan(Ф) ≠ -2 anywhere
The second term tan(Ф) - 1 = 0 has two solutions of $\frac{\pi}{4}$ and $\frac{5\pi}{4}$ so these are the solutions to the problem

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PIT_PIT [208]

A cylinder of radius r cm and height h cm has a curved surface area A cm². Where –

A = 2πrh cm²

a) We are asked to find formula for h.

$\qquad$ $\purple{ \bf \longrightarrow A=2 \pi rh }$

First, overturn the equation

$\qquad$ $\sf \longrightarrow 2 \pi rh =A$

Divide both sides by 2πr

$\qquad$ $\sf \longrightarrow \dfrac{2\pi rh}{2\pi r } = \dfrac{A}{2\pi r}$

$\qquad$ $\sf \longrightarrow \dfrac{\cancel{2 \pi r }h}{\cancel{2\pi r} } = \dfrac{A}{2\pi r}$

$\qquad$ $\purple{\bf \longrightarrow h = \dfrac{A}{2 \pi r }}$

b) Again, we are given –

Curved surface area, A = 93 cm²
Radius, r = 2.5 cm
π = 3.1

$\qquad\qquad\quad\underline{\sf{Substituting \ Values \ :}}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad$ $\bf \longrightarrow h = \dfrac{A}{2\pi r }$

$\qquad$ $\sf \longrightarrow h = \dfrac{93}{2 \times 3.1 \times 2.5 }$

$\qquad$ $\sf \longrightarrow h = \dfrac{93}{15.5}$

$\qquad$ $\sf \longrightarrow h =\cancel{ \dfrac{93}{15.5}}$

$\qquad$ $\pink{ \bf \longrightarrow h = 6\: cm }$

Henceforth, height of the cylinder is 6 cm.

5 0

2 years ago

Read 2 more answers

A study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes versus teache

Ber [7]

The Critical z-values are -1.96 and 1.96 option second is correct.

It is given that the teachers were allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes.

It is required to find the critical z-values.

<h3>What is the critical value of Z?</h3>

It is defined as the area region enclosed by the standard normal curve or bell curve. It gives an idea about every variable, and what value of probability the variables acquire.

We are assuming the data given below:

x = 3.5

$\mu =3.3$

$\sigma = 0.6$

n = 40

We know the formula for the Z score:

$\rm Z = \frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }$

$\rm Z = \frac{3.5-3.3}{\frac{0.6}{\sqrt{40} } }$

Z = 2.10

The area under the normal distribution curve:

P(Z= 2.10) = 0.9821 ( from the z table)

We have null hypothesis H0: in the two groups, the level of job satisfaction is the same ie. with no difference.

H1: There is a significant difference in levels of job satisfaction.

The above hypothesis defined that the test is two-tailed which means there will be two rejection regions.

The critical z-values are:

-1.96 and 1.96 (from the critical value calculator at a 5% significance level with two-tailed)

Thus, the Critical z-values are -1.96 and 1.96 option second is correct.

Learn more about the critical value here:

brainly.com/question/13686040

4 0

2 years ago

A dime has the same value as 10 pennies. marley brought 290 pennie to the bank.How many dimes did marley get?

DanielleElmas [232]

Answer:

Explanation:

10 pennies= 1 dime

so you divide 290÷10

which equals 29

So Marley got 29 dimes

8 0

3 years ago

Jan has a budget of $600 for catering. The catering company charges $12.50 per guest. Enter and solve an inequality to show the

pantera1 [17]

Answer:

g ≤ 48

Step-by-step explanation:

Let g = # of guest

12.50(g) ≤ 600

$\frac{12.50g}{12.50} \leq \frac{600}{12.50}$

g ≤ 48

6 0

3 years ago

Please someone help me with this ASAP especially with the workout!!

Serjik [45]

Answer:

78°

Step-by-step explanation:

From the diagram,

Applying sine rule,

SinA/a = sinC/c................... Equation 1

Given: c = 29 cm, C = 50°, a = 37 cm

Substitute into equation 1 and solve for A.

sinA/37 = sin50°/29

sinA = (37×sin50°)/29

sinA = (37×0.766)/29

sinA = 28.34/29

sinA = 0.9774

A = sin⁻¹(0.9774)

A = 77.8°

A ≈ 78°

Hence the measure of angle A = 78°

6 0

3 years ago