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3 years ago

Find all solutions to the equation. cos2x + 2 cos x + 1 = 0

1 answer:

5 0

For cos(2x) * (2cos(x) + 1) = 0, use the double angle identity for cos(2x), which is cos^2 x - sin^2 x = cos^2 x - (1-cos^2) = 2cos^2 x - 1.
So we have (2cos^2 x - 1)(2cos x + 1) = 0. So 2cos^2 x -1 = 0 or x = 0 and 2pi.
For 2sec^2 x + tan^2 x - 3 = 0, use the identity sec^2 x = tan^2 x + 1, so we have
2(tan^2 x + 1) + tan^2 x - 3 = 0 or
<span>2tan^2 x + tan^2 x - 1 = 0 or
</span>3 tan^2 x = 1.

So x = pi/2, pi/2 + pi = 3pi/2.

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The temperature in Montreal was -8°C

atroni [7]

Answer:

id say about 19 degrees

Step-by-step explanation:

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3 years ago

Read 2 more answers

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

nika2105 [10]

Step-by-step explanation:

13 + 22 = 35 degree change. 10-3 = 7. 35/7 = 5 degrees per hour.

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3 years ago

(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

Which of the following is the ratio of 5 cm to 10 km

pshichka [43]

Answer:

1/200000

Step-by-step explanation:

first 10 km equals to 1000000cm

so 5/1000000cm

equals to 1/200000

3 0

2 years ago

Esmeralda received a bag of jellybeans that contained a mixture of regular flavored jellybeans and "surprise" jellybeans. The ba

Firlakuza [10]

Answer:

6 "surprise" flavors jellybeans

Step-by-step explanation:

From the information given:

The bag contained a mixture of regular flavored jellybeans and "surprise" jellybeans.

There are 40 jellybeans in the bag.

If 15% of the jellybean were "surprise" flavors.

Then, the number of expected "surprise" jellybeans will be:

= 15% of 40 jellybeans

= (15/100) × 40

= 6 "surprise" flavors jellybeans

If 6 surprise jellybean is contained in the bag;

Thus, the number of regular flavored jellybean will be

= 40 - 6

= 34 regular flavored jellybean

5 0

2 years ago