Solve for x

What is this shape called

gizmo_the_mogwai [7]

Answer:

curved ramp

or quadrant circle map

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Could someone please help me:) I am stick and I am not sure what to do

Delicious77 [7]

Answer:

Part 5.1.1:

$\displaystyle \cos 2A = \frac{7}{8}$

Part 5.1.2:

$\displaystyle \cos A = \frac{\sqrt{15}}{4}$

Step-by-step explanation:

We are given that:

$\displaystyle \sin 2A = \frac{\sqrt{15}}{8}$

Part 5.1.1

Recall that:

$\displaystyle \sin^2 \theta + \cos^2 \theta = 1$

Let θ = 2A. Hence:

$\displaystyle \sin ^2 2A + \cos ^2 2A = 1$

Square the original equation:

$\displaystyle \sin^2 2A = \frac{15}{64}$

Hence:

$\displaystyle \left(\frac{15}{64}\right) + \cos ^2 2A = 1$

Subtract:

$\displaystyle \cos ^2 2A = \frac{49}{64}$

Take the square root of both sides:

$\displaystyle \cos 2A = \pm\sqrt{\frac{49}{64}}$

Since 0° ≤ 2A ≤ 90°, cos(2A) must be positive. Hence:

$\displaystyle \cos 2A = \frac{7}{8}$

Part 5.1.2

Recall that:

$\displaystyle \begin{aligned} \cos 2\theta &= \cos^2 \theta - \sin^2 \theta \\ &= 1- 2\sin^2\theta \\ &= 2\cos^2\theta - 1\end{aligned}$

We can use the third form. Substitute:

$\displaystyle \left(\frac{7}{8}\right) = 2\cos^2 A - 1$

Solve for cosine:

$\displaystyle \begin{aligned} \frac{15}{8} &= 2\cos^2 A\\ \\ \cos^2 A &= \frac{15}{16} \\ \\ \cos A& = \pm\sqrt{\frac{15}{16}} \\ \\ \Rightarrow \cos A &= \frac{\sqrt{15}}{4}\end{aligned}$

In conclusion:

$\displaystyle \cos A = \frac{\sqrt{15}}{4}$

(Note that since 0° ≤ 2A ≤ 90°, 0° ≤ A ≤ 45°. Hence, cos(A) must be positive.)

4 0

3 years ago

Which are the solutions of x2 = –7x – 8?

Yanka [14]

You can start by rewriting the equation so that the right side equals zero. Add $-7x$ and $8$ to both sides.

$x^2+7x+8=0$

You can now use the quadratic equation (below), where $a=1, b=7,$ and $c=8$ , to find solutions. Plug in these values for $a, b,$ and $c$ into the equation and simplify.

$\frac{-b \pm \sqrt{b^2-4(ac)}} {2a}$
$\frac{-7 \pm \sqrt{7^2-4(1 \times 8)}} {2 \times 1}$
$\frac{-7 \pm \sqrt{49-32}} {2}$
$\frac{-7 \pm \sqrt{17}} {2}$

The final answer is the combination of both solutions.
$x=\frac{-7}{2} \pm \frac{\sqrt{17}} {2} \approx -3.5 \pm 2.06.$

Or approximately...
$x=(-3.5-2.06) \approx -5.56, (-3.5+2.06) \approx-1.44$

8 0

3 years ago

Read 2 more answers

a car is travelling at x kilometres per hour find the cars speed, in terms of x in metres per second give your answer in its sim

andrey2020 [161]

Its distance divided by time takrn × 60

7 0

3 years ago

When Gabby went food shopping, she spent $14.90 on 5 bags of marshmallows to make Rice Krispie treats. She has to go to the stor

dusya [7]

the answer is $20.70

3 0

3 years ago