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3 years ago

In a right triangle, Sin (4x + 10) º = Cos (6x) º. What is the value of x?

Mathematics

1 answer:

frez [133]3 years ago

6 0

Answer:

Step-by-step explanation:

These angles will be equal when each of them measures 45 degrees. On the unit circle, 45 degrees and reference angles of 45 degrees are the only places where sin and cos are the same. This means that

sin(4x + 10) = 45 and cos(6x) = 45

If we add the angles together (the angles being 4x+10 and 6x) we get a 90 degree angle. Thus,

4x + 10 + 6x = 90 and

10x = 80 so

x = 8. Let's try it out:

sin(4(8) + 10) = sin(42) = .6691306064 and

cos(6(8)) = cos(48) = .6691306064

Yay!!!!!

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Which number line shows the correct placement of 20%, 1/3, and 2/3?

BigorU [14]

Answer with Step-by-step explanation:

We are given that

20%

When we change percent into fraction we will divide the percent by 100

$\frac{20}{100}=\frac{1}{5}$

$\frac{1}{3}$

$\frac{2}{3}$

We have to find the line which shows the correct placement of given numbers.

Lcm(3,5)=15

$\frac{1\times 3}{5\times 3}=\frac{3}{15}$

$\frac{1\times 5}{3\times 5}=\frac{5}{15}$

$\frac{2\times 5}{3\times 5}=\frac{10}{15}$

7 0

3 years ago

Two similiar rectangles have corresponding sides in the ratio 10:3. What is the ratio of their areas

lianna [129]

Answer:

Step-by-step explanation:

The ratio of its areas is equal to

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

In this problem the scale factor is equal to the ratio 10:3

Let

z-------> the scale factor

z2=(10/3)2=100/9

7 0

3 years ago

In triangle abc, m of acb = 90, cd is perpendicular to ab , m of acd is 60. and bd is 5 cm. find ad

weeeeeb [17]

Let us draw a picture to make the things more clear.

Attached is the image.

We have been given that

$\angle acd = 60 ^{\circ}$

Therefore, we have

$\angle dcb =90- 60= 30 ^{\circ}$

Now, in triangle bcd, we have

$\tan30 = \frac{5}{cd}\\
\\
\frac{1}{\sqrt 3}=\frac{5}{cd}\\
\\
cd=5\sqrt 3$

Now, in triangle acb, we have

$tan 60 = \frac{ad}{5\sqrt3} \\
\\
\sqrt 3= \frac{ad}{5\sqrt3}\\
\\
ad= 5\sqrt3 \times \sqrt 3\\
\\
ad= 5\times 3\\
\\
ad=15$

Thus, ad is 15 cm.

4 0

3 years ago

Dinosaur fossils are often dated by using an element other than carbon, like potassium-40, that has a longer half life (in this

Firlakuza [10]

The amount of substance left of a radioactive element of half life, $t_{\frac{1}{2}}$ after a time, t, is given by:

$N(t)=N_0\left( \frac{1}{2} \right)^ \frac{t}{t_{ \frac{1}{2} }}$

Given that <span>potassium-40 has a half life of approximately 1.25 billion years.

The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:

$0.1=100\left( \frac{1}{2} \right)^ \frac{t}{1.25}} \\ \\ \Rightarrow\left( \frac{1}{2} \right)^ \frac{t}{1.25}}=0.001 \\ \\ \Rightarrow\frac{t}{1.25}\ln\left( \frac{1}{2} \right)=\ln(0.001) \\ \\ \Rightarrow \frac{t}{1.25}= \frac{\ln(0.001)}{\ln\left( \frac{1}{2} \right)} =9.966 \\ \\ t=9.966(1.25)=12.5$

Therefore, </span><span>the maximum age of a fossil that we could date using 40k is 12.5 billion years.</span>

3 0

3 years ago

Help me with number 1 please

viva [34]

17 25 and 1/2 34. 42 and 1/2

3 0

3 years ago