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Illusion [34]
2 years ago
7

Find A and B. Using the image above.

Mathematics
1 answer:
NeX [460]2 years ago
7 0

Answer:

a = 7, b = \frac{7\sqrt{3} }{3}

Step-by-step explanation:

Using the sine ratio in the left right triangle and the exact value

sin45° = \frac{1}{\sqrt{2} } , then

sin45° = \frac{opposite}{hypotenuse} = \frac{a}{7\sqrt{2} } = \frac{1}{\sqrt{2} } ( cross- multiply )

a × \sqrt{2} = 7\sqrt{2} ( divide both sides by \sqrt{2} )

a = 7

--------------------------------------------------------

Using the tangent ratio in the right triangle on the right and the exact value

tan60° = \sqrt{3} , then

tan60° = \frac{opposite}{adjacent} = \frac{a}{b} = \frac{7}{b} = \sqrt{3} ( multiply both sides by b )

b × \sqrt{3} = 7 ( divide both sides by \sqrt{3} )

b = \frac{7}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } = \frac{7\sqrt{3} }{3}

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234 students in 9 different classrooms. What is the ratio of students to classrooms?
Vilka [71]

Answer:

26 students per classroom

Step-by-step explanation:

To solve this, the ratio 234 students:9 classrooms must be converted to:

s students:1 classroom

To convert the ratio, 9 was divided by 9 to get 1, and so you must also divide 234 by 9 to maintain the same ratio, which gives us the answer:

26 students: 1 classroom

5 0
2 years ago
The graph of function g is a vertical stretch of the graph of function f ​​by a factor of 3. Which equation describes function g
anyanavicka [17]

Answer:


Step-by-step explanation:

A vertical stretch by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x), where k <1.

If k =1, then same graph we obtain and if k>1 we get a vertically shrink graph.

In our question, there is a vertical stretch of 3. This means new graph would have points as (x,y/3)

i.e. instead of f(x) = y, we have now f(x) = y/3

So transformation is g(x) = 3f(x)

Option A is correct.

2) Here f(x) = 3x+8 is transformed to g(x) =3x+6

i.e. y intercept is reduced by 2 units.  Hence there is a translation of 2 units down.


8 0
3 years ago
Read 2 more answers
Jack crawled 3 ft and Christine crawled 3⁄4 the distance Jack crawled. If you add the distance they each crawled together, what
LUCKY_DIMON [66]
Christine crawled:
3 ft* (3/4)= 2.25 ft.

3 ft+ 2.25 ft= 5.25 ft

We already know that 1 ft= 12 in.

5.25 ft* (12in/ 1 ft)= 63 in.

The total distance the two children crawled together is 63 in~
5 0
3 years ago
"find the reduction formula for the integral" sin^n(18x)
dexar [7]
Let

I(n,a)=\displaystyle\int\sin^nax\,\mathrm dx
For demonstration on how to tackle this sort of problem, I'll only work through the case where n is odd. We can write

\displaystyle\int\sin^nax\,\mathrm dx=\int\sin^{n-2}ax\sin^2ax\,\mathrm dx=\int\sin^{n-2}ax(1-\cos^2ax)\,\mathrm dx
\implies I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx

For the remaining integral, we can integrate by parts, taking

u=\sin^{n-3}ax\implies\mathrm du=a(n-3)\sin^{n-4}ax\cos ax\,\mathrm dx\mathrm dv=\sin ax\cos^2ax\,\mathrm dx\implies v=-\dfrac1{3a}\cos^3ax

\implies\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx=-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{a(n-3)}{3a}\int\sin^{n-4}ax\cos^4ax\,\mathrm dx

For this next integral, we rewrite the integrand

\sin^{n-4}ax\cos^4ax=\sin^{n-4}ax(1-\sin^2ax)^2=\sin^{n-4}ax-2\sin^{n-2}ax+\sin^nax
\implies\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx=I(n-4,a)-2I(n-2,a)+I(n,a)

So putting everything together, we found

I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx
I(n,a)=I(n-2,a)-\left(-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{n-3}3\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx\right)
I(n,a)=I(n-2,a)-\dfrac{n-3}3\bigg(I(n-4,a)-2I(n-2,a)+I(n,a)\bigg)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax
\dfrac n3I(n,a)=\dfrac{2n-3}3I(n-2,a)-\dfrac{n-3}3I(n-4,a)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax

\implies I(n,a)=\dfrac{2n-3}nI(n-2,a)-\dfrac{n-3}nI(n-4,a)+\dfrac1{na}\sin^{n-3}ax\cos^3ax
7 0
3 years ago
A dice is thrown four times in a row. Find the probability of getting different result each throw.
MatroZZZ [7]

Answer:

the answer is b 1/4 its means got it 1 time same after throwing it 4 times

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
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