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pshichka [43]
3 years ago
15

Please help with the following problem asap!!

Mathematics
1 answer:
umka21 [38]3 years ago
4 0

Answer:

8^7

Step-by-step explanation:

\dfrac{8^{15}}{8^7 \cdot 8} =

Remember that 8 = 8^1.

= \dfrac{8^{15}}{8^7 \cdot 8^1}

When you multiply powers with the same base, add the exponents. Do this in the denominator.

= \dfrac{8^{15}}{8^{7+1}}

= \dfrac{8^{15}}{8^{8}}

When  you divide powers with the same base, subtract the exponents.

= 8^{15-8}

= 8^7

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after geting 5 new rocks geogre gave half of his collection to susan.if george gave susan 36 rocks which equation could be used
sergiy2304 [10]
36×2=72
72-5=67
George started with 67 rocks.
3 0
3 years ago
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I need to solve this using l'hopital's rule and logarithmic diferentiation.
arlik [135]

Yo sup??

For our convenience let h=x+1

therefore

when x tends to -1, h tends to 0

hence we can rewrite it as

\lim_{h \to \ 0 } (cos(h))^{(cot(h^2 )}

This inequality is of the form 1∞

We will now apply the formula

e^(^g^(^x^)^(^f^(^x^)^-^1^)^)

plugging in the values of g(x) and f(x)

e^{lim_{h \to \ 0}{(cot(h)^2(cos(h)-1))}

express coth² as cosh²/sinh² and also write cosh-1 as 2sin²(h/2)

(by applying the property that cos2x=1-sin²x)

After this multiply the numerator and denominator with h² so that we can apply the property that

\lim_{x \to \ 0 } sinx/x =1

Now your equation will look like this.

e^{lim_{h \to \ 0}{((cos(h)^2(2sin^2(h/2)*h^2)/(sin(h)^2*h^2)}

We will now apply the result

\lim_{x \to \ 0 } sinx/x =1

where x=h²

we get

e^{lim_{h \to \ 0}{((cos(h)^2(2sin^2(h/2))/(h^2)}

we now multiply the numerator and denominator with 4 so that we can say

\lim_{h^2 \to \ 0 } sin^2(h/2)/(h^2/4) = 1

e^{lim_{h \to \ 0}{((cos(h)^2(2sin^2(h/2))/(h^2*4/4)}

=e^{lim_{h \to \ 0}{((cos(h)^2*2)/(4)}

Apply the limits and you will get

e^{cos(0)^2*2/4

=e^{1/2}

Hope this helps.

7 0
3 years ago
A passbook savings account has a rate of 5%. Find the effective annual yield if the interest is compounded quarterly.
Temka [501]

Answer:

Effective annual yield = 0.05094534 or 5.094%

Step-by-step explanation:

Given:

Rate of interest (r) = 5% = 0.05

Interest = compounded quarterly

Find:

Effective annual yield = Y

Computation:

Y=(1+\frac{r}{n} )^n-1\\\\Y=(1+\frac{0.05}{4} )^4-1\\\\Y=(1+0.0125 )^4-1\\\\Y=(1.0125 )^4-1\\\\ Y=1.05094534-1\\\\Y=0.05094534\\\\\\

Effective annual yield = 0.05094534 or 5.094%

6 0
3 years ago
If the hypotenuse of a 45°-45°-90° triangle is 13, what is the length of one of the legs?
stiv31 [10]

Answer:

9.19

Step-by-step explanation:

Using Law of sines to find other two lengths:

a/sinA=b/sinB

let a be length of side unknown and b be hypotenuse then sinB=sin90 and sinA=sin45

a/sin45=13/sin90

a=13sin45

a=13(0.707)

  =9.19

As the given triangle is isosceles hence the length of other two legs will be same i.e 9.19 !

6 0
3 years ago
I accidentally posted a question that I knew the answer to so this is my question!!!
Kitty [74]

Engla ongla le para de santo

6 0
3 years ago
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