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3 years ago

Please answer from the picture

Mathematics

1 answer:

expeople1 [14]3 years ago

7 0

Answer:

Agree, log $_{5}$ equals 6.

Step-by-step explanation:

$log_{5}15635 = 6.00039$

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Divide ( - 3 z 2 – 15z )÷ ( z + 5 )

blondinia [14]

Factor the numerator to get:

(-3z(z+5))/(z+5) now you notice that (x+5) cancel out leaving:

-3z

4 0

3 years ago

The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. A) Use differentials to estimate the max

siniylev [52]

Answer:

A) The maximum error in the calculated surface area: $25cm^2$

Relative error: $0.013$

B) The maximum error in the calculated volume: $162cm^2$

Relative error: $0.019$

Step-by-step explanation:

A) The formula for the surface area is:

$A=4\pi r^2$

The measured value is the circumference which is equal to:

$C=2\pi r$

then the radius is:

$r=\frac{C}{2\pi}$

Substituting in the formula of the surface:

$A=4\pi(\frac{C}{2\pi})^2\\A=4\pi(\frac{C^2}{4\pi^2})\\A=\frac{C^2}{\pi}$

Using the formula to calculate the error:

$dy=f'(x)dx$

Where $x$ is the variable measured and $y$ is a function of $x$ ( $y=f(x)$ ).

$dA=f'(C)dC\\dA=\frac{2C^{(2-1)}}{\pi}dC\\dA=\frac{2C}{\pi}dC$

We have C=80cm and dC=0.5cm

$dA=\frac{2C}{\pi}dC\\dA=\frac{2(80)}{\pi}(0.5)\\dA=\frac{160}{\pi}(0.5)\\dA=50.9296(0.5)\\dA=25.4648\approx25cm^2$

The relative error is the maximum error divide by the total area. The total area is: $A=\frac{C^2}{\pi}=\frac{(80)^2}{\pi}=\frac{6400}{\pi}=2037.1833cm^2$

$\frac{dA}{A}=\frac{25.4648}{2037.1833} =0.0125\approx0.013$

B) The formula for the volume is:

$V=\frac{4}{3} \pi r^3$

Using $r=\frac{C}{2\pi}$

$V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (\frac{C}{2\pi})^3\\V=\frac{4}{3} \pi (\frac{C^3}{8\pi^3})\\V=\frac{1}{3}(\frac{C^3}{2\pi^2})\\V=\frac{C^3}{6\pi^2}$

The maximum error is:

$dV=\frac{3C^{3-1}}{6\pi^2}dC\\dV=\frac{C^{2}}{2\pi^2}dC\\dV=\frac{(80)^{2}}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=(324.2278)(0.5)\\dV=162.1139\approx162cm^2$

The calculated volume is:

$V=\frac{C^3}{6\pi^2}\\V=\frac{(80)^3}{6\pi^2}\\V=\frac{512000}{6\pi^2}\\V=8646.0743$

The relative error is:

$\frac{dV}{V}=\frac{162.1139}{8646.0743}=0.0188\approx0.019$

3 0

3 years ago

Which value for x makes the sentence true? 2.45 + x = 3.64

Scrat [10]

Answer:

1.19

Step-by-step explanation:

You're trying to figure out what x is here.

So you'll want to isolate the x. That means, get it alone.

Since both sides are equivalent, when you subtract 2.45 from the x side, you also subtract it from the other side too.

x = 3.64 - 2.45

x = 1.19

7 0

3 years ago

Read 2 more answers

If a publisher of nontechnical books takes great pains to ensure that its books are free of typos, so that the probability of an

Troyanec [42]

Answer:

(a) 0.2707

(b) 0.8576

Step-by-step explanation:

5 0

3 years ago

Using the rules for significant figures, what do you get when you multiply 67.6 by 1.2?

Mumz [18]

If we use the rules we say that when we multiply two numbers we get the result in the numbers the least significant number has in the multiplication. So we may proceed like this:

67.6 x 1.2 = 81.12

As the decimal part does not continue indefinitely we can leave the answer as it is. if the answer was 81.123612356213 then we leave it like 81.1 as the rules say

4 0

3 years ago

Read 2 more answers