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fenix001 [56]
3 years ago
14

-4d - 5 = -1 answer for me pls

Mathematics
1 answer:
PolarNik [594]3 years ago
4 0

\\ \sf\longmapsto -4d-5=-1

  • Cancel - from both sides

\\ \sf\longmapsto -(4d+5)=-(1)

\\ \sf\longmapsto 4d+5=1

\\ \sf\longmapsto 4d=1-5

\\ \sf\longmapsto 4d=-4

\\ \sf\longmapsto d=\dfrac{-4}{4}

\\ \sf\longmapsto d=-1

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Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).
lutik1710 [3]

Answer:

The arc length is \dfrac{21}{16}

Step-by-step explanation:

Given that,

The given curve between the specified points is

x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}

The points from (\dfrac{9}{16},1) to (\dfrac{9}{8},2)

We need to calculate the value of \dfrac{dx}{dy}

Using given equation

x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}

On differentiating w.r.to y

\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})

\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})

\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})

\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}

We need to calculate the arc length

Using formula of arc length

L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}

Put the value into the formula

L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}

L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}

L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}

L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}

L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}

L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}

L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}

L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}

Put the limits

L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})

L=\dfrac{21}{16}

Hence, The arc length is \dfrac{21}{16}

6 0
3 years ago
How many triangles can be constructed with sides measuring 5 m, 16 m, and 5 m?
lidiya [134]

Q. How many triangles can be constructed with sides measuring 5 m, 16 m, and 5 m?

Solution:

Here we are given with the sides of the triangle as 5m, 16m and 5.

As the Triangle inequality we know that

The sum of the length of the two sides should be greater than the length of the third side. But this inequality fails here.

Hence no triangle can be made.

So the correct option is None.

Q.How many triangles can be constructed with sides measuring 6 cm, 2 cm, and 7 cm?

Solution:

Here we are given with the sides of the triangle as 6m, 2m and 7m.

As the Triangle inequality we know that

The sum of the length of the two sides should be greater than the length of the third side. The given values follows the triangle inequality.

Hence one triangle can be formed.

So the correct option is  one.

8 0
3 years ago
Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if a 0 b
jeka94

Answer:

Step-by-step explanation:

From the given information; Let's assume that  R should represent the set of all possible outcomes generated from  a bit string of length 10 .

So; as each place is fitted with either 0 or 1

\mathbf{|R|= 2^{10}}

Similarly; the event E signifies the randomly generated bit string of length 10 does not contain a 0

Now;

if  a 0 bit and a 1 bit are equally likely

The probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if a 0 bit and a 1 bit are equally likely is;

\mathbf{P(E) = \dfrac{|E|}{|R|}}

so ; if bits string should not contain a 0 and all other places should be occupied by 1; Then:

\mathbf{{|E|}=1 }   ; \mathbf{|R|= 2^{10}}

\mathbf{P(E) = \dfrac{1}{2^{10}}}

4 0
3 years ago
When will the equation p(b)=520(0.88)^b have a value less than 100?
yulyashka [42]

Answer:

The given equation will have value less than 100 whenever the value of b is greater than 12.89

Step-by-step explanation:

For the given equation, p(b) = 520 × 0.88^{b} to have a value less than 100 we can establish inequality as:

                     p(b) < 100

         or,  520 × 0.88^{b} < 100

         or, \frac{520}{520} × 0.88^{b} < \frac{100}{520}

         or, 0.88^{b} < \frac{1}{5.2}

         or, ㏒ ( 0.88^{b} ) < ㏒  (\frac{1}{5.2})

         or, b× ㏒ 0.88 < ㏒  (\frac{1}{5.2})

         or,  \frac{log (\frac{1}{5.2}) }{log (0.88)}   <  b

         or, 12.89 < b

Hence for the equation to have value less than 100, b must be greater than 12.89.

3 0
4 years ago
Which value of x makes the equation below true? 7 + x = 84 A. 12 B. 77 C. 83 D. 91
garri49 [273]

Answer:

B. 77

Step-by-step explanation:

7 + x = 84

Subtract 7 from both sides

x = 77

8 0
2 years ago
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