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3 years ago

I WILL GIVE BRIANLEST TO THE PERSON WHO ANSWER IT WRITE.

Mathematics

2 answers:

Whitepunk [10]3 years ago

8 0

The first one is D and the second one is B

kykrilka [37]3 years ago

4 0

The answer to the first part is D

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Find the area enclosed by x2=2y and y2=16x

jekas [21]

Answer: $\dfrac{32}{3}$

Step-by-step explanation:

Given

The parabolas are $x^2=2y$ and $y^2=16x$

Find the point of intersection of two parabolas

$\Rightarrow \left(\dfrac{x^2}{2}\right)^2=16x\\\\\Rightarrow x^4=64x\\\Rightarrow x(x^3-64)=0\\\Rightarrow x=0,4$

Obtain y using x

$(x,y)\rightarrow (0,0)\ \text{and }(4,8)$

Area enclosed between the two is

$\Rightarrow I=\int\limits^4_0 ({4\sqrt{x}-\dfrac{x^2}{2}}) \, dx\\\\\Rightarrow I=\left ( 4\times \dfrac{2}{3}x^{\frac{3}{2}}-\dfrac{x^3}{2\times 3} \right) _0^4\\\\\Rightarrow I=\left ( \dfrac{8}{3}\times 8-\dfrac{4^3}{6} \right )-0\\\\\Rightarrow I=\dfrac{128-64}{6}\\\\\Rightarrow I=\dfrac{64}{6}\\\\\Rightarrow I=\dfrac{32}{3}$

Thus, the area bounded by the two parabolas is $\dfrac{32}{3}$ sq. units.

4 0

2 years ago

Use synthetic division to solve (4x^3-3x^2+5x+6) divide(x+6). What is the quotient?

NARA [144]

4 -3 5 6
-6 -24 162 -1002
-----------------------------------
4 -27 167 -996

4x^2 - 27x + 167 remainder - 996

7 0

3 years ago

Read 2 more answers

What should be filled in the blank spot you’ll be marked as brainliest if you are correct

Vikentia [17]

Answer:

-4 square inches

Step-by-step explanation:

its because the 5 pictures together make 21

7 0

3 years ago

The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle? 2 cm 2 StartRoot 2 EndRoo

Oxana [17]

Answer:

$2\sqrt{2} cm$

Step-by-step explanation:

In order to solve this you just have to remember the formula for the sides and hypotenuse of the triangle rectangle:

$c^{2} =a^{2} +b^{2}$

Since A and B are equal we will use X to represent them both:

$c^{2} =a^{2} +b^{2}\\4^{2} =x^{2} +x^{2}\\16 =2x^{2}\\8=x^{2} \\x=\sqrt{8}=\sqrt{4*2}=2\sqrt{2}$

ANd by solving the equation we get that the length of the legs of the triangle rectangle with a hypotenuse of 4cm is $2\sqrt{2} cm$

7 0

3 years ago

Read 2 more answers

Write the product using exponents -3/7×3/7×3/7<br>

zlopas [31]

Answer:

$-(\frac{3}{7})^3$

Step-by-step explanation:

Since we see that 3/7 is multiplied by itself three times, we can use exponents as a shorter way to write this. The expontent tells us how many times the base number, 3/7, is multiplied by itself.

$-1 * (\frac{3}{7})^3$ = $-1 * \frac{3}{7} * \frac{3}{7} * \frac{3}{7}$

We then multiply by -1 to (3/7)^3 to get the exact answer.

$-(\frac{3}{7})^3$

8 0

3 years ago