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3 years ago

Will mark brainliest for correct answer!

Mathematics

1 answer:

Darya [45]3 years ago

8 0

Answer:

...............

Step-by-step explanation:

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Jakes elevation decreases 350 meteors as he rides his bike to the bottom of the hill he completes the ride in 5 equal stages how

andrew-mc [135]

Answer:

70 decreases each stage

Step-by-step explanation:

350 / 5 = 70 decreases each stage

Since all decreases are equal and in 5 stages:

decreases * stages = total decreases

70 * 5 = 350

3 0

3 years ago

Evaluate the integral. (sec2(t) i t(t2 1)8 j t7 ln(t) k) dt

polet [3.4K]

If you're just integrating a vector-valued function, you just integrate each component:

$\displaystyle\int(\sec^2t\,\hat\imath+t(t^2-1)^8\,\hat\jmath+t^7\ln t\,\hat k)\,\mathrm dt$

$=\displaystyle\left(\int\sec^2t\,\mathrm dt\right)\hat\imath+\left(\int t(t^2-1)^8\,\mathrm dt\right)\hat\jmath+\left(\int t^7\ln t\,\mathrm dt\right)\hat k$

The first integral is trivial since $(\tan t)'=\sec^2t$ .

The second can be done by substituting $u=t^2-1$ :

$u=t^2-1\implies\mathrm du=2t\,\mathrm dt\implies\displaystyle\frac12\int u^8\,\mathrm du=\frac1{18}(t^2-1)^9+C$

The third can be found by integrating by parts:

$u=\ln t\implies\mathrm du=\dfrac{\mathrm dt}t$

$\mathrm dv=t^7\,\mathrm dt\implies v=\dfrac18t^8$

$\displaystyle\int t^7\ln t\,\mathrm dt=\frac18t^8\ln t-\frac18\int t^7\,\mathrm dt=\frac18t^8\ln t-\frac1{64}t^8+C$

8 0

3 years ago

The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form

azamat

Answer:

$\large \boxed{y = (x - 5)^{2} + 2 }$

Step-by-step explanation:

y = x² - 10x + 27

y = ax² + bx + c

This is the general form of the equation for a parabola.

We must convert it to the vertex form

y = (x - h)² + k, where (h,k) are the coordinates of the vertex.

We can do this by completing the square.

$\begin{array}{rcll}y & = & x^{2} - 10x + 27 & \\y - 27 & = & x^{2} - 10x & \text{Subtracted 27 from each side}\\y - 27&= & x^{2} - 10x + 25 - 25 & \text{Added and subtracted (b/2)}^{2}\\y - 27&= & (x - 5)^{2} - 25 & \text{Wrote the first three terms as the square of a binomial}\\y& = & \mathbf{(x - 5)^{2} + 2} & \text{Added 27 to each side}\\\end{array}\\\text{The vertex form of the parabola is $\large \boxed{\mathbf{y = (x - 5)^{2} + 2 }}$}$ The figure below shows that your parabola has its vertex at (5,2).

4 0

3 years ago

If x² - y² = 55, and x - y = 11, then y = a. 8 b. 5 c. 3 d. -8 e. -3

irina1246 [14]

X^2-y^2=55
this means that
(x+y)(x-y)=55
we know that x-y=11 so we can write
(x+y)(11)=55
x+y=55/11 we divide by 11 and we obtain
x+y=5

x-y=11 this means
x=y+11 we replace in the other equation (x+y=5)

y+11+y=5
2y=5-11
2y=-6
y=-3
and you find out that also
x=8

7 0

3 years ago

PLEASE HELP!! I NEED ANSWER ASAP!!! (The directions are to Find the area of the Circle.)

Maslowich

1. Use the formula: A = π x r^2
2. Find the radius.
3. Multiply the radius by itself to square it.
4. Multiply the result by pi.
5. Use the result as your answer.

3 0

2 years ago