What is the x and y intercept of the parabola y=x^2-6x+10 and ow do you graph the equation

1 answer:

7 0

The x- intercept is where y = 0 on the graph and the y- intercept is where x= 0 on the graph. When X=0, all the terms, except for the constant are equal to zero, thus the y- intercept is the constant. y=10 when x=0. Use the quadratic formula to find the x value where y=0.
x= (-b +or- sqrt(b^2 -4ac))/2a

y=ax^2 +bx +c

The answer for the x- int is imaginary. This happens because 10 is the parabola's minimum value and it never touches the x- axis. y-int is 10

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Carly mowed 2 more lawns than Rocco each week for 6 weeks. Carley mowed a total of 18 lawns. How many lawns did Rocco mow each w

Reptile [31]

Rocco mowed 1 lawn a week.

You wanna divide Carley’s total mowed lawns by the amount of weeks she mowed for.
18/6 = 3
Carley mowed 3 lawns a week.
We’ll take away two from that because she mowed two more that Rocco each week, resulting in Rocco mowing one lawn a week.
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8 0

3 years ago

Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, proj,u

11Alexandr11 [23.1K]

Answer:

Take $b = \frac{-17}{25}(7,1)$ as the projection of u onto v and $w \frac{1}{25}(-31,217)$ as the vector such that b+w =u

Step-by-step explanation:

The formula of projection of a vector u onto a vector v is given by

$\frac{u\cdot v}{v\cdot v}v$ , where $cdot$ is the dot product between vectors.

First, let b ve the projection of u onto v. Then

$b = \frac{u\cdot v}{v\cdot v}v= \frac{-6\cdot 7+8\cdot 1}{7\cdot 7+1\cdot 1}(7,1) = \frac{-34}{50}(7,1) = \frac{-17}{25}(7,1)$

We want a vector w, that is orthogonal to b and that b+w = u. From this equation we have that w = u-b = (-6,8)-\frac{-17}{25}(7,1)= \frac{1}{25}(-31,217)[/tex]

By construction, we have that w+b=u. We need to check that they are orthogonal. To do so, the dot product between w and b must be zero. Recall that if we have vectors a,b that are orthogonal then for every non-zero escalar r,k the vector ra and kb are also orthogonal. Then, we can check if w and b are orthogonal by checking if the vectors (7,1) and (-31, 217) are orthogonal.

We have that $(7,1)\cdot(-31,217) = 7\cdot -31 + 217 \cdot 1 = -217+217 =0$ . Then this vectors are orthogonal, and thus, w and b are orthogonal.